4 CREATING GRAPHS A PICTURE REALLY IS WORTH A THOUSAND WORDS
4: MEDIA LIBRARY
Premium Videos
Core Concepts in Stats Video
· Examining Data: Tables and Figures
Lightboard Lecture Video
· Creating a Simple Chart
Time to Practice Video
· Chapter 4: Problem 3
Difficulty Scale
(moderately easy but not a cinch)
WHAT YOU WILL LEARN IN THIS CHAPTER
· Understanding why a picture is really worth a thousand words
· Creating a histogram and a polygon
· Understanding the different shapes of different distributions
· Using SPSS to create incredibly cool charts
· Creating different types of charts and understanding their application and uses
WHY ILLUSTRATE DATA?
In the previous two chapters, you learned about the two most important types of descriptive statistics—measures of central tendency and measures of variability. Both of these provide you with the one best number for describing a group of data (central tendency) and a number reflecting how diverse, or different, scores are from one another (variability).
What we did not do, and what we will do here, is examine how differences in these two measures result in different-looking distributions. Numbers alone (such as M = 3 and s = 3) may be important, but a visual representation is a much more effective way of examining the characteristics of a distribution as well as the characteristics of any set of data.
So, in this chapter, we’ll learn how to visually represent a distribution of scores as well as how to use different types of graphs to represent different types of data.
CORE CONCEPTS IN STATS VIDEO
Examining Data: Tables and Figures
X-TIMESTAMP-MAP=LOCAL: Examining data helps find data entry errors, evaluate research methodology, identify outliers, and determine the shape of a distribution in a data set. Researchers typically examine collected data in two ways, by creating tables and figures. Imagine you asked a group of friends to rate a movie they've seen on a one to five scale. A table helps identify the variable and the possible values of the variable. The sample size, often referred to as n, is 14 because there are ratings reported from 14 people. This is how large the total sample is. From this, we can determine how many in the sample have each value of the variable. We can also determine the percentage that the sample has of each possible value. Figures display variables from the table. Nominal and ordinal variables can be depicted with bar charts, while interval and ratio variables can be depicted using histograms and frequency polygons. For this data set, we can use a bar chart. Distributions of data can be characterized along three aspects or dimensions, modality, symmetry, and variability. In a unimodal distribution, a small range of values has the greatest frequency or mode of the set. However, it's possible for a distribution to have more than one mode. For a bimodal distribution, we see two values that seem to occur w.
Chapter 4 Problem 31. For problem three in chapter four, a teac.docxrobertad6
Chapter 4: Problem 3
1. For problem three in chapter four, a teacher wants to display her students number of responses for each day of the week. And she wants to do that with a bar chart. Since she hasn't taken a stats class, she comes to you for help. You first enter her data into SPSS and the results look like this-- When you look at your data set, you'll see that it actually has the wrong level of measurement. Notice that there's a little Venn diagram at the top of each column, which indicates that your data has been entered as nominal. That would be correct if you were noting which day of the week a student participated, but since you're noting how often a given student participated, the correct level of measurement is a scale. Go ahead and change that. Watch how I do that. Under variable view, under measure, you just want to click each one and turn it into a scale. You can also cut and paste these, and I can show you that in another video. Once you have them changed, go back to data view, and you'll see that at the top it has changed in two little rulers. The next question is, how do I get SPSS to display the average score per day rather the total number of individual scores, which might look like a mess, and it's why this question is a toughie. To do that we go under graphs, and you'll see that you have two options, you can do a Chart Builder or a Legacy Dialog. For this question we want to use the Legacy Dialog. We go to Bar and when we click that, there are two questions-- one, what type of bar chart? We want a simple one. And then, how do you want the data in their area displayed? Do we want to summarize for the groups? We really don't. We want summary of separate variables where each day of the week is a variable. We click on Define and then here you'll see every day of the week. You want to bring that over and you see your bar charts are going to represent the mean for every day of the week. As a good habit you want to make sure you title it, I called it "Students' Engagement During Group Discussion." The second one is by day of week. We hit Continue, and then when we hit OK, you're going to see your output pop up. And here is our bar chart-- every day of the week showing the average student engagement. And this is how you answer problem 3 in chapter 4. Good luck.
2. Identify whether these distributions are negatively skewed, positively skewed, or not skewed at all and explain why you describe them that way.
a. This talented group of athletes scored very high on the vertical jump task.
b. On this incredibly crummy test, everyone received the same score.
c. On the most difficult spelling test of the year, the third graders wept as the scores were delivered and then their parents complained.
3. Use the data available as Chapter 4 Data Set 3 on pie preference to create a pie chart ☺ using SPSS.
4. For each of the followin.
Focus on what you learned that made an impression, what may have s.docxkeugene1
Focus on what you learned that made an impression, what may have surprised you, and what you found particularly beneficial and why. Specifically:
What did you find that was really useful, or that challenged your thinking?
What are you still mulling over?
Was there anything that you may take back to your classroom?
Is there anything you would like to have clarified?
ANSWER THE ABOVE QUESTIONS BASED ON THE DOCUMENTS BELOW
Introduction & Goals
This week, we will investigate the distribution of a variable and look at ways to best see the key features of a quantitative variable’s distribution. We will look at visualizations of data, including line plots, frequency tables, stemplots, and histograms. We will hone our ability to describe key features of a distribution from visualizations and use them to compare distributions. We will begin to think about ideas for the Comparative Study by brainstorming in our project groups.
Goals
:
Reinforce the idea that data will vary
Explain what the distribution of variable is
Identify five key features of a distribution: center, spread, shape, clusters & outliers
Identify and create appropriate displays for categorical and quantitative data in one variable, including bar graphs, line plots, frequency tables, and histograms
Analyze distributions using stemplots and histograms
Recognize advantages and limitations of histograms
Begin to explore technology for use in statistics
Begin work on Comparative Study Final Project
DOW #2: How Long Is A Minute?
In week 1, we gathered data for this week’s DoW, addressing the question:
“How long is a minute to an adult?”
This week we'll:
In investigations 1 & 2, you will analyze the data with dot plots, frequency tables, stemplots, and histograms.
In Exercise B2, you will post your initial analysis and interpretation to the discussion board by Wednesday, 10 PM EST and create at least three follow-up posts by Friday, 10 PM EST.
In Exercise D2 & E2, you will post your best histogram to the discussion board by Friday, 10 PM EST. Compare the histograms and choose the one you think best represents the distribution by Sunday, 10 PM EST
Investigation 1: Seeing the Distribution
As we emphasized in Week 1,
data varies
. This point may seem trivial, but it encapsulates one of the most fundamental concepts of statistics:
variability
. Statistical Analysis is really a study of the patterns we find within this variation in the data. The pattern(s) in the variation is called the
distribution
of the variable. Much of statistics focuses on ways to represent and describe the distribution of a variable.
Activities A & B in this investigation focus on representing and describing the distribution.
Activity C introduces Excel as a tool for looking at a distribution.
Inv 1, Activity A: Patterns in the Variation
As we emphasized in Week 1,
data varies
. This point may seem trivial, but it encapsulates one of the most fundamental concepts of statistics:
variability
. Statistical Analy.
De vry math 399 ilabs & discussions latest 2016lenasour
This document provides information and discussion questions for several weeks of a statistics course (MATH 399) at DeVry University. It includes discussion questions and assignments related to topics like descriptive statistics, regression, probability, confidence intervals, and hypothesis testing. For each week, it provides the discussion question, any relevant instructions, and sometimes a short summary of the statistical concept being covered. It also includes information about completing iLabs (interactive labs) and assignments in Excel to reinforce these statistical topics.
De vry math 399 ilabs & discussions latest 2016 novemberlenasour
This document provides materials and instructions for several weekly discussions and iLabs for a DeVry University MATH 399 course. It includes discussion prompts and questions for weeks 1 through 7 on topics such as descriptive statistics, regression, probability, confidence intervals, and hypothesis testing. It also provides instructions and questions for iLabs on related statistical concepts involving Excel, probability distributions, descriptive statistics, and confidence intervals. Students are asked to perform calculations, create graphs and charts, interpret results, and answer questions demonstrating their understanding of the statistical content.
Here are my recommendations for graphs to use for each data set:
- Comparison of annual snowfall between resorts: Bar graph or line graph. Both would clearly show the snowfall amounts and how they compare each year.
- Time spent watching TV: Histogram. It can accommodate a large data set and show the distribution of hours watched.
- Wind speed over 3 weeks: Line graph. A line graph is best to show changes in a measurement over time.
- Favorite summer activity: Pie or bar graph. These are best for categorical data to compare proportions for each category.
Graphical Presentation of Data - Rangga Masyhuri Nuur LLU 27.pptxRanggaMasyhuriNuur
The document discusses various graphical methods for presenting data, including histograms, polygons, pie charts, ogives, and stem-and-leaf plots. Histograms display the frequency distribution of data using bars of varying heights. Polygons connect the midpoints of histogram bars with straight lines. Pie charts represent proportions using circular slices. Ogives show cumulative frequencies with class limits on the x-axis and cumulative counts on the y-axis. Stem-and-leaf plots break values into "stems" and "leaves" for an organized display of the raw data. Examples are provided for constructing each type of graph using sample data sets.
This document provides a tutorial on principal components analysis (PCA). It begins with an introduction to PCA and its applications. It then covers the necessary background mathematical concepts, including standard deviation, covariance, and eigenvalues/eigenvectors. The tutorial includes examples throughout and recommends a textbook for further mathematical information.
This chapter introduces how to analyze simple questionnaires using SPSS. It will teach how to structure datasets for computer analysis, perform basic statistical techniques to describe data patterns, and display data visually. The chapter uses a lateralization questionnaire as a sample dataset to demonstrate simple analyses. It describes how to code questionnaire responses numerically and organize the data in a matrix format with rows for participants and columns for questions. This initial dataset captures patterns of right or left laterality preferences among the first six participants.
Chapter 4 Problem 31. For problem three in chapter four, a teac.docxrobertad6
Chapter 4: Problem 3
1. For problem three in chapter four, a teacher wants to display her students number of responses for each day of the week. And she wants to do that with a bar chart. Since she hasn't taken a stats class, she comes to you for help. You first enter her data into SPSS and the results look like this-- When you look at your data set, you'll see that it actually has the wrong level of measurement. Notice that there's a little Venn diagram at the top of each column, which indicates that your data has been entered as nominal. That would be correct if you were noting which day of the week a student participated, but since you're noting how often a given student participated, the correct level of measurement is a scale. Go ahead and change that. Watch how I do that. Under variable view, under measure, you just want to click each one and turn it into a scale. You can also cut and paste these, and I can show you that in another video. Once you have them changed, go back to data view, and you'll see that at the top it has changed in two little rulers. The next question is, how do I get SPSS to display the average score per day rather the total number of individual scores, which might look like a mess, and it's why this question is a toughie. To do that we go under graphs, and you'll see that you have two options, you can do a Chart Builder or a Legacy Dialog. For this question we want to use the Legacy Dialog. We go to Bar and when we click that, there are two questions-- one, what type of bar chart? We want a simple one. And then, how do you want the data in their area displayed? Do we want to summarize for the groups? We really don't. We want summary of separate variables where each day of the week is a variable. We click on Define and then here you'll see every day of the week. You want to bring that over and you see your bar charts are going to represent the mean for every day of the week. As a good habit you want to make sure you title it, I called it "Students' Engagement During Group Discussion." The second one is by day of week. We hit Continue, and then when we hit OK, you're going to see your output pop up. And here is our bar chart-- every day of the week showing the average student engagement. And this is how you answer problem 3 in chapter 4. Good luck.
2. Identify whether these distributions are negatively skewed, positively skewed, or not skewed at all and explain why you describe them that way.
a. This talented group of athletes scored very high on the vertical jump task.
b. On this incredibly crummy test, everyone received the same score.
c. On the most difficult spelling test of the year, the third graders wept as the scores were delivered and then their parents complained.
3. Use the data available as Chapter 4 Data Set 3 on pie preference to create a pie chart ☺ using SPSS.
4. For each of the followin.
Focus on what you learned that made an impression, what may have s.docxkeugene1
Focus on what you learned that made an impression, what may have surprised you, and what you found particularly beneficial and why. Specifically:
What did you find that was really useful, or that challenged your thinking?
What are you still mulling over?
Was there anything that you may take back to your classroom?
Is there anything you would like to have clarified?
ANSWER THE ABOVE QUESTIONS BASED ON THE DOCUMENTS BELOW
Introduction & Goals
This week, we will investigate the distribution of a variable and look at ways to best see the key features of a quantitative variable’s distribution. We will look at visualizations of data, including line plots, frequency tables, stemplots, and histograms. We will hone our ability to describe key features of a distribution from visualizations and use them to compare distributions. We will begin to think about ideas for the Comparative Study by brainstorming in our project groups.
Goals
:
Reinforce the idea that data will vary
Explain what the distribution of variable is
Identify five key features of a distribution: center, spread, shape, clusters & outliers
Identify and create appropriate displays for categorical and quantitative data in one variable, including bar graphs, line plots, frequency tables, and histograms
Analyze distributions using stemplots and histograms
Recognize advantages and limitations of histograms
Begin to explore technology for use in statistics
Begin work on Comparative Study Final Project
DOW #2: How Long Is A Minute?
In week 1, we gathered data for this week’s DoW, addressing the question:
“How long is a minute to an adult?”
This week we'll:
In investigations 1 & 2, you will analyze the data with dot plots, frequency tables, stemplots, and histograms.
In Exercise B2, you will post your initial analysis and interpretation to the discussion board by Wednesday, 10 PM EST and create at least three follow-up posts by Friday, 10 PM EST.
In Exercise D2 & E2, you will post your best histogram to the discussion board by Friday, 10 PM EST. Compare the histograms and choose the one you think best represents the distribution by Sunday, 10 PM EST
Investigation 1: Seeing the Distribution
As we emphasized in Week 1,
data varies
. This point may seem trivial, but it encapsulates one of the most fundamental concepts of statistics:
variability
. Statistical Analysis is really a study of the patterns we find within this variation in the data. The pattern(s) in the variation is called the
distribution
of the variable. Much of statistics focuses on ways to represent and describe the distribution of a variable.
Activities A & B in this investigation focus on representing and describing the distribution.
Activity C introduces Excel as a tool for looking at a distribution.
Inv 1, Activity A: Patterns in the Variation
As we emphasized in Week 1,
data varies
. This point may seem trivial, but it encapsulates one of the most fundamental concepts of statistics:
variability
. Statistical Analy.
De vry math 399 ilabs & discussions latest 2016lenasour
This document provides information and discussion questions for several weeks of a statistics course (MATH 399) at DeVry University. It includes discussion questions and assignments related to topics like descriptive statistics, regression, probability, confidence intervals, and hypothesis testing. For each week, it provides the discussion question, any relevant instructions, and sometimes a short summary of the statistical concept being covered. It also includes information about completing iLabs (interactive labs) and assignments in Excel to reinforce these statistical topics.
De vry math 399 ilabs & discussions latest 2016 novemberlenasour
This document provides materials and instructions for several weekly discussions and iLabs for a DeVry University MATH 399 course. It includes discussion prompts and questions for weeks 1 through 7 on topics such as descriptive statistics, regression, probability, confidence intervals, and hypothesis testing. It also provides instructions and questions for iLabs on related statistical concepts involving Excel, probability distributions, descriptive statistics, and confidence intervals. Students are asked to perform calculations, create graphs and charts, interpret results, and answer questions demonstrating their understanding of the statistical content.
Here are my recommendations for graphs to use for each data set:
- Comparison of annual snowfall between resorts: Bar graph or line graph. Both would clearly show the snowfall amounts and how they compare each year.
- Time spent watching TV: Histogram. It can accommodate a large data set and show the distribution of hours watched.
- Wind speed over 3 weeks: Line graph. A line graph is best to show changes in a measurement over time.
- Favorite summer activity: Pie or bar graph. These are best for categorical data to compare proportions for each category.
Graphical Presentation of Data - Rangga Masyhuri Nuur LLU 27.pptxRanggaMasyhuriNuur
The document discusses various graphical methods for presenting data, including histograms, polygons, pie charts, ogives, and stem-and-leaf plots. Histograms display the frequency distribution of data using bars of varying heights. Polygons connect the midpoints of histogram bars with straight lines. Pie charts represent proportions using circular slices. Ogives show cumulative frequencies with class limits on the x-axis and cumulative counts on the y-axis. Stem-and-leaf plots break values into "stems" and "leaves" for an organized display of the raw data. Examples are provided for constructing each type of graph using sample data sets.
This document provides a tutorial on principal components analysis (PCA). It begins with an introduction to PCA and its applications. It then covers the necessary background mathematical concepts, including standard deviation, covariance, and eigenvalues/eigenvectors. The tutorial includes examples throughout and recommends a textbook for further mathematical information.
This chapter introduces how to analyze simple questionnaires using SPSS. It will teach how to structure datasets for computer analysis, perform basic statistical techniques to describe data patterns, and display data visually. The chapter uses a lateralization questionnaire as a sample dataset to demonstrate simple analyses. It describes how to code questionnaire responses numerically and organize the data in a matrix format with rows for participants and columns for questions. This initial dataset captures patterns of right or left laterality preferences among the first six participants.
1. The document discusses statistical analysis techniques for describing and comparing data sets, including calculating the mean, standard deviation, and using t-tests.
2. It explains how to calculate the mean and standard deviation of data sets to analyze the central tendency and variability. The standard deviation summarizes how tightly values cluster around the mean.
3. T-tests are used to determine if differences between two data sets are statistically significant by comparing the means relative to the standard deviations and considering the degree of overlap between the sets.
This document discusses data, how it can be organized and represented visually. It provides definitions of key terms like data, raw data, and grouped data. It also describes various visual representations of data like bar graphs, pie charts, and histograms. These visual representations make data easier to understand, compare and analyze. The document also discusses how raw data can be organized and grouped into frequency distribution tables for clearer interpretation.
The Central Limit Theorem states that the distribution of sample means approximates a normal distribution as the sample size increases, regardless of the population distribution. It can be used to estimate the mean height of students in sports teams by taking random samples, calculating the mean of each sample, finding the mean of the sample means, and observing the results form a bell curve. Discrete and continuous data can be summarized using tables, histograms, stem-and-leaf plots, and other graphs depending on whether the values are countable categories or measured on a scale. Standard deviation is commonly used to measure the dispersion of samples from the same population.
The document discusses descriptive statistics and various statistical concepts. It covers measures of central tendency like mean, median and mode. It also discusses measures of variability/dispersion such as range, mean deviation and standard deviation. Additionally, it covers different scales of measurement like nominal, ordinal, interval and ratio scales. Finally, it discusses various methods of graphical representation of data like pie charts, bar graphs, histograms and frequency polygons. The key aspects of each concept are defined along with examples.
QUESTION 1Question 1 Describe the purpose of ecumenical servic.docxmakdul
This document contains a summary of a research article that examines the relationship between patient satisfaction scores and inpatient admission volumes at teaching and non-teaching hospitals. The study found a statistically significant positive correlation between patient satisfaction and admissions at teaching hospitals, but a non-significant negative correlation at non-teaching hospitals. When combined, teaching and non-teaching hospitals showed a statistically significant negative correlation. The findings suggest patient satisfaction may impact admissions more at teaching hospitals. The conclusion provides recommendations for healthcare organizations to strategically focus on patient satisfaction to strengthen performance.
Are you eager to unlock the full potential of SPSS for data analysis and research? Look no further! This SlideShare presentation is your ultimate guide to mastering SPSS, equipping you with the knowledge and skills to harness the power of this versatile statistical software.
Overview:
In this comprehensive presentation, we delve into the fundamental concepts of SPSS and guide you through its various features, functions, and practical applications. Whether you're a student, researcher, analyst, or professional seeking to elevate your data analysis capabilities, this presentation is tailored for all skill levels.
Key Topics Covered:
Introduction to SPSS: Get acquainted with the interface, workspace, and essential tools to kickstart your SPSS journey.
Data Preparation: Learn best practices for data entry, cleaning, and transforming, ensuring the accuracy and reliability of your analysis.
Descriptive Statistics: Explore various methods to summarize and present data, including measures of central tendency, dispersion, and graphical representations.
Inferential Statistics: Dive into hypothesis testing, t-tests, ANOVA, regression, and other techniques to draw meaningful conclusions from your data.
Advanced Analysis: Uncover the power of multivariate analysis, factor analysis, and cluster analysis for complex research scenarios.
Data Visualization: Master the art of creating compelling charts, graphs, and visualizations to communicate your findings effectively.
Reporting and Interpretation: Learn how to interpret SPSS output and craft clear, insightful reports for diverse audiences.
Why Attend?
Gain Confidence: Build your confidence in using SPSS through step-by-step tutorials and real-world examples.
Enhance Research Skills: Acquire the skills to conduct robust and in-depth data analysis for your research projects.
Career Advancement: Enhance your professional profile and open doors to new opportunities with strong SPSS proficiency.
Join a Learning Community: Connect with like-minded professionals, researchers, and enthusiasts to exchange knowledge and insights.
De vry math 399 all ilabs latest 2016 novemberlenasour
This document provides information about obtaining assistance with coursework from an online service called ACEHOMEWORK.NET. It lists various courses and assignments they can help with, such as accounting, marketing, finance, economics, mathematics, statistics, programming, and more. It emphasizes they can help students get an A grade and provide original, plagiarism-free work by the deadline. Contact information is provided to obtain more details and pricing information.
Introduction to Statistics - Chapter 3-5 Notes.pptGurumurthy B R
This document provides an overview and lecture notes for chapters 3-5 of an introductory statistics course. It discusses preparing preliminary analyses of categorical and quantitative variables through graphs and descriptive statistics. For categorical variables, it describes frequency tables, contingency tables, bar charts, and pie charts. For quantitative variables, it introduces histograms, boxplots, dot plots, and stem-and-leaf displays. It emphasizes using graphs to understand the shape, center, and spread of variable distributions. The document also briefly discusses Simpson's paradox and performing preliminary analyses by hand.
Introduction to Statistics - Chapter 3-5 Notes.pptMohamedAmir79
This document provides an overview and lecture notes for chapters 3-5 of an introductory statistics course. It discusses preparing preliminary analyses of categorical and quantitative variables through graphs and descriptive statistics. For categorical variables, it describes frequency tables, contingency tables, bar charts, and pie charts. For quantitative variables, it introduces histograms, boxplots, dot plots, and stem-and-leaf displays. It emphasizes using graphs to understand the shape, center, and spread of variable distributions. The lecture also warns of Simpson's Paradox and provides examples of analyzing real data.
Introduction to Statistics - Chapter 3-5 Notes.pptsadafshahbaz7777
This document provides an overview and lecture notes for chapters 3-5 of an introductory statistics course. It discusses preparing preliminary analyses of categorical and quantitative variables through graphs and descriptive statistics. For categorical variables, it describes frequency tables, contingency tables, bar charts, and pie charts. For quantitative variables, it introduces histograms, boxplots, dot plots, and stem-and-leaf displays. It emphasizes using graphs to understand the shape, center, and spread of variable distributions. The lecture also warns of Simpson's Paradox and provides examples of analyzing real data.
This document provides an overview and lecture notes for chapters 3-5 of an introductory statistics course. It discusses preparing preliminary analyses of categorical and quantitative variables through graphs and descriptive statistics. For categorical variables, it describes frequency tables, contingency tables, bar charts, and pie charts. For quantitative variables, it introduces histograms, boxplots, dot plots, and stem-and-leaf displays. It emphasizes using graphs to understand the shape, center, and spread of variable distributions. The lecture also warns of Simpson's Paradox and provides examples of analyzing real data.
This document provides examples and explanations of various graphical methods for describing data, including frequency distributions, bar charts, pie charts, stem-and-leaf diagrams, histograms, and cumulative relative frequency plots. It demonstrates how to construct these graphs using sample data on student weights, grades, ages, and other examples. The goal is to help readers understand different ways to visually represent data distributions and patterns.
1.MATH 221 Statistics for Decision MakingWeek 2 iLabName.docxAlyciaGold776
This document provides instructions for a statistics lab assignment. Students are asked to analyze survey data provided in an Excel spreadsheet. The assignment involves creating graphs in Excel, including a pie chart for car color, a histogram for heights, and a stem-and-leaf plot for money. Students then calculate descriptive statistics for heights by gender and answer questions interpreting the graphs and statistics.
Sheet1Number of Visits Per DayNumber of Status Changes Per WeekAge.docxlesleyryder69361
Sheet1Number of Visits Per DayNumber of Status Changes Per WeekAge5138VariableMeanMedianModeRangeVarianceStandard Deviation15527Visits Per Day5121Status Changes Per Week25319Age50525631881024Data from:http://www.statcrunch.com/5.0/index.php?dataid=48537311028331910120114210481032112715118207190040003015526417311219414110320302051325324511851205621301201512053411551933190049543111182120422000520027101013531841219511820194121211811218124202019101018501002230224532050142337205120113331841514102541547319402010019004215320412800401166103145220122910524005032173119206310018212125719152202020002533310025512021332024002000211021002750201031911195718213810002221211532600361010245018511942202149311884185126013220102131371551500561502000285656185136001421471053022211012061352511800422083200212223113715520514520719106211581120332128241328233810540522111122113522632370035108540013761181120104194120004800.52351012128458221911390033321973025114820532022211272514471043405030191111004535281424602019201529105192002010140052342620718212630321120231800401910520151721942221071910719305041200058362143102251237120215119332632193832721356301810519421832351128531931193810221822310127425820234339204183218321900532238105411007519424318102362020171022040283850100292121286143250232319101025121823198204219442831293218203451432143117021181031815418530202521825104010263120101952243325102201511930220114131171051944240065231920220121443015121531851193024757144246203210213125621920275121104319121725104626191048102581181167441643400556320452051182024474181001841192312562481932339525214210494810255132310561312191155013650100181152101910552224191039210043302500560136814151263020107323262260415152124303193061004758108180039103900550050315910322602048404411354020http://www.statcrunch.com/5.0/index.php?dataid=485373
Sheet2
Sheet3
PSYC 354
Excel Homework 3
(70 pts possible)
The objective of your third Excel assignment is to learn to describe a data set using measures of central tendency and variability. First, be sure you view the presentation that covers computing central tendency and variability in Excel found in the Reading & Study folder in Module/Week 3. This presentation goes through the steps you will need to be familiar with in order to complete this assignment.
In Module/Week 3, the goal is to use Excel formulas to calculate specific measures of central tendency and variability of a given data set, using the steps you learned during the presentation. Open “Data Set 3,” found in the Assignment Instructions folder, under “Excel Homework 3,” then follow the steps below to complete Module/Week 3’s assignment.
1. Research Question: In Module/Week 3, the data comes from an internet survey that assessed the frequency of use of the social networking site Facebook ™. A psychologist interested in time spent visiting a social networking site collected data from 366 respondents concerning: 1.) number of visits to FB per day; 2.) number of times participants changed FB “status” per w.
The document discusses various graphical methods for describing data, including bar charts, pie charts, stem-and-leaf diagrams, histograms, and cumulative relative frequency plots. It provides examples of each using sample student data on vision correction methods, weights, ages, and GPAs to illustrate how to construct and interpret the different graph types.
The document discusses various graphical methods for describing data, including bar charts, pie charts, stem-and-leaf diagrams, histograms, and cumulative relative frequency plots. It provides examples of each using sample student data on vision correction, weights, ages, and GPAs to illustrate how to construct and interpret the different graph types.
This document describes how to perform common statistical tests in Excel to analyze biological data from A-level experiments. It explains how to calculate descriptive statistics like the mean, standard deviation, and confidence interval. It also covers how to create graphs with error bars and perform tests to analyze correlations, linear regressions, and compare multiple data sets, including t-tests, ANOVA, and chi-squared tests. Excel simplifies statistics by automating calculations and interpretations that were previously difficult to perform by hand.
3Type your name hereType your three-letter and -number cours.docxlorainedeserre
3
Type your name here
Type your three-letter and -number course code here
The date goes here
Type instructor’s name here
Your Title Goes Here
This is an electronic template for papers written in GCU style. The purpose of the template is to help you follow the basic writing expectations for beginning your coursework at GCU. Margins are set at 1 inch for top, bottom, left, and right. The first line of each paragraph is indented a half inch (0.5"). The line spacing is double throughout the paper, even on the reference page. One space after punctuation is used at the end of a sentence. The font style used in this template is Times New Roman. The font size is 12 point. When you are ready to write, and after having read these instructions completely, you can delete these directions and start typing. The formatting should stay the same. If you have any questions, please consult with your instructor.
Citations are used to reference material from another source. When paraphrasing material from another source (such as a book, journal, website), include the author’s last name and the publication year in parentheses.When directly quoting material word-for-word from another source, use quotation marks and include the page number after the author’s last name and year.
Using citations to give credit to others whose ideas or words you have used is an essential requirement to avoid issues of plagiarism. Just as you would never steal someone else’s car, you should not steal his or her words either. To avoid potential problems, always be sure to cite your sources. Cite by referring to the author’s last name, the year of publication in parentheses at the end of the sentence, such as (George & Mallery, 2016), and page numbers if you are using word-for-word materials. For example, “The developments of the World War II years firmly established the probability sample survey as a tool for describing population characteristics, beliefs, and attitudes” (Heeringa, West, & Berglund, 2017, p. 3).
The reference list should appear at the end of a paper (see the next page). It provides the information necessary for a reader to locate and retrieve any source you cite in the body of the paper. Each source you cite in the paper must appear in your reference list; likewise, each entry in the reference list must be cited in your text. A sample reference page is included below; this page includes examples (George & Mallery, 2016; Heeringa et al., 2017; Smith et al., 2018; “USA swimming,” 2018; Yu, Johnson, Deutsch, & Varga, 2018) of how to format different reference types (e.g., books, journal articles, and a website). For additional examples, see the GCU Style Guide.
References
George, D., & Mallery, P. (2016). IBM SPSS statistics 23 step by step: A simple guide and reference. New York, NY: Routledge.
Heeringa, S. G., West, B. T., & Berglund, P. A. (2017). Applied survey data analysis (2nd ed.). New York, NY: Chapman & Hall/CRC Press.
Smith, P. D., Martin, B., Chewning, B., ...
This document provides notes for online students about quantitative data analysis and SPSS. It discusses that the lecture series will cover basic ideas in quantitative data analysis. It notes that many different statistical software programs are available but that the course will use SPSS because it is easy to use and popular for statistical analysis.
Group Presentation Once during the quarter, each student will.docxgilbertkpeters11344
Group Presentation
: Once during the quarter, each student will prepare a brief presentation on a specific neighborhood, a racial or cultural group, or a historical event, migration or shift in the urban landscape,
related to the themes for that week
. Students will select preferred weeks in advance and be scheduled by Week 2 as best as your professor can allow. The presentation is open in form and format but should be 20 minutes in duration, consist mostly of your own original words and discussion, but involve some form of visual, quotes, or data, and represent some amount of additional research beyond the readings for that week, and include 5 or more questions for discussion to be presented to the class. Your group grade will reflect an average of 4 grades in content, delivery, relevance and engagement with the class in discussion.
.
Group Presentation Outline
•
Slide 1: Title slide
•
This contains your topic title, your names, and the course.
•
Slide 2: Introduction slide
•
Remember that you are presenting this information to others. Acknowledge the audience, and mention the purpose of the
presentation.
•
This slide should contain at least 50–100 words of speaker notes.
•
Slides 3–10 (or more): Content slides
•
Describe the topic and structure
•
Outline and discuss the issues/components each separately
•
Discuss theories, laws, policies, and other labor relations related topics
•
Provide support for your perspective and analysis
•
Lessons learned documented, what you have learned
•
Conclusion
•
The slides should each contain at least
50–100 words of speaker notes.
•
Final slide(s): Reference slide(s)
•
List your references according to the APA sty
.
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Sheet1Number of Visits Per DayNumber of Status Changes Per WeekAge5138VariableMeanMedianModeRangeVarianceStandard Deviation15527Visits Per Day5121Status Changes Per Week25319Age50525631881024Data from:http://www.statcrunch.com/5.0/index.php?dataid=48537311028331910120114210481032112715118207190040003015526417311219414110320302051325324511851205621301201512053411551933190049543111182120422000520027101013531841219511820194121211811218124202019101018501002230224532050142337205120113331841514102541547319402010019004215320412800401166103145220122910524005032173119206310018212125719152202020002533310025512021332024002000211021002750201031911195718213810002221211532600361010245018511942202149311884185126013220102131371551500561502000285656185136001421471053022211012061352511800422083200212223113715520514520719106211581120332128241328233810540522111122113522632370035108540013761181120104194120004800.52351012128458221911390033321973025114820532022211272514471043405030191111004535281424602019201529105192002010140052342620718212630321120231800401910520151721942221071910719305041200058362143102251237120215119332632193832721356301810519421832351128531931193810221822310127425820234339204183218321900532238105411007519424318102362020171022040283850100292121286143250232319101025121823198204219442831293218203451432143117021181031815418530202521825104010263120101952243325102201511930220114131171051944240065231920220121443015121531851193024757144246203210213125621920275121104319121725104626191048102581181167441643400556320452051182024474181001841192312562481932339525214210494810255132310561312191155013650100181152101910552224191039210043302500560136814151263020107323262260415152124303193061004758108180039103900550050315910322602048404411354020http://www.statcrunch.com/5.0/index.php?dataid=485373
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Your Title Goes Here
This is an electronic template for papers written in GCU style. The purpose of the template is to help you follow the basic writing expectations for beginning your coursework at GCU. Margins are set at 1 inch for top, bottom, left, and right. The first line of each paragraph is indented a half inch (0.5"). The line spacing is double throughout the paper, even on the reference page. One space after punctuation is used at the end of a sentence. The font style used in this template is Times New Roman. The font size is 12 point. When you are ready to write, and after having read these instructions completely, you can delete these directions and start typing. The formatting should stay the same. If you have any questions, please consult with your instructor.
Citations are used to reference material from another source. When paraphrasing material from another source (such as a book, journal, website), include the author’s last name and the publication year in parentheses.When directly quoting material word-for-word from another source, use quotation marks and include the page number after the author’s last name and year.
Using citations to give credit to others whose ideas or words you have used is an essential requirement to avoid issues of plagiarism. Just as you would never steal someone else’s car, you should not steal his or her words either. To avoid potential problems, always be sure to cite your sources. Cite by referring to the author’s last name, the year of publication in parentheses at the end of the sentence, such as (George & Mallery, 2016), and page numbers if you are using word-for-word materials. For example, “The developments of the World War II years firmly established the probability sample survey as a tool for describing population characteristics, beliefs, and attitudes” (Heeringa, West, & Berglund, 2017, p. 3).
The reference list should appear at the end of a paper (see the next page). It provides the information necessary for a reader to locate and retrieve any source you cite in the body of the paper. Each source you cite in the paper must appear in your reference list; likewise, each entry in the reference list must be cited in your text. A sample reference page is included below; this page includes examples (George & Mallery, 2016; Heeringa et al., 2017; Smith et al., 2018; “USA swimming,” 2018; Yu, Johnson, Deutsch, & Varga, 2018) of how to format different reference types (e.g., books, journal articles, and a website). For additional examples, see the GCU Style Guide.
References
George, D., & Mallery, P. (2016). IBM SPSS statistics 23 step by step: A simple guide and reference. New York, NY: Routledge.
Heeringa, S. G., West, B. T., & Berglund, P. A. (2017). Applied survey data analysis (2nd ed.). New York, NY: Chapman & Hall/CRC Press.
Smith, P. D., Martin, B., Chewning, B., ...
This document provides notes for online students about quantitative data analysis and SPSS. It discusses that the lecture series will cover basic ideas in quantitative data analysis. It notes that many different statistical software programs are available but that the course will use SPSS because it is easy to use and popular for statistical analysis.
Similar to 4 CREATING GRAPHS A PICTURE REALLY IS WORTH A THOUSAND WORDS4 M.docx (20)
Group Presentation Once during the quarter, each student will.docxgilbertkpeters11344
Group Presentation
: Once during the quarter, each student will prepare a brief presentation on a specific neighborhood, a racial or cultural group, or a historical event, migration or shift in the urban landscape,
related to the themes for that week
. Students will select preferred weeks in advance and be scheduled by Week 2 as best as your professor can allow. The presentation is open in form and format but should be 20 minutes in duration, consist mostly of your own original words and discussion, but involve some form of visual, quotes, or data, and represent some amount of additional research beyond the readings for that week, and include 5 or more questions for discussion to be presented to the class. Your group grade will reflect an average of 4 grades in content, delivery, relevance and engagement with the class in discussion.
.
Group Presentation Outline
•
Slide 1: Title slide
•
This contains your topic title, your names, and the course.
•
Slide 2: Introduction slide
•
Remember that you are presenting this information to others. Acknowledge the audience, and mention the purpose of the
presentation.
•
This slide should contain at least 50–100 words of speaker notes.
•
Slides 3–10 (or more): Content slides
•
Describe the topic and structure
•
Outline and discuss the issues/components each separately
•
Discuss theories, laws, policies, and other labor relations related topics
•
Provide support for your perspective and analysis
•
Lessons learned documented, what you have learned
•
Conclusion
•
The slides should each contain at least
50–100 words of speaker notes.
•
Final slide(s): Reference slide(s)
•
List your references according to the APA sty
.
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Group Portion
As a group, discuss and develop a paper of 10 pages that addresses the following questions. Work together to determine who will complete each section:
Who will comprise your planning committee? Explain.
Identify public- and private-sector partner agencies and elected officials (if any) that should serve on the planning committee.
What are the component parts of the plan (be specific and detailed)? Explain.
What participating agencies may be more or less involved in which parts of the plan development? Explain.
Are there subject matter experts (SMEs) or other entities that should be involved in any one specific area of the plan development? Explain.
Based upon the emergency management concept of incident management that includes the phases of preparedness and mitigation, response, and recovery, identify the actions that will need to be taken in each phase as they relate to the hazard you have selected.
Identify the major challenges that the community and responders will encounter when responding to the hazard.
What solutions exist (e.g., mutual aid, contract services) to overcome those challenges? Explain in detail.
What should be the short- and long-term recovery goals of the community following this event’s occurrence?
Be sure to reference all sources using APA style.
Please add your file.
Individual Portion
Develop a PowerPoint presentation of 6–7 slides that provides details about your plan.
Include speaker notes of 200–300 words that will be used when presenting the plan to your superiors.
.
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Group Behavior in Organizations
At an organizational level, group behavior is necessary for continued functioning of the
organization. Within an organization, there are established rules, procedures, and processes
developed that define how an organization operates. In addition, there are systems in place
to reward behaviors of those who effectively participate in the organization's operations.
Besides, there are also systems that define consequences that can take place in case
individuals behave outside the accepted practices of the organization. What develops out of
this is an employee's attachment to the organization based on common beliefs, values, and
traditions. The shared attachment and even the commitment to common beliefs, values, and
traditions make up an organization's culture (Helms & Stern, 2001; Lok & Crawford, 2001).
What Is Organization Culture?
Sheard and Kakabadse (2002) explained organizational culture in terms of solidarity and
sociability. Solidarity, in this case, referred to a group's willingness to pursue and maintain
conformity in shared objectives, processes, and systems. Sociability referred to a group's
sense of belongingness by its members and level of camaraderie.
They also mentioned there might be differences between hierarchies or levels within an
organization's culture. Based on the solidarity and sociability of each, upper management
might differ from the decisions made by middle management and line staff. These differences
might also occur between functional departments and, in larger organizations, between
geographically distinct sections of the organization.
What Sheard and Kakabadse wanted to emphasize through this discussion was there might
be distinct subcultures within an organization's culture.
According to De Long and Fahey (2000), "Subcultures consist of distinct sets of values,
norms, and practices exhibited by specific groups or units in an organization." Subcultures
may be readily observed in larger, more bureaucratic organizations or organizations having
well-established departments with employees that have highly specialized or possessing
unique skills.
De Long, D., & Fahey, L. (2000). Diagnosing cultural barriers to knowledge management. The
Academy of Management Executive, 14(4), 113–127.
Helms, M., & Stern, R. (2001). Exploring the factors that influence employees 'perceptions of
their organization's culture. Journal of Management in Medicine, 15(6), 415–429.
Lok, P., & Crawford, J. (2001). Antecedents of organizational commitment and the mediating
role of job satisfaction. Journal of Managerial Psychology, 16(8), 594–613.
Sheard, A., & Kakabadse, A. (2002). Key roles of the leadership landscape. Journal of
Managerial Psychology, 17(1/2), 129–144.
3-17 Kenneth Brown is the principal owner of Brown Oil, Inc. After quitting his university teaching job,
Ken has been able to increase his annual salary by a factor of over 100. At the present time, Ken is
f.
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Group assignment: Only responsible for writing 275 words on the following
Explain immigration and how that is connected.
Identify current and future issues in serving diverse clients and legally protected classes.
GroupgrAssignment content:
Access
the
Prison Rape Elimination Act
website.
Write
a 1,000- to 1,400-word report for an audience of potential new employees in human services in a correctional setting in which you:
Summarize current and future civil rights issues that affect the criminal justice system.
Identify why PREA affects the future of corrections.
Explain immigration and how that is connected.
Identify current and future issues in serving diverse clients and legally protected classes.
Explain options for advocacy.
Identify
boundaries in advocacy for human service workers.
Format
your resources consistent with APA guidelines.
.
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Group 2: WG is a 41-year-old female brought herself into the ER last night asking to "detox from vodka." She tells you she has a long-standing history of alcohol dependence with multiple relapses. She also reports that she has experienced alcohol withdrawal seizures before. Current CIWA-Ar is 17. She denies any past medical history but lab work indicates hepatic insufficiency (LFTs x3 ULN). All other lab work is normal. She denies taking any medications.
How will you manage this patient’s withdrawal syndrome?
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.
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Group 2: Discuss the limitations of treatment for borderline and histrionic PD and what can be done from a psychopharmacological perspective.
Post must be a minimum of 200 words, scholarly written, APA formatted, and referenced. A minimum of 2
scholarly
references are required
(other than your text
).
.
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Group 3: Discuss the limitations of treatment for antisocial and narcissistic PD and what can be done from a psychopharmacological perspective.
Post your initial response by Wednesday at midnight. Respond to at least one student
with a different assigned DB question
by Sunday at midnight. Both responses must be a minimum of 200 words, scholarly written, APA formatted, and referenced. A minimum of 2
scholarly
references are required
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Group 1: Describe the differences between Naloxone, Naltrexone, and Buprenorphine/Naloxone. Include the properties of each, their classification, mechanism of actions, onset, half-life, and formulations (routes of delivery). Please discuss the implications of differences in the clinical setting (including pre-hospital)
Responses must be a minimum of 200 words, scholarly written, APA7 formatted, and referenced. A minimum of 2 references is required (other than your text). Plagiarism and grammatical errors free.
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Grotius, Hobbes
Development of INR – Week 3
Hobbes
Relationship between Natural Law and Law of Nations?
Mediated by the idea of the state of nature as the predicament of insecurity:
Natural right: self-preservation.
Natural law: the observation of promises and contracts.
For states: minimum observation of natural law in the form of consenting to agreements.
Written agreement: treaty-making
Unwritten agreements: customary law
Hobbes
State of Nature: the condition in which individuals find themselves in a perpetual condition of war.
Natural right to self-preservation:
We each have the right to judge what is in our interest for self-preservation.
Conflict occurs because of:
Competition
Diffidence
Glory
Different meanings for words in the State of Nature; no ability in the State of Nature to determine whose judgment is valid (Wolin).
Life in the state of nature: “Solitary, poor, nasty, brutish, and short”
Commonwealth
Commonwealth by institution:
Social contract: it is the collective agreement among all individuals in the state of nature to establish:
Sovereign power
Able to speak and act for a multiplicity of people (which becomes a unified group).
State
The unity of sovereign power and the unified people.
Sovereign is the man or assembly that carries the person of the State.
State is the Leviathan: the mortal God on earth.
Sovereigns come and go but the State remains.
Consequences
The implication: fear is displaced from the condition of the state of nature to the relation between individual and state.
What continues to bind the state is fear of a return to the State of Nature:
the relation between individual and state is one of protection in exchange for obedience.
Private vs. public conscious: does one need to truly believe (i.e. like a Christian) or does the appearance of belief suffice?
“belief and unbelief never follow men’s commands.”
Loyalty only to those that are in power?
Historical context: The Norman Yoke and the English Civil Wars
Stability should not sacrificed as a result of ‘injustice’.
The rise of the ‘mechanical’ centralized administrative state.
Grotius
Dutch legal theorist 16th century;
Along with Vitoria and Gentili laid the foundation for the Law of Nations (Public European Law) on Natural Law.
Moves away from a theological conceptualization of Natural Law to a secular one.
Develops the notion of Natural Rights which becomes key for understanding human morality and law.
Notion of natural right emerged out of the massacre of St. Bartholomew (25 August 1572).
Attempted to establish limitation on the Sovereign’s power:
notion of individual right that the state cannot transgress.
Grotius: “a RIGHT is a moral quality annexed to the person, justly entitling him to possess some privilege, or to perform some particular act”
Four Fundamental Rights
1) the right for others not to take my possessions.
2) the right of restoration of property in case of injury.
3) honoring promises.
4) punish wrongdoing.
Natural.
GROUP 1 Case 967-- A Teenage Female with an Ovarian MassCLI.docxgilbertkpeters11344
GROUP 1: Case 967-- A Teenage Female with an Ovarian Mass
CLINICAL HISTORY
A teenage female presented with secondary amenorrhea (https://www.healthline.com/health/secondary-amenorrhea#causes). The patient had 1 menstrual cycle 3 years ago and has had no menses since. Laboratory work-up was negative for pregnancy test, mildly increased calcium level (11.7 mg/dL, normal range: 8.5-10.2 mg/dL) and CA 125 (43 Units/ml, normal range: 0-20 Units/ml). Prolactin, TSH, AFP, Inhibin A, Inhibin B and CEA were normal. Imaging revealed a 13 x 11.8 x 8.6 cm, predominately cystic left pelvis mass, with multiple internal septations. Her past medical history was not contributory. Patient underwent left salpingo-oophorectomy (https://www.healthline.com/health/salpingo-oophorectomy), omentectomy (https://moffitt.org/cancers/ovarian-cancer/omentectomy/) and tumor debulking (https://en.wikipedia.org/wiki/Debulking) with intraoperative frozen section consultation.
GROSS EXAMINATION
The 930.9 g tubo-ovarian complex consisted of a 20.0 x 16.0 x 8.0 cm large mass, with no recognizable normal ovarian parenchyma grossly and an unremarkable fallopian tube. The cut surface was gray, "fish-flesh", soft with foci of hemorrhage and necrosis.
MICROSCOPIC EXAMINATION
Microscopically, the majority of main tumor was growing in large nests, sheets and cords with focal follicle-like structures and geographic areas of necrosis. It was predominantly composed of small cells with hyperchromatic nuclei, round to oval nucleus with irregular nuclear contour, inconspicuous to occasional conspicuous nucleoli and minimal cytoplasm. This component was variably admixed with a population of larger cells, which as the name implies composed of cells with abundant eosinophilic cytoplasm, with central or eccentric round to oval nuclei, pale chromatin and prominent nuclei. Both, the small and large cell components demonstrated brisk mitotic activity. All staging biopsies and omentectomy were composed of large cell component.
An extensive panel of immunohistochemical stains was performed. Overall, the staining pattern was strong and diffuse in small cell component compared to patchy weak staining pattern in the large cell component.
FINAL DIAGNOSIS
Small cell carcinoma (https://en.wikipedia.org/wiki/Small-cell_carcinoma) of the ovary, hypercalcemic type (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4939673/)
DISCUSSION
Small cell carcinoma of the ovary, hypercalcemic type (SCCOHT) is an aggressive and highly malignant tumor affecting the women under 40. It was first described as a distinct entity by Dickersin et al in 1982 (1). Fewer than 500 cases have been described in the literature and it accounts for less than 1% of all ovarian cancer diagnoses. Due to the initial consideration of epithelial origin, the term of SCCOHT has been used to distinguish this entity from its mimicker, the neuroendocrine or pulmonary type (2). In fact epithelial origin of SCCOHT was recently challenged as new imm.
Greek Drama Further Readings and Short Report GuidelinesOur s.docxgilbertkpeters11344
Greek Drama: Further Readings and Short Report Guidelines
Our study of Greek drama will begin with an overview of Greek theater in general and focus on Aeschylus’ Agamemnon (Norton rental text, Vol. A). You will be completing a quiz/worksheet on Agamemnon (open book) and that play will be the focus of our class from March 26 through April 2. After that, each of you will have the opportunity to focus more intensively on one of three other Greek plays, Sophocles’ Philoctetes, Euripides’ Medea, or Aristophanes’ Lysistrata.
I will be asking you to submit a short report that focuses primarily on the play you chose to study in more depth. Your first task, though, is to choose which of the three plays you want to work on. Here are brief overviews of the three plays.
Sophocles’ Philoctetes(available in the Sophocles II purchase text). Philoctetes, an outstanding Greek warrior, was abandoned by Odysseus, Agamemnon and Menelaos on the way to fight in Troy because they could not bear the agonies of his suffering from a poisonous snake bite. The hero, an exceptional archer who wields the bow of Heracles, has been living in isolation on the wild island of Lemnos for nine years. Now the Greek forces have received a prophecy that they cannot conquer Troy without Philoctetes’ help. Odysseus, whom Philoctetes hates, and Neoptolemus, the son of Achilles, are sent to lure Philoctetes back to the war, by persuasion, treachery or force.
Euripides’ Medea (available in Norton rental text, Vol. A. Medea, the sorceress who helped the hero Jason find the Golden Fleece and also helped save his life, is living with Jason in exile from her homeland with their two children. She has learned that, in order to advance his fortune and social standing, Jason wants to jilt Medea and marry a younger woman. Out of despair and rage, Medea contrives to take revenge against Jason in the most horrific way she can.
Aristophanes’ Lysistrata (available in Norton rental text, Vol. A). Fed up with the emotional and economic hardships caused by the Peloponnesian War (431-404 BC), the Athenian and Spartan women, under the leadership of Lysistrata, unite to undertake two group actions: first, to refuse to have sex with their men until the men agree to stop fighting and, second, to cut off funding for the war by occupying the Athenian treasury. Aristophanes’ comedy still raises questions today about who should wield political power and why, as well as about how much humans really value peace.
NOTE: While I am requiring you to focus on only one of the three plays, I strongly encourage you to read all three. I will be saying something about each of the three plays before the short report is due, after we spend some time with Aeschylus’ Agamemnon.
Guidelines for Short Report on Greek Drama
For the short report on Greek drama, please write complete, incisiveresponses to each of the following five topics or questions concerning the play—Philoctetes,Medea or Lysistrata—that you h.
Graph 4 (You must select a different graph than one that you hav.docxgilbertkpeters11344
Graph 4 (You must select a different graph than one that you have previously discussed)
Select a data presentation from chapter 6 of the text (Grey Section).
Answer the following:
What is the visual that you selected?
What is the purpose of the visual?
What kind of data should be compiled in the selected visual?
What kinds of data should not be compiled in the selected visual?
How can you avoid making the visual misleading?
.
Graphs (Help! Really challenging assignment. Would appreciate any bi.docxgilbertkpeters11344
Graphs (Help! Really challenging assignment. Would appreciate any bit of help!)
Family tree's and genealogy software has become more and more prevalent in recent years. From the name you might expect that a family tree would be easily represented by a tree structure, but that is not the case! A more appropriate data structure to represent a family tree would be a type of graph. Using the description of the family that accompanies this assignment, you must represent this family using a graph structure. The graph needs to be a weighted graph. The weights will constitute the types of relationships, I recommend using some kind mapping between numbers and strings to represent the relationships. When adding family members to the graph, this can be done programmatically for the provided family members within the description file. Additionally, I also want there to be an interface in which a user can create a new family member and add them to the tree. This can be a simple CLI where the user provides a name, gender, and age to create a person. Then another simple CLI where they select which member of the family they want the original relationship to be with and what kind of relationship it should be. Finally, they can edit the family member using another CLI and selecting the family member they wish to edit, the operation they wish to perform (edit name, edit age, edit relationship), and then add new relationship between family members which can call a function that you create in order to add the original relationship. Remember the DRY philosophy, where code can be modularized or made into a function, it should be if you plan on using the logic again.
Finally, I want you to make data assertions within the
FamilyTree
class that enforce certain "rules" that exist in a typical human family. An example would be a person should not have any kind of relationship to itself (a person can not marry themselves, a person can not be their own brother, sister, father, mother, etc.). There should be at least 3 data assertions. These should exists as part of the family tree, not as part of the graph.
As a hint, for a successful design: I would recommend using layers of abstraction. Your graph class is the backing structure to the family tree class. Your family tree should implement methods that interface with the graph class, i.e. add_family_member() should call the constructor to create a node and then call a function within the graph class to add a node to the graph. Then using the relationships function parameter, you can add edges to the graph between the new nodes and the existing nodes. The family tree should be what enforces what relationships can exist through the data assertions, the graph does not care about what relationships are made between family members. Your functions that the user would interface with would be greatly reduced compared to the total number of methods within the classes themselves. The user should be able to add, remove, and modi.
Grandparenting can be highly rewarding. Many grandparents, though, u.docxgilbertkpeters11344
Grandparenting can be highly rewarding. Many grandparents, though, unexpectedly become guardians and raise small children. How might this responsibility affect their normal course of adult development? What components might require transitions? How would a professional counselor encourage these older guardians in their new roles? Just need 135 words (ASAP)!
.
Great Marketing Moves The evolving art of getting noticed Ov.docxgilbertkpeters11344
Great Marketing Moves The evolving art of getting noticed
Over three decades,
Inc.
has seen entrepreneurs, often with little cash but lots of creativity)', produce clever marketing campaigns time and again. Here are 3U classic examples from the archives. —
Kelly Fairdoth
Make a article summary from 2-3 paragraphs.
.
“GREAT MIGRATION”
Dr. G. J. Giddings
Characteristics
Human
Propelled – push-pull (E. Lee, 1966)
Impactful – consequential … cause/effect
Dynamic – leaderless …democratic …
Demographics
Demographics
1.2 million, 1915-’30
6.4 million, 1980
(Caribbean:
140,000,1899-1937)
Precursors
Post-Reconstruction, 1877-1914
Rural - Urban
Westward – “Black Exodus”
Henry Adams (LA)
89,000 migrants/interest
Benjamin “Pap” Singleton (TN)
“Advantage of Living in a Free State”
Thousands migrated
Emigration
Bishop Henry M. Turner,
Mary Ann Shadd Cary
Precursors …
U.S. Empire
Berlin Conf.,1884
Philippines, 1898
Puerto Rico, Guam
Hawaii,
(Cuba)
Haiti, (1915-’34)
U.S. Virgin Isl.,1916
Guyana, 1941
Atkinson Airstrip
6
Great Migration
Caribbean
140,000,1899-1937
M. M. Garvey
C. Powel
DJ Kool Herc
S. Chisholm
G. J. Giddings
Great Migration
“PUSH”
-Boll weevil, 1915/6
-Mississippi flood, 1927
-Racist Terroism
-Racist laws: Jim Crow
Great Migration
“PULL”
E. World War I, 1914-1919
(367,000 AAs served)
European immigration desisted
Chicago Defender
“To die from the bite of frost is more glorious than by the hands of a lynch mob”
“Every Black man for the sake of his wife and daughter should lave even at a financial sacrifice every spot in the south where his worth is not appreciated enough to give him the standing of a man and a citizen in the community.”
Great Migration
IMPACT
Detroit, MI
611 % increase
Urban League, 1911
National League of Urban Conditions among Negroes, NY
Rep. Oscar DePriest (R)
Chicago Alderman, 1915; U.S. Rep, 1929-’35
1970s: Chicago had more Blacks than Mississippi!
Harlem Renaissance, 1919-1932
L. Hughes, “Negro Artist …”
Some pastors followed migrants.
Return Migration/RE-PATRIATION
Post-Industrial
“Reverse migration”
1980-present
Service economy
“Sun Belt” industrial service areas
Destinations
Atlanta, GA; Charlotte, NC, Houston, TX, …
(F&H, chap. 23)
GREAT MIGRATION
Franklin & Higginbotham (F&H)
1, (12),13, 14, 15, 16, 17, 19, 23 …
Great Migration
The Warmth of Other Suns, 2010
Isabel Wilkerson, Pulitzer laureate
National Book Critics Circle award
“best non-fiction ...” NY Times
1,200 interviews
I.M. Gladney
G. Starling
R. P. Foster
Wilkerson …
Ida Mae Gladney
1934
MS – Chicago, IL
Wilkerson …
George Starling
1945
Florida–New York
(.
Grand theory and Middle-range theoryHow are Nursing Theories c.docxgilbertkpeters11344
Grand theory and Middle-range theory
How are Nursing Theories classified?
What are the differences between grand theory and middle-range Theory?
Examples of grand Theory and Middle range Theory?
Write an Essay.
Use the APA style 7
Avoid plagiarism by submitting your work to SafeAssign.
.
Grand Rounds Hi, and thanks for attending this case presen.docxgilbertkpeters11344
Grand Rounds
Hi, and thanks for attending this case presentation. My name is Dr. Stephen Brewer and I am a licensed
clinical psychologist in San Diego, California and Assistant Professor of Psychology and Applied
Behavioral Sciences at Ashford University. Today, I will be sharing with you the story of Bob.
Presenting problem
Bob Smith is a 36-year-old man who came to me approximately six months ago with concerns about his
career choice and life direction. He did not have any significant psychiatric symptoms, besides some
understandable existential anxiety regarding his future. Bob was cooperative, friendly, open, and
knowledgeable about psychology during our first few sessions together. I noticed that he seemed
guarded only when talking about his family and childhood experiences. To confirm his identity, I checked
his driver’s license to ensure his name was indeed Bob Smith and that he lived close by in a mobile home
in Spring Valley. Given his relatively mild symptoms, we decided to meet once a week for supportive
psychotherapy so he could work through his anxieties. I gave him a diagnosis of adjustment disorder
with anxiety.
History
Here’s some background on Bob to give you a sense of who he is.
Family
Bob grew up as an only child in Edmonton, Canada, in a low-income, conservative, and very religious
household.
He shared that his father was largely absent during his childhood, as he spent most of the week residing
north of Edmonton, where he worked as a mechanic in the oil fields near Fort McMurray. On weekends,
Bob’s father would return home and spend as much time as possible with his family. Bob described his
father as warm, caring, and a hard worker. His father reportedly died one year ago.
Bob’s mother was described as a strict, rule-based woman who had a short temper and was prone to
furious outbursts over trivial matters. She worked in Bob’s junior high as a janitor, which meant that Bob
often crossed paths with his mother at school, where she would often check up on him. During Bob’s
high school years, Bob’s mother got a new job as a high school librarian.
At 18, Bob moved to San Diego to study psychology at San Diego State University. He lived in the dorms
for his first few years, where he easily made friends and joined a fraternity. Bob maintained contact with
his parents, but ceased all contact when his mother suggested she would move to San Diego to be closer
to him. He graduated with a 3.2 GPA and began working for the county as a psychiatric technician. He
worked as a psych tech for 14 years and described it as “fun at first, but it got boring and predictable
after a while.”
Treatment
Bob shared that he has a medical doctor that he visits once every few years for his routine physical. He
denied having any significant medical problems. Additionally, he denied using any illicit substances and
reported drinking only on occasion with friends from his fratern.
Graduate Level Writing Required.DUEFriday, February 1.docxgilbertkpeters11344
Graduate Level Writing Required.
DUE:
Friday, February 14, 2020 by 5pm Eastern Standard Time.
Resources: U.S. Department of Labor, Bureau of Labor Statistics, U.S. Department of Labor Wages, U.S. Department of Education, U.S. Census Bureau
Based
on
Dallas, Texas
Write a 900- to 1,050-word paper in which you analyze the criminal profile of Dallas, Texas.
Include the following information in your analysis:
-Characterization of the city in terms of social and intellectual context
-Identity of social factors that contribute to crime
-Linking of events or attitudes to a description of beliefs people living there would accept for explaining criminal behavior
-Consideration of changes in land use, property values, transportation, and retail as one moves away from the city center
-If there are changes, what distance do you estimate exist between these areas?
-How noticeable are the changes?
-Discussion of whether or not zones of transition apply to this city
-Identification of criminal hot spots
-Relevant data to support answers
-How your findings relate to the role of socioeconomic status and values in criminological theory
-Identification and rationale for the choice of one sociologic theory that best explains the crime in your chosen city
-Format your paper consistent with APA guidelines
.
-Provide at least 4 Academic / Scholarly references
.
-100% Original Work. ZERO Plagiarism.
-Must Be Graduate Level Writing.
.
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
How to Make a Field Mandatory in Odoo 17Celine George
In Odoo, making a field required can be done through both Python code and XML views. When you set the required attribute to True in Python code, it makes the field required across all views where it's used. Conversely, when you set the required attribute in XML views, it makes the field required only in the context of that particular view.
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UPRAHUL
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...PECB
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
-------------------------------------------------------------------------------
Find out more about ISO training and certification services
Training: ISO/IEC 27001 Information Security Management System - EN | PECB
ISO/IEC 42001 Artificial Intelligence Management System - EN | PECB
General Data Protection Regulation (GDPR) - Training Courses - EN | PECB
Webinars: https://pecb.com/webinars
Article: https://pecb.com/article
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Facebook: https://www.facebook.com/PECBInternational/
Slideshare: http://www.slideshare.net/PECBCERTIFICATION
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
Main Java[All of the Base Concepts}.docxadhitya5119
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar Kanvaria
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.
How to Build a Module in Odoo 17 Using the Scaffold MethodCeline George
Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
How to Fix the Import Error in the Odoo 17Celine George
An import error occurs when a program fails to import a module or library, disrupting its execution. In languages like Python, this issue arises when the specified module cannot be found or accessed, hindering the program's functionality. Resolving import errors is crucial for maintaining smooth software operation and uninterrupted development processes.
4 CREATING GRAPHS A PICTURE REALLY IS WORTH A THOUSAND WORDS4 M.docx
1. 4 CREATING GRAPHS A PICTURE REALLY IS WORTH A
THOUSAND WORDS
4: MEDIA LIBRARY
Premium Videos
Core Concepts in Stats Video
· Examining Data: Tables and Figures
Lightboard Lecture Video
· Creating a Simple Chart
Time to Practice Video
· Chapter 4: Problem 3
Difficulty Scale
(moderately easy but not a cinch)
WHAT YOU WILL LEARN IN THIS CHAPTER
· Understanding why a picture is really worth a thousand words
· Creating a histogram and a polygon
· Understanding the different shapes of different distributions
· Using SPSS to create incredibly cool charts
· Creating different types of charts and understanding their
application and uses
WHY ILLUSTRATE DATA?
In the previous two chapters, you learned about the two most
important types of descriptive statistics—measures of central
tendency and measures of variability. Both of these provide you
with the one best number for describing a group of data (central
tendency) and a number reflecting how diverse, or different,
scores are from one another (variability).
What we did not do, and what we will do here, is examine how
differences in these two measures result in different-looking
distributions. Numbers alone (such as M = 3 and s = 3) may be
important, but a visual representation is a much more effective
way of examining the characteristics of a distribution as well as
the characteristics of any set of data.
So, in this chapter, we’ll learn how to visually represent a
distribution of scores as well as how to use different types of
2. graphs to represent different types of data.
CORE CONCEPTS IN STATS VIDEO
Examining Data: Tables and Figures
X-TIMESTAMP-MAP=LOCAL: Examining data helps find
data entry errors, evaluate research methodology, identify
outliers, and determine the shape of a distribution in a data
set. Researchers typically examine collected data in two ways,
by creating tables and figures. Imagine you asked a group of
friends to rate a movie they've seen on a one to five scale.
A table helps identify the variable and the possible values of
the variable. The sample size, often referred to as n, is 14
because there are ratings reported from 14 people. This is how
large the total sample is. From this, we can determine how
many in the sample have each value of the variable. We can
also determine the percentage that the sample has of each
possible value. Figures display variables from the table.
Nominal and ordinal variables can be depicted with bar charts,
while interval and ratio variables can be depicted using
histograms and frequency polygons. For this data set, we can
use a bar chart. Distributions of data can be characterized
along three aspects or dimensions, modality, symmetry, and
variability. In a unimodal distribution, a small range of values
has the greatest frequency or mode of the set. However, it's
possible for a distribution to have more than one mode. For a
bimodal distribution, we see two values that seem to occur
with the greatest frequency. A distribution is symmetrical if
folding it in half makes each half mirror the other. When a
distribution isn't symmetrical, it's called asymmetrical or
skewed. This distribution is often called positively skewed
because the tail-- or narrow end-- of the distribution is on the
right end. Variability in a distribution is the amount of
spread or dispersion of values for a variable. Peak
distributions look like a tall mountain and reflect little
variability in the scores. This means that almost everyone has
given the same score to the movie. A flat distribution has a
lot of variability, where almost everyone's scores are different.
3. In between is a normal distribution. It stands apart from the
distributions that are neither peak nor flat, unimodal, or
symmetrical.
TEN WAYS TO A GREAT FIGURE (EAT LESS AND
EXERCISE MORE?)
Whether you create illustrations by hand or use a computer
program, the same principles of decent design apply. Here are
10 to copy and put above your desk:
1. Minimize chart or graph junk. “Chart junk” (a close cousin to
“word junk”) happens when you use every function, every
graph, and every feature a computer program has to make your
charts busy, full, and uninformative. With graphs, more is
definitely less.
2. Plan out your chart before you start creating the final
copy. Use graph paper even if you will be using a computer
program to generate the graph. Actually, why not just use your
computer to generate and print out graph paper
(try www.printfreegraphpaper.com).
3. Say what you mean and mean what you say—no more and no
less. There’s nothing worse than a cluttered (with too much text
and fancy features) graph to confuse the reader.
4. Label everything so nothing is left to the misunderstanding of
the audience.
5. A graph should communicate only one idea—a description of
data or a demonstration of a relationship.
6. Keep things balanced. When you construct a graph, center
titles and labels.
7. Maintain the scale in a graph. “Scale” refers to the
proportional relationship between the horizontal and vertical
axes. This ratio should be about 3 to 4, so a graph that is 3
inches wide will be about 4 inches tall.
8. Simple is best and less is more. Keep the chart simple but not
simplistic. Convey one idea as straightforwardly as possible,
with distracting information saved for the accompanying text.
Remember, a chart or graph should be able to stand alone, and
the reader should be able to understand the message.
4. 9. Limit the number of words you use. Too many words, or
words that are too large (both in terms of physical size and
idea-wise), can detract from the visual message your chart
should convey.
10. A chart alone should convey what you want to say. If it
doesn’t, go back to your plan and try it again.
FIRST THINGS FIRST: CREATING A FREQUENCY
DISTRIBUTION
The most basic way to illustrate data is through the creation of a
frequency distribution. A frequency distribution is a method of
tallying and representing how often certain scores occur. In the
creation of a frequency distribution, scores are usually grouped
into class intervals, or ranges of numbers.
Here are 50 scores on a test of reading comprehension on which
a frequency distribution is based:
47
10
31
25
20
2
11
31
25
21
44
14
15
26
21
41
14
16
26
21
7
6. 2
35–39
4
30–34
8
25–29
10
20–24
10
15–19
8
10–14
4
5–9
2
0–4
1
People Who Loved Statistics
Helen M. Walker (1891–1983) began her college career
studying philosophy and then became a high school math
teacher. She got her master’s degree, taught mathematics at the
University of Kansas (your authors’ favorite college) where she
was tenured, and then studied the history of statistics (at least
up to 1929, when she wrote her doctoral dissertation at
Columbia). Dr. Walker’s greatest interest was in the teaching of
statistics, and many years after her death, a scholarship was
endowed in her name at Columbia for students who want to
teach statistics! Her publications included a whole book
teaching about the best way to show statistics using tables. Oh,
and along the way, she became the first woman president of the
American Statistical Association. All this achievement from
someone who actually loved teaching statistics. Just like your
professor!
The Classiest of Intervals
As you can see from the above table, a class interval is a range
of numbers, and the first step in the creation of a frequency
7. distribution is to define how large each interval will be. As you
can see in the frequency distribution that we created, each
interval spans five possible scores, such as 5–9 (which includes
scores 5, 6, 7, 8, and 9) and 40–44 (which includes scores 40,
41, 42, 43, and 44). How did we decide to have an interval that
includes only five scores? Why not five intervals, each
consisting of 10 scores? Or two intervals, each consisting of 25
scores?
Here are some general rules to follow in the creation of a class
interval, regardless of the size of values in the data set you are
dealing with:
1. Select a class interval that has a range of 2, 5, 10, 15, or 20
data points. In our example, we chose 5.
2. Select a class interval so that 10 to 20 such intervals cover
the entire range of data. A convenient way to do this is to
compute the range and then divide by a number that represents
the number of intervals you want to use (between 10 and 20). In
our example, there are 50 scores, and we wanted 10 intervals:
50/10 = 5, which is the size of each class interval. If you had a
set of scores ranging from 100 to 400, you could start with an
estimate of 20 intervals and see if the interval range makes
sense for your data: 300/20 = 15, so 15 would be the class
interval.
3. Begin listing the class interval with a multiple of that
interval. In our frequency distribution of reading comprehension
test scores, the class interval is 5, and we started the lowest
class interval at 0.
4. Finally, the interval made up of the largest scores goes at the
top of the frequency distribution.
There are some simple steps for creating class intervals on the
way to creating a frequency distribution. Here are six general
rules:
1. Determine the range.
2. Decide on the number of class intervals.
3. Decide on the size of the class interval.
4. Decide the starting point for the first class.
8. 5. Create the class intervals.
6. Put the data into the class intervals.
Once class intervals are created, it’s time to complete the
frequency part of the frequency distribution. That’s simply
counting the number of times a score occurs in the raw data and
entering that number in each of the class intervals represented
by the count.
In the frequency distribution that we created for our reading
comprehension data, the number of scores that occur between 30
and 34 and thus are in the 30–34 class interval is 8. So, an 8
goes in the column marked Frequency. There’s your frequency
distribution. As you might realize, it is easier to do this
counting if you have your scores listed in order.
Sometimes it is a good idea to graph your data first and then do
whatever calculations or analysis is called for. By first looking
at the data, you may gain insight into the relationship between
variables, what kind of descriptive statistic is the right one to
use to describe the data, and so on. This extra step might
increase your insights and the value of what you are doing.
LIGHTBOARD LECTURE VIDEO
Creating a Simple Chart
So statisticians and professor types use graphs and charts all
the time. Let's take a second to figure out what's in a chart,
like, what are the pieces that puts this all together. Here's
some scores. See here, different scores people could get, and
here's the number of people that got those scores. Very
typical data that people like to graph all the time. And when
you make a graph, you usually have these two lines, two
dimensions. And along the bottom, you often put the actual
scores. So here are the actual scores are 8, 9, 1 And along the
top, it's very common to put something that shows how many
people got that score or the frequency. OK. So, for instance,
the 8 here, one person got that. And the 9, three people got
that. One, two, three. And the 1 Six people got that. I don't
know if we have room for that. That's up here somewhere.
And then for the 11, two people got to that. That'd be about
9. there. And the 12, only one person got that. So these dots
represent the different people. It's sort of hard to look at those
dots, so instead we make these bars. And the taller the bar,
you can see, then the more people got it. So, like, the 1
that's way up here around a 6. And only one person got an 8,
so that's down here around a 1. But this, now, is a picture of
what your scores look like. And if you look at just the tops of
these bars, you can see, like, where we get a normal curve.
THE PLOT THICKENS: CREATING A HISTOGRAM
Now that we’ve got a tally of how many scores fall in what
class intervals, we’ll go to the next step and create what is
called a histogram, a visual representation of the frequency
distribution where the frequencies are represented by bars.
Depending on the book or journal article or report you read and
the software you use, visual representations of data are called
graphs (such as in SPSS) or charts (such as in the Microsoft
spreadsheet Excel). It really makes no difference. All you need
to know is that a graph or a chart is the visual representation of
data.
To create a histogram, do the following:
1. Using a piece of graph paper, place values at equal distances
along the x-axis, as shown in Figure 4.1. Now, identify
the midpoint of each class interval, which is the middle point in
the interval. It’s pretty easy to just eyeball, but you can also
just add the top and bottom values of the class interval and
divide by 2. For example, the midpoint of the class interval 0–4
is the average of 0 and 4, or 4/2 = 2.
2. Draw a bar or column centered on each midpoint that
represents the entire class interval to the height representing the
frequency of that class interval. For example, in Figure 4.2, you
can see that in our first entry, the class interval of 0–4 is
represented by the frequency of 1 (representing the one time a
value between 0 and 4 occurs). Continue drawing bars or
columns until each of the frequencies for each of the class
intervals is represented. Figure 4.2 is a nice hand-drawn
10. (really!) histogram for the frequency distribution of the 50
scores that we have been working with so far.
Notice that each class interval is represented by a range of
scores along the x-axis.
Figure 4.1 ⬢ Class intervals along the x-axis
The Tallyho Method
You can see by the simple frequency distribution at the
beginning of the chapter that you already know more about the
distribution of scores than you’d learn from just a simple listing
of them. You have a good idea of what values occur with what
frequency. But another visual representation (besides a
histogram) can be done by using tallies for each of the
occurrences, as shown in Figure 4.3.
Figure 4.2 ⬢ A hand-drawn histogram
Figure 4.3 ⬢ Tallying scores
We used tallies that correspond with the frequency of scores
that occur within a certain class. This gives you an even better
visual representation of how often certain scores occur relative
to other scores.THE NEXT STEP: A FREQUENCY POLYGON
Creating a histogram or a tally of scores wasn’t so difficult, and
the next step (and the next way of illustrating data) is even
easier. We’re going to use the same data—and, in fact, the
histogram that you just saw created—to create a frequency
polygon. (Polygon is a word for shape.) A frequency polygon is
a continuous line that represents the frequencies of scores
within a class interval, as shown in Figure 4.4.
Figure 4.4 ⬢ A hand-drawn frequency polygon
How did we draw this? Here’s how:
1. Place a midpoint at the top of each bar or column in a
histogram (see Figure 4.2).
2. Connect the lines and you’ve got it—a frequency polygon!
11. Note that in Figure 4.4, the histogram on which the frequency
polygon is based is drawn using vertical and horizontal lines,
and the polygon is drawn using curved lines. That’s because,
although we want you to see what a frequency polygon is based
on, you usually don’t see the underlying histogram.
Why use a frequency polygon rather than a histogram to
represent data? For two reasons. Visually, a frequency polygon
appears more dynamic than a histogram (a line that represents
change in frequency always looks neat). Also, the use of a
continuous line suggests that the variable represented by the
scores along the x-axis is also a theoretically continuous,
interval-level measurement as we talked about in Chapter 2. (To
purists, the fact that the bars touch each other in a histogram
suggests the interval-level nature of the variable, as well.)
Cumulating Frequencies
Once you have created a frequency distribution and have
visually represented those data using a histogram or a frequency
polygon, another option is to create a visual representation of
the cumulative frequency of occurrences by class intervals. This
is called a cumulative frequency distribution.
A cumulative frequency distribution is based on the same data
as a frequency distribution but with an added column
(Cumulative Frequency), as shown below.
Class Interval
Frequency
Cumulative Frequency
45–49
1
50
40–44
2
49
35–39
4
47
30–34
12. 8
43
25–29
10
35
20–24
10
25
15–19
8
15
10–14
4
7
5–9
2
3
0–4
1
1
The cumulative frequency distribution begins with the creation
of a new column labeled “Cumulative Frequency.” Then, we add
the frequency in a class interval to all the frequencies below it.
For example, for the class interval of 0–4, there is 1 occurrence
and none below it, so the cumulative frequency is 1. For the
class interval of 5–9, there are 2 occurrences in that class
interval and one below it for a total of 3 (2 + 1) occurrences.
The last class interval (45–49) contains 1 occurrence, and there
are now a total of 50 occurrences at or below that class interval.
Once we create the cumulative frequency distribution, then we
can plot it as a histogram or a frequency polygon. Only this
time, we’ll skip right ahead and plot the midpoint of each class
interval as a function of the cumulative frequency of that class
interval. You can see the cumulative frequency distribution
in Figure 4.5 based on these same 50 scores. Notice this
frequency polygon is shaped a little like a letter S. If the scores
13. in a data set are distributed the way scores typically are,
cumulative frequencies will often graph this way.
Figure 4.5 ⬢ A hand-drawn cumulative frequency distribution
Another name for a cumulative frequency polygon is an ogive.
And, if the distribution of the data is normal or bell shaped
(see Chapter 8 for more on this), then the ogive represents what
is popularly known as a bell curve or a normal distribution.
SPSS creates a really nice ogive—it’s called a P-P plot (for
probability plot) and is easy to create. See Appendix A for an
introduction to creating graphs using SPSS, as well as the
material toward the end of this chapter.
OTHER COOL WAYS TO CHART DATA
What we did so far in this chapter is take some data and show
how charts such as histograms and polygons can be used to
communicate visually. But several other types of charts are also
used in the behavioral and social sciences, and although it’s not
necessary for you to know exactly how to create them
(manually), you should at least be familiar with their names and
what they do. So here are some popular charts, what they do,
and how they do it.
There are several very good personal computer applications for
creating charts, among them the spreadsheet Excel (a Microsoft
product) and, of course, SPSS. The charts in the “Using the
Computer to Illustrate Data” section were created using SPSS as
well.
Bar Charts
A bar or column chart should be used when you want to
compare the frequencies of different categories with one
another. Categories are organized horizontally on the x-axis,
and values are shown vertically on the y-axis. Here are some
examples of when you might want to use a column chart:
· Number of participants in different water exercise activities
· The sales of three different types of products
· Number of children in each of six different grades
Figure 4.6 shows a graph of number of participants in different
14. water activities.
Figure 4.6 ⬢ A bar chart that compares different water activities
Column Charts
A column chart is identical to a bar chart, but in this chart,
categories are organized on the y-axis (which is the vertical
one), and values are shown on the x-axis (the horizontal one).
Line Charts
A line chart should be used when you want to show a trend in
the data at equal intervals. This sort of graph is often used when
the x-axis represents time. Here are some examples of when you
might want to use a line chart:
· Number of cases of mononucleosis (mono) per season among
college students at three state universities
· Toy sales for the T&K company over four quarters
· Number of travelers on two different airlines for each quarter
In Figure 4.7, you can see a chart of sales in units over four
quarters.
Figure 4.7 ⬢ Using a line chart to show a trend over time
Pie Charts
A pie chart should be used when you want to show the
proportion or percentage of people or things in various
categories. The rule is that the percentages in each “slice” must
add up to 100%, to make a whole pie. Here are some examples
of when you might want to use a pie chart:
· Of children living in poverty, the percentage who represent
various ethnicities
· Of students enrolled, the proportion who are in night or day
classes
· Of participants, the percentage in various age groups
Note that a pie chart describes a nominal-level variable (such as
ethnicity, time of enrollment, and age groups).
In Figure 4.8, you can see a pie chart of voter preference. And
we did a few fancy-schmancy things, such as separating and
15. labeling the slices.
Figure 4.8 ⬢ A pie chart illustrating the relative proportion of
one category to others
USING THE COMPUTER (SPSS, THAT IS) TO ILLUSTRATE
DATA
Now let’s use SPSS and go through the steps in creating some
of the charts that we explored in this chapter. First, here are
some general SPSS charting guidelines.
1. Although there are a couple options, we will use the Chart
Builder option on the Graphs menu. This is the easiest way to
get started and well worth learning how to use.
2. In general, you click Graphs → Chart Builder, and you see a
dialog box from which you will select the type of graph you
want to create.
3. Click the type of graph you want to create and then select the
specific design of that type of graph.
4. Drag the variable names to the axis where each belongs.
5. Click OK, and you’ll see your graph.
Let’s practice.
Creating a Histogram
1. Enter the data you want to use to create the graph. Use those
50 scores we’ve been using in this chapter or make some up just
to practice with.
2. Click Graphs → Chart Builder and you will see the Chart
Builder dialog box, as shown in Figure 4.9. If you see any other
screen, click OK.
3. Click the Histogram option in the Choose from: list and
double-click the first image.
4. Drag the variable you wish to graph to the “x-axis?” location
in the preview window.
5. Click OK and you will see a histogram, as shown in Figure
4.10.
Figure 4.9 ⬢ The Chart Builder dialog box
16. The histogram in Figure 4.10 looks a bit different from the
hand-drawn one representing the same data shown earlier in this
chapter, in Figure 4.2. The difference is that SPSS defines class
intervals using its own idiosyncratic method. SPSS took as the
middle of a class interval the bottom number of the interval
(such as 10) rather than the midpoint (such as 12.5).
Consequently, scores are allocated to different groups. The
lesson here? How you group data makes a big difference in the
way they look in a histogram. And, once you get to know SPSS
well, you can make all kinds of fine-tuned adjustments to make
graphs appear exactly as you want them.
Creating a Bar Graph
To create a bar graph, follow these steps:
1. Enter the data you want to use to create the graph. We used
the following data that show the number of people in a club who
belong to each of three political parties. 1 = Democrat, 2 =
Republican, 3 = Independent
1, 1, 2, 3, 2, 1, 1, 2, 1
2. Click Graphs → Chart Builder, and you will see the Chart
Builder dialog box, as shown in Figure 4.11. If you see any
other screen, click OK.
3. Click the Bar option in the Choose from: list and double-
click the first image.
4. Drag the variable named Party to the x-axis? location in the
preview window.
5. Drag the variable named Number to the Count axis.
6. Click OK and you will see the bar graph, as shown in Figure
4.12.
Figure 4.11 ⬢ The Chart Builder dialog box
Figure 4.12 ⬢ A bar graph created using the Chart Builder
17. Creating a Line Graph
To create a line graph, follow these steps:
1. Enter the data you want to use to create the graph. In this
example, we will be using the percentage of the total student
body who attended the first day of classes each year over the
duration of a 10-year program. Here are the data. You can type
them into SPSS exactly as shown here, with the top row being
the names you will give the two variables (columns).
Year
Attendance
1
87
2
88
3
89
4
76
5
80
6
96
7
91
8
97
9
89
10
79
2. Click Graphs → Chart Builder and you will see the Chart
Builder dialog box, as shown in Figure 4.11. If you see any
other screen, click OK.
18. 3. Click the Line option in the Choose from: list and double-
click the first image.
4. Drag the variable named Year to the x-axis? location in the
preview window.
5. Drag the variable named Attendance to the y-axis? location.
6. Click OK, and you will see the line graph, as shown in Figure
4.13. We used the SPSS Chart Editor to change the minimum
and maximum values on the y-axis.
Figure 4.13 ⬢ A line graph created using the Chart Builder
Creating a Pie Chart
To create a pie chart, follow these steps:
1. Enter the data you want to use to create the chart. In this
example, the pie chart represents the percentage of people
buying different brands of doughnuts. Here are the data:
Brand
Percentage
Krispies
55
Dunks
35
Other
10
2. Click Graphs → Chart Builder, and you will see the Chart
Builder dialog box, as shown in Figure 4.11. If you see any
other screen, click OK.
3. Click the Pie/Polar option in the Choose from: list and
double-click the only image.
4. Drag the variable named Brand to the Slice by? axis label.
5. Drag the variable named Percentage to the Angle Variable?
axis label.
6. Click OK, and you will see the pie chart, as shown in Figure
4.14.
Figure 4.14 ⬢ A pie chart created using the Chart Builder
19. Real-World Stats
Graphs work, and a picture really is worth more than a thousand
words.
In this article, an oldie but goodie, the researchers examined
how people perceive and process statistical graphs. Stephen
Lewandowsky and Ian Spence reviewed empirical studies
designed to explore how suitable different types of graphs are
and how what is known about human perception can have an
impact on the design and utility of these charts.
They focused on some of the theoretical explanations for why
certain elements work and don’t, the use of pictorial symbols
(like a happy face symbol, which could make up the bar in a bar
chart), and multivariate displays, where more than one set of
data needs to be represented. And, as is very often the case with
any paper, they concluded that not enough data were available
yet. Given the increasingly visual world in which we live
(emojis, anyone? ☹ ☺), this is interesting and useful reading to
gain a historical perspective on how information was (and still
is) discussed as a scientific topic.
Want to know more? Go online or to the library and find …
Lewandowsky, S., & Spence, I. (1989). The perception of
statistical graphs. Sociological Methods Research, 18, 200–242.
Summary
There’s no question that charts are fun to create and can add
enormous understanding to what might otherwise appear to be
disorganized data. Follow our suggestions in this chapter and
use charts well but only when they enhance, not duplicate,
what’s already there.
Time to Practice
1. A data set of 50 comprehension scores (named
Comprehension Score) called Chapter 4 Data Set 1 is available
in Appendix C and on the website. Answer the following
questions and/or complete the following tasks:
a. Create a frequency distribution and a histogram for the set.
b. Why did you select the class interval you used?
20. 2. Here is a frequency distribution. Create a histogram by hand
or by using SPSS.
Class Interval
Frequency
261–280
140
241–260
320
221–240
3,380
201–220
600
181–200
500
161–180
410
141–160
315
121–140
300
100–120
200
3. A third-grade teacher wants to improve her students’ level of
engagement during group discussions and instruction. She keeps
track of each of the 15 third graders’ number of responses every
day for 1 week, and the data are available as Chapter 4 Data Set
2. Use SPSS to create a bar chart with one bar for each day (and
warning—this may be a toughie).Time to Practice VideoChapter
4: Problem 3
1. For problem three in chapter four, a teacher wants to display
her students number of responses for each day of the week.
And she wants to do that with a bar chart. Since she hasn't
taken a stats class, she comes to you for help. You first enter
her data into SPSS and the results look like this-- When you
look at your data set, you'll see that it actually has the wrong
level of measurement. Notice that there's a little Venn
21. diagram at the top of each column, which indicates that your
data has been entered as nominal. That would be correct if you
were noting which day of the week a student participated, but
since you're noting how often a given student participated, the
correct level of measurement is a scale. Go ahead and change
that. Watch how I do that. Under variable view, under
measure, you just want to click each one and turn it into a
scale. You can also cut and paste these, and I can show you
that in another video. Once you have them changed, go back to
data view, and you'll see that at the top it has changed in two
little rulers. The next question is, how do I get SPSS to
display the average score per day rather the total number of
individual scores, which might look like a mess, and it's why
this question is a toughie. To do that we go under graphs, and
you'll see that you have two options, you can do a Chart
Builder or a Legacy Dialog. For this question we want to use
the Legacy Dialog. We go to Bar and when we click that, there
are two questions-- one, what type of bar chart? We want a
simple one. And then, how do you want the data in their area
displayed? Do we want to summarize for the groups? We
really don't. We want summary of separate variables where
each day of the week is a variable. We click on Define and
then here you'll see every day of the week. You want to bring
that over and you see your bar charts are going to represent the
mean for every day of the week. As a good habit you want to
make sure you title it, I called it "Students' Engagement
During Group Discussion." The second one is by day of
week. We hit Continue, and then when we hit OK, you're
going to see your output pop up. And here is our bar chart--
every day of the week showing the average student engagement.
And this is how you answer problem 3 in chapter 4. Good luck.
2. Identify whether these distributions are negatively skewed,
positively skewed, or not skewed at all and explain why you
describe them that way.
a. This talented group of athletes scored very high on the
vertical jump task.
22. b. On this incredibly crummy test, everyone received the same
score.
c. On the most difficult spelling test of the year, the third
graders wept as the scores were delivered and then their parents
complained.
3. Use the data available as Chapter 4 Data Set 3 on pie
preference to create a pie chart ☺ using SPSS.
4. For each of the following, indicate whether you would use a
pie, line, or bar chart and why.
a. The proportion of freshmen, sophomores, juniors, and seniors
in a particular university
b. Change in temperature over a 24-hour period
c. Number of applicants for four different jobs
d. Percentage of test takers who passed
e. Number of people in each of 10 categories
5. Provide an example of when you might use each of the
following types of charts. For example, you would use a pie
chart to show the proportion of children who receive a reduced-
price lunch that are in Grades 1 through 6. When you are done,
draw the fictitious chart by hand.
a. Line
b. Bar
c. Scatter/dot (extra credit)
6. Go to the library or online and find a journal article in your
area of interest that contains empirical data but does not contain
any visual representation of them. Use the data to create a chart.
Be sure to specify what type of chart you are creating and why
you chose the one you did. You can create the chart manually or
using SPSS or Excel.
7. Create the worst-looking chart that you can, crowded with
chart and font junk. Nothing makes as lasting an impression as
a bad example.
8. And, finally, what is the purpose of a chart or graph?
Student Study Site
Get the tools you need to sharpen your study skills!
23. Visit edge.sagepub.com/salkindfrey7e to access practice
quizzes, eFlashcards, original and curated videos, data sets, and
more!5 COMPUTING CORRELATION COEFFICIENTS ICE
CREAM AND CRIME5: MEDIA LIBRARY
Premium VideosCore Concepts in Stats Video
· CorrelationLightboard Lecture Video
· Partial CorrelationsTime to Practice Video
· Chapter 5: Problem 6
Difficulty Scale
(moderately hard)WHAT YOU WILL LEARN IN THIS
CHAPTER
· Understanding what correlations are and how they work
· Computing a simple correlation coefficient
· Interpreting the value of the correlation coefficient
· Understanding what other types of correlations exist and when
they should be usedWHAT ARE CORRELATIONS ALL
ABOUT?
Measures of central tendency and measures of variability are
not the only descriptive statistics that we are interested in using
to get a picture of what a set of scores looks like. You have
already learned that knowing the values of the one most
representative score (central tendency) and a measure of spread
or dispersion (variability) is critical for describing the
characteristics of a distribution.
However, sometimes we are as interested in the relationship
between variables—or, to be more precise, how the value of one
variable changes when the value of another variable changes.
The way we express this interest is through the computation of a
simple correlation coefficient. For example, what’s the
relationship between age and strength? Income and years of
education? Memory skills and amount of drug use? Your
political attitudes and the attitudes of your parents?
A correlation coefficient is a numerical index that reflects the
relationship or association between two variables. The value of
this descriptive statistic ranges between −1.00 and +1.00. A
24. correlation between two variables is sometimes referred to as
a bivariate (for two variables) correlation. Even more
specifically, the type of correlation that we will talk about in
the majority of this chapter is called the Pearson product-
moment correlation, named for its inventor, Karl Pearson.
The Pearson correlation coefficient examines the relationship
between two variables, but both of those variables are
continuous in nature. In other words, they are variables that can
assume any value along some underlying continuum; examples
include height (you really can be 5 feet 6.1938574673 inches
tall), age, test score, and income. Remember in Chapter 2, when
we talked about levels of measurement? Interval and ratio levels
of measurement are continuous. But a host of other variables are
not continuous. They’re called discrete or categorical variables,
and examples are race (such as black and white), social class
(such as high and low), and political affiliation (such as
Democrat and Republican). In Chapter 2, we called these types
of variables nominal level. You need to use other correlational
techniques, such as the phi correlation, in these cases. These
topics are for a more advanced course, but you should know
they are acceptable and very useful techniques. We mention
them briefly later on in this chapter.
Other types of correlation coefficients measure the relationship
between more than two variables, and we’ll talk about one of
these in some more advanced chapters later on (which you are
looking forward to already, right?).
Types of Correlation Coefficients: Flavor 1 and Flavor 2
A correlation reflects the dynamic quality of the relationship
between variables. In doing so, it allows us to understand
whether variables tend to move in the same or opposite
directions in relationship to each other. If variables change in
the same direction, the correlation is called a direct
correlation or a positive correlation. If variables change in
opposite directions, the correlation is called an indirect
correlation or a negative correlation. Table 5.1 shows a
25. summary of these relationships.
Table 5.1 ⬢ Types of Correlations
What Happens to Variable X
What Happens to Variable Y
Type of Correlation
Value
Example
X increases in value.
Y increases in value.
Direct or positive
Positive, ranging from .00 to +1.00
The more time you spend studying, the higher your test score
will be.
X decreases in value.
Y decreases in value.
Direct or positive
Positive, ranging from .00 to +1.00
The less money you put in the bank, the less interest you will
earn.
X increases in value.
Y decreases in value.
Indirect or negative
Negative, ranging from −1.00 to .00
The more you exercise, the less you will weigh.
X decreases in value.
Y increases in value.
Indirect or negative
Negative, ranging from –1.00 to .00
The less time you take to complete a test, the more items you
will get wrong.
Now, keep in mind that the examples in the table reflect
generalities, for example, regarding time to complete a test and
the number of items correct on that test. In general, the less
time that is taken on a test, the lower the score. Such a
conclusion is not rocket science, because the faster one goes,
the more likely one is to make careless mistakes such as not
26. reading instructions correctly. But, of course, some people can
go very fast and do very well. And other people go very slowly
and don’t do well at all. The point is that we are talking about
the average performance of a group of people on two different
variables. We are computing the correlation between the two
variables for the group of people, not for any one particular
person.
There are several easy (but important) things to remember about
the correlation coefficient:
· A correlation can range in value from −1.00 to +1.00.
· The absolute value of the coefficient reflects the strength of
the correlation. So a correlation of −.70 is stronger than a
correlation of +.50. One frequently made mistake regarding
correlation coefficients occurs when students assume that a
direct or positive correlation is always stronger (i.e., “better”)
than an indirect or negative correlation because of the sign and
nothing else.
· To calculate a correlation, you need exactly two variables and
at least two people.
· Another easy mistake is to assign a value judgment to the sign
of the correlation. Many students assume that a negative
relationship is not good and a positive one is good. But think of
the example from Table 5.1 where exercise and weight have a
negative correlation. That negative correlation is a positive
thing! That’s why, instead of using the
terms negative and positive, you might prefer to use the
terms indirect and direct to communicate meaning more clearly.
· The Pearson product-moment correlation coefficient is
represented by the small letter r with a subscript representing
the variables that are being correlated. You’d think that P for
Pearson might be used as the symbol for this correlation, but in
Greek, the P letter actually is similar to the English “r” sound,
so r is used. P is used for the theoretical correlation in a
population, so don’t feel sorry for Pearson. (If it helps, think
of r as standing for relationship.) For example,
· rxy is the correlation between variable X and variable Y.
27. · rweight-height is the correlation between weight and height.
· rSAT.GPA is the correlation between SAT score and grade
point average (GPA).
The correlation coefficient reflects the amount of variability
that is shared between two variables and what they have in
common. For example, you can expect an individual’s height to
be correlated with an individual’s weight because these two
variables share many of the same characteristics, such as the
individual’s nutritional and medical history, general health, and
genetics, and, of course, taller people have more mass usually.
On the other hand, if one variable does not change in value and
therefore has nothing to share, then the correlation between it
and another variable is zero. For example, if you computed the
correlation between age and number of years of school
completed, and everyone was 25 years old, there would be no
correlation between the two variables because there is literally
no information (no variability) in age available to share.
Likewise, if you constrain or restrict the range of one variable,
the correlation between that variable and another variable will
be less than if the range is not constrained. For example, if you
correlate reading comprehension and grades in school for very
high-achieving children, you’ll find the correlation to be lower
than if you computed the same correlation for children in
general. That’s because the reading comprehension score of
very high-achieving students is quite high and much less
variable than it would be for all children. The moral? When you
are interested in the relationship between two variables, try to
collect sufficiently diverse data—that way, you’ll get the truest
representative result. And how do you do that? Measure a
variable as precisely as possible (use higher, more informative
levels of measurement) and use a sample that varies greatly on
the characteristics you are interested in.COMPUTING A
SIMPLE CORRELATION COEFFICIENT
The computational formula for the simple Pearson product-
moment correlation coefficient between a variable
labeled X and a variable labeled Y is shown in Formula
28. 5.1:COMPUTING A SIMPLE CORRELATION COEFFICIENT
The computational formula for the simple Pearson product-
moment correlation coefficient between a variable
labeled X and a variable labeled Y is shown in Formula 5.1:
(5.1)
rxy=n∑XY−∑X∑Y√[n∑X2−(∑X)2][n∑Y2−(∑Y)2],rxy=n∑XY−
∑X∑Y[n∑X2−(∑X)2][n∑Y2−(∑Y)2],
where
· rxy is the correlation coefficient between X and Y;
· n is the size of the sample;
· X is each individual’s score on the X variable;
· Y is each individual’s score on the Y variable;
· XY is the product of each X score times its
corresponding Y score;
· X2 is each individual’s X score, squared; and
· Y2 is each individual’s Y score, squared.
Here are the data we will use in this example:
X
Y
X2
Y2
XY
2
3
4
9
6
4
2
16
4
8
5
30. 4
36
16
24
7
5
49
25
35
Total, Sum, or ∑
54
43
320
201
247
Before we plug the numbers in, let’s make sure you understand
what each one represents:
· ∑X, or the sum of all the X values, is 54.
· ∑Y, or the sum of all the Y values, is 43.
· ∑X 2, or the sum of each X value squared, is 320.
· ∑Y 2, or the sum of each Y value squared, is 201.
· ∑XY, or the sum of the products of X and Y, is 247.
It’s easy to confuse the sum of a set of values squared and the
sum of the squared values. The sum of a set of values squared is
taking values such as 2 and 3, summing them (to be 5), and then
squaring that (which is 25). The sum of the squared values is
taking values such as 2 and 3, squaring them (to get 4 and 9,
respectively), and then adding those together (to get 13). Just
look for the parentheses as you work.
Here are the steps in computing the correlation coefficient:
1. List the two values for each participant. You should do this
in a column format so as not to get confused. Use graph paper if
working manually or SPSS or some other data analysis tool if
working digitally.
31. 2. Compute the sum of all the X values and compute the sum of
all the Y values.
3. Square each of the X values and square each of the Y values.
4. Find the sum of the XY products.
These values are plugged into the equation you see in Formula
5.2:
(5.2)
rxy=(10×247)−(54×43)√[(10×320)−542][(10×201)−432].rxy=(1
0×247)−(54×43)[(10×320)−542][(10×201)−432].
Ta-da! And you can see the answer in Formula 5.3:
(5.3)
rxy=148213.83=.692.rxy=148213.83=.692.
What’s really interesting about correlations is that they measure
the amount of distance that one variable covaries in relation to
another. So, if both variables are highly variable (have lots of
wide-ranging values), the correlation between them is more
likely to be high than if not. Now, that’s not to say that lots of
variability guarantees a higher correlation, because the scores
have to vary in a systematic way. But if the variance is
constrained in one variable, then no matter how much the other
variable changes, the correlation will be lower. For example,
let’s say you are examining the correlation between academic
achievement in high school and first-year grades in college and
you look at only the top 10% of the class. Well, that top 10% is
likely to have very similar grades, introducing no variability
and no room for the one variable to vary as a function of the
other. Guess what you get when you correlate one variable with
another variable that does not change (that is, has no
variability)? rxy = 0, that’s what. The lesson here? Variability
works, and you should not artificially limit it.
The Scatterplot: A Visual Picture of a Correlation
There’s a very simple way to visually represent a correlation:
Create what is called a scatterplot, or scattergram (in SPSS
lingo it’s a scatter/dot graph). This is simply a plot of each set
of scores on separate axes.
32. Here are the steps to complete a scattergram like the one you
see in Figure 5.1, which plots the 10 sets of scores for which we
computed the sample correlation earlier.
Figure 5.1 ⬢ A simple scattergram
1. Draw the x-axis and the y-axis. Usually, the X variable goes
on the horizontal axis and the Y variable goes on the vertical
axis.
2. Mark both axes with the range of values that you know to be
the case for the data. For example, the value of the X variable in
our example ranges from 2 to 8, so we marked the x-axis from 0
to 9. There’s no harm in marking the axes a bit low or high—
just as long as you allow room for the values to appear. The
value of the Y variable ranges from 2 to 6, and we marked that
axis from 0 to 9. Having similarly labeled (and scaled) axes can
sometimes make the finished scatterplot easier to understand.
3. Finally, for each pair of scores (such as 2 and 3, as shown
in Figure 5.1), we entered a dot on the chart by marking the
place where 2 falls on the x-axis and 3 falls on the y-axis. The
dot represents a data point, which is the intersection of the two
values.
When all the data points are plotted, what does such an
illustration tell us about the relationship between the variables?
To begin with, the general shape of the collection of data points
indicates whether the correlation is direct (positive) or indirect
(negative).
A positive slope occurs when the data points group themselves
in a cluster from the lower left-hand corner on the x- and y-axes
through the upper right-hand corner. A negative slope occurs
when the data points group themselves in a cluster from the
upper left-hand corner on the x- and y-axes through the lower
right-hand corner.
Here are some scatterplots showing very different correlations
where you can see how the grouping of the data points reflects
33. the sign and strength of the correlation coefficient.
Figure 5.2 shows a perfect direct correlation, where rxy = 1.00
and all the data points are aligned along a straight line with a
positive slope.
Figure 5.2 ⬢ A perfect direct, or positive, correlation
If the correlation were perfectly indirect, the value of the
correlation coefficient would be −1.00, and the data points
would align themselves in a straight line as well but from the
upper left-hand corner of the chart to the lower right. In other
words, the line that connects the data points would have a
negative slope. And, remember, in both examples, the strength
of the association is the same; it is only the direction that is
different.
Don’t ever expect to find a perfect correlation between any two
variables in the behavioral or social sciences. Such a correlation
would say that two variables are so perfectly related, they share
everything in common. In other words, knowing one is exactly
like knowing the other. Just think about your classmates. Do
you think they all share any one thing in common that is
perfectly related to another of their characteristics across all
those different people? Probably not. In fact, r values
approaching .7 and .8 are just about the highest you’ll see.
In Figure 5.3, you can see the scatterplot for a strong (but not
perfect) direct relationship where rxy = .70. Notice that the data
points align themselves along a positive slope, although not
perfectly.
Now, we’ll show you a strong indirect, or negative, relationship
in Figure 5.4, where rxy = −.82. Notice that the data points
align themselves on a negative slope from the upper left-hand
corner of the chart to the lower right-hand corner.
That’s what different types of correlations look like, and you
can really tell the general strength and direction by examining
the way the points are grouped.
Figure 5.3 ⬢ A strong, but not perfect, direct relationship
34. Not all correlations are reflected by a straight line showing
the X and the Y values in a relationship called a linear
correlation (see Chapter 16 for tons of fun stuff about this). The
relationship may not be linear and may not be reflected by a
straight line. Let’s take the correlation between age and
memory. For the early years, the correlation is probably highly
positive—the older children get, the better their memory. Then,
into young and middle adulthood, there isn’t much of a change
or much of a correlation, because most young and middle adults
maintain a good (but not necessarily increasingly better)
memory. But with old age, memory begins to suffer, and there is
an indirect relationship between memory and aging in the later
years. If you take these together and look at the relationship
over the life span, you find that the correlation between memory
and age tends to look something like a curve where age
continues to grow at the same rate but memory increases at
first, levels off, and then decreases. It’s
a curvilinear relationship, and sometimes, the best description
of a relationship is that it is curvilinear.CORE CONCEPTS IN
STATS VIDEOCorrelation
People who perform well in high school tend to do well in
college-- right? Say you wanted to measure the relationship
between students' GPA in high school and their GPA in
college-- you would calculate a Pearson correlation between
the two variables. To see the relationship between two
variables, we draw a picture of the data using a scatter plot.
We plot each person's high school GPA on the x-axis and their
college GPA on the y-axis. Notice how the dots have a pattern.
Next, we compute a line called a regression line that runs
through the center of the dots. This line is computed using the
average. We use a formula to measure how much each GPA
varies independently and how much the two GPA is very
together. The variance is the average amount that each
student's high school GPA differs from the mean of all of the
35. high school GPAs. Of course, each student's college GPA
also varies from the mean of the college GPAs. But high
school GPA and college GPA also very together. People who
do well in high school tend to do well in college. Varying
together is called covariance. The Pearson correlation is
calculated by dividing the covariance of the two variables by
the variance of the two variables. Sometimes the dots are
spread out from the line-- that means there is a lot of
independent variance. The relationship between the two
variables is weaker. Sometimes the dots are close to the line--
the relationship is stronger. Sometimes the line looks like this-
- as one goes up, the other goes up. Sometimes the line is
like this-- as one goes up, the other goes down. College GPA
is negatively related to the amount of time spent partying.
We use correlation to understand the strength and the direction
of the relationship between the variables. The Correlation
Matrix: Bunches of Correlations
What happens if you have more than two variables and you want
to see correlations among all pairs of variables? How are the
correlations illustrated? Use a correlation matrix like the one
shown in Table 5.2—a simple and elegant solution.
As you can see in these made-up data, there are four variables
in the matrix: level of income (Income), level of education
(Education), attitude toward voting (Attitude), and how sure
they are that they will vote (Vote).
Table 5.2 ⬢ Correlation Matrix
Income
Education
Attitude
Vote
Income
1.00
.574
−.08
−.291
36. Education
.574
1.00
−.149
−.199
Attitude
−.08
−.149
1.00
−.169
Vote
−.291
−.199
−.169
1.00
For each pair of variables, there is a correlation coefficient. For
example, the correlation between income level and education is
.574. Similarly, the correlation between income level and how
sure people are that they will vote in the next election is −.291
(meaning that the higher the level of income, the less confident
people were that they would vote).
In such a matrix with four variables, there are really only six
correlation coefficients. Because variables correlate perfectly
with themselves (those are the 1.00s down the diagonal), and
because the correlation between Income and Vote is the same as
the correlation between Vote and Income, the matrix creates a
mirror image of itself.
You can use SPSS—or almost any other statistical analysis
package, such as Excel—to easily create a matrix like the one
you saw earlier. In applications like Excel, you can use the Data
Analysis ToolPak.
You will see such matrices (the plural of matrix) when you read
journal articles that use correlations to describe the
relationships among several variables.
Understanding What the Correlation Coefficient Means
Well, we have this numerical index of the relationship between
37. two variables, and we know that the higher the value of the
correlation (regardless of its sign), the stronger the relationship
is. But how can we interpret it and make it a more meaningful
indicator of a relationship?
Here are different ways to look at the interpretation of that
simple rxy.
Using-Your-Thumb (or Eyeball) Method
Perhaps the easiest (but not the most informative) way to
interpret the value of a correlation coefficient is by eyeballing it
and using the information in Table 5.3. This is based on
customary interpretations of the size of a correlation in the
behavioral sciences.
So, if the correlation between two variables is .3, you could
safely conclude that the relationship is a moderate one—not
strong but certainly not weak enough to say that the variables in
question don’t share anything in common.
Table 5.3 ⬢ Interpreting a Correlation Coefficient
Size of the Correlation
Coefficient General Interpretation
.5 to 1.0
Strong relationship
.4
Moderate to strong relationship
.3
Moderate relationship
.2
Weak to moderate relationship
0 to .1
Weak or no relationship
This eyeball method is perfectly acceptable for a quick
assessment of the strength of the relationship between variables,
such as when you briefly evaluate data presented visually. But
because this rule of thumb depends on a subjective judgment (of
what’s “strong” or “weak”), we would like a more precise
method. That’s what we’ll look at now.
Special Effects! Correlation Coefficient
38. Throughout the book, we will learn about various effect sizes
and how to interpret them. An effect size is an index of the
strength of the relationship among variables, and with most
statistical procedures we learn about, there will be an associated
effect size that should be reported and interpreted. The
correlation coefficient is a perfect example of an effect size as
it quite literally is a measure of the strength of a relationship.
Thanks to Table 5.3, we already know how to interpret it.
SQUARING THE CORRELATION COEFFICIENT: A
DETERMINED EFFORT
Here’s the much more precise way to interpret the correlation
coefficient: computing the coefficient of determination.
The coefficient of determination is the percentage of variance in
one variable that is accounted for by the variance in the other
variable. Quite a mouthful, huh?
Earlier in this chapter, we pointed out how variables that share
something in common tend to be correlated with one another. If
we correlated math and language arts grades for 100 fifth-grade
students, we would find the correlation to be moderately strong,
because many of the reasons why children do well (or poorly) in
math tend to be the same reasons why they do well (or poorly)
in language arts. The number of hours they study, how bright
they are, how interested their parents are in their schoolwork,
the number of books they have at home, and more are all related
to both math and language arts performance and account for
differences between children (and that’s where the variability
comes in).
The more these two variables share in common, the more they
will be related. These two variables share variability—or the
reason why children differ from one another. And on the whole,
the brighter child who studies more will do better.
To determine exactly how much of the variance in one variable
can be accounted for by the variance in another variable, the
coefficient of determination is computed by squaring the
correlation coefficient.
For example, if the correlation between GPA and number of
39. hours of study time is .70 (or r GPA.time = .70), then the
coefficient of determination, represented
by r2GPA.timerGPA.time2 , is .702, or .49. This means that
49% of the variance in GPA “can be explained by” or “is shared
by” the variance in studying time. And the stronger the
correlation, the more variance can be explained (which only
makes good sense). The more two variables share in common
(such as good study habits, knowledge of what’s expected in
class, and lack of fatigue), the more information about
performance on one score can be explained by the other score.
However, if 49% of the variance can be explained, this means
that 51% cannot—so even for a very strong correlation of .70,
many of the reasons why scores on these variables tend to be
different from one another go unexplained. This amount of
unexplained variance is called the coefficient of alienation (also
called the coefficient of nondetermination). Don’t worry. No
aliens here. This isn’t X-Files or Walking Dead stuff—it’s just
the amount of variance in Y not explained by X (and, of course,
vice versa since the relationship goes both ways).
How about a visual presentation of this sharing variance idea?
Okay. In Figure 5.5, you’ll find a correlation coefficient, the
corresponding coefficient of determination, and a diagram that
represents how much variance is shared between the two
variables. The larger the shaded area in each diagram (and the
more variance the two variables share), the more highly the
variables are correlated.
· The first diagram in Figure 5.5 shows two circles that do not
touch. They don’t touch because they do not share anything in
common. The correlation is zero.
· The second diagram shows two circles that overlap. With a
correlation of .5 (and r2xy=.25rxy2=.25 ), they share about 25%
of the variance between them.
· Finally, the third diagram shows two circles placed almost on
top of each other. With an almost perfect correlation of rxy =
.90 (r2xy=.81rxy2=.81 ), they share about 81% of the variance
between them.
40. Figure 5.5 ⬢ How variables share variance and the resulting
correlationAs More Ice Cream Is Eaten … the Crime Rate Goes
Up (or Association vs. Causality)
Now here’s the really important thing to be careful about when
computing, reading about, or interpreting correlation
coefficients.
Imagine this. In a small midwestern town, a phenomenon
occurred that defied any logic. The local police chief observed
that as ice cream consumption increased, crime rates tended to
increase as well. Quite simply, if you measured both, you would
find the relationship was direct, meaning that as people eat
more ice cream, the crime rate increases. And as you might
expect, as they eat less ice cream, the crime rate goes down.
The police chief was baffled until he recalled the Stats 1 class
he took in college and still fondly remembered. (He probably
also pulled out his copy of this book that he still owned. In fact,
it was likely one of three copies he had purchased to make sure
he always had one handy.)
He wondered how this could be turned into an aha! “Very
easily,” he thought. The two variables must share something or
have something in common with one another. Remember that it
must be something that relates to both level of ice cream
consumption and level of crime rate. Can you guess what that
is?
The outside temperature is what they both have in common.
When it gets warm outside, such as in the summertime, more
crimes are committed (it stays light longer, people leave the
windows open, bad guys and girls are out more, etc.). And
because it is warmer, people enjoy the ancient treat and art of
eating ice cream. Conversely, during the long and dark winter
months, less ice cream is consumed and fewer crimes are
committed as well.
Joe, though, recently elected as a city commissioner, learns
about these findings and has a great idea, or at least one that he
thinks his constituents will love. (Keep in mind, he skipped the
statistics offering in college.) Why not just limit the
41. consumption of ice cream in the summer months to reduce the
crime rate? Sounds good, right? Well, on closer inspection, it
really makes no sense at all.
That’s because of the simple principle that correlations express
the association that exists between two or more variables; they
have nothing to do with causality. In other words, just because
level of ice cream consumption and crime rate increase together
(and decrease together as well) does not mean that a change in
one results in a change in the other.
For example, if we took all the ice cream out of all the stores in
town and no more was available, do you think the crime rate
would decrease? Of course not, and it’s preposterous to think
so. But strangely enough, that’s often how associations are
interpreted—as being causal in nature—and complex issues in
the social and behavioral sciences are reduced to trivialities
because of this misunderstanding. Did long hair and hippiedom
have anything to do with the Vietnam conflict? Of course not.
Does the rise in the number of crimes committed have anything
to do with more efficient and safer cars? Of course not. But they
all happen at the same time, creating the illusion of being
associated.
People Who Loved Statistics
Katharine Coman (1857–1915) was such a kind and caring
researcher that a famous book of poetry and prose was written
about her after her death from cancer at the age of 57. Her love
for statistics was demonstrated in her belief that the study of
economics could solve social problems and urged her college,
Wellesley, to let her teach economics and statistics. She may
have been the first woman statistics professor. Coman was a
prominent social activist in her life and in her writings, and she
frequently cited industrial and economic statistics to support her
positions, especially as they related to the labor movement and
the role of African American workers. The artistic biography
written about Professor Coman was Yellow Clover (1922), a
tribute to her by her longtime companion (and coauthor of the
42. song “America the Beautiful”), Katherine Lee Bates.
Using SPSS to Compute a Correlation Coefficient
Let’s use SPSS to compute a correlation coefficient. The data
set we are using is an SPSS data file named Chapter 5 Data Set
1.
There are two variables in this data set:
Variable
Definition
Income
Annual income in dollars
Education
Level of education measured in years
To compute the Pearson correlation coefficient, follow these
steps:
1. Open the file named Chapter 5 Data Set 1.
2. Click Analyze → Correlate → Bivariate, and you will see the
Bivariate Correlations dialog box, as shown in Figure 5.6.
3. Double-click on the variable named Income to move it to the
Variables: box.
4. Double-click on the variable named Education to move it to
the Variables: box. You can also hold down the Ctrl key to
select more than one variable at a time and then use the “move”
arrow in the center of the dialog box to move them both.
5. Click OK.
Figure 5.6 ⬢ The Bivariate Correlations dialog box
Understanding the SPSS Output
The output in Figure 5.7 shows the correlation coefficient to be
equal to .574. Also shown are the sample size, 20, and a
measure of the statistical significance of the correlation
coefficient (we’ll cover the topic of statistical significance
in Chapter 9).
Figure 5.7 ⬢ SPSS output for the computation of the correlation
coefficient
43. The SPSS output shows that the two variables are related to one
another and that as level of income increases, so does level of
education. Similarly, as level of income decreases, so does level
of education. The fact that the correlation is significant means
that this relationship is not due to chance.
As for the meaningfulness of the relationship, the coefficient of
determination is .5742 or .329 or .33, meaning that 33% of the
variance in one variable is accounted for by the other.
According to our eyeball strategy, this is a relatively weak
relationship. Once again, remember that low levels of income
do not cause low levels of education, nor does not finishing
high school mean that someone is destined to a life of low
income. That’s causality, not association, and correlations speak
only to association.
Creating a Scatterplot (or Scattergram or Whatever)
You can draw a scatterplot by hand, but it’s good to know how
to have SPSS do it for you as well. Let’s take the same data that
we just used to produce the correlation matrix in Figure 5.7 and
use it to create a scatterplot. Be sure that the data set
named Chapter 5 Data Set 1 is on your screen.
1. Click Graphs → Chart Builder → Scatter/Dot, and you will
see the Chart Builder dialog box shown in Figure 5.8.
2. Double-click on the first Scatter/Dot example.
3. Highlight and drag the variable named Income to the y-axis.
4. Highlight and drag the variable named Education to the x-
axis.
5. Click OK, and you’ll have a very nice, simple, and easy-to-
understand scatterplot like the one you see in Figure 5.9.
Figure 5.8 ⬢ The Chart Builder dialog box
OTHER COOL CORRELATIONS
There are different ways in which variables can be assessed. For
example, nominal-level variables are categorical in nature;
44. examples are race (e.g., black or white) and political affiliation
(e.g., Independent or Republican). Or, if you are measuring
income and age, you are measuring interval-level variables,
because the underlying continuum on which they are based has
equally appearing intervals. As you continue your studies,
you’re likely to come across correlations between data that
occur at different levels of measurement. And to compute these
correlations, you need some specialized techniques. Table
5.4 summarizes what these different techniques are and how
they differ from one another.
Table 5.4 ⬢ Correlation Coefficient Shopping, Anyone?
Level of Measurement and Examples
Variable X
Variable Y
Type of Correlation
Correlation Being Computed
Nominal (voting preference, such as Republican or Democrat)
Nominal (biological sex, such as male or female)
Phi coefficient
The correlation between voting preference and sex
Nominal (social class, such as high, medium, or low)
Ordinal (rank in high school graduating class)
Rank biserial coefficient
The correlation between social class and rank in high school
Nominal (family configuration, such as two-parent or single-
parent)
Interval (grade point average)
Point biserial
The correlation between family configuration and grade point
average
Ordinal (height converted to rank)
Ordinal (weight converted to rank)
Spearman rank coefficient
The correlation between height and weight
Interval (number of problems solved)
Interval (age in years)
45. Pearson correlation coefficient
The correlation between number of problems solved and age in
years
PARTING WAYS: A BIT ABOUT PARTIAL CORRELATION
Okay, now you have the basics about simple correlation, but
there are many other correlational techniques that are
specialized tools to use when exploring relationships between
variables.
A common “extra” tool is called partial correlation, where the
relationship between two variables is explored, but the impact
of a third variable is removed from the relationship between the
two. Sometimes that third variable is called a mediating or
a confounding variable.
For example, let’s say that we are exploring the relationship
between level of depression and incidence of chronic disease
and we find that, on the whole, the relationship is positive. In
other words, the more chronic disease is evident, the higher the
likelihood that depression is present as well (and of course vice
versa). Now remember, the relationship might not be causal, one
variable might not “cause” the other, and the presence of one
does not mean that the other will be present as well. The
positive correlation is just an assessment of an association
between these two variables, the key idea being that they share
some variance in common.
And that’s exactly the point—it’s the other variables they share
in common that we want to control and, in some cases, remove
from the relationship so we can focus on the key relationship we
are interested in.
For example, how about level of family support? Nutritional
habits? Severity or length of illness? These and many more
variables can all explain the relationship between these two
variables, or they may at least account for some of the variance.
And think back a bit. That’s exactly the same argument we
made when focusing on the relationship between the
consumption of ice cream and the level of crime. Once outside
temperature (the mediating or confounding variable) is removed
46. from the equation … boom! The relationship between the
consumption of ice cream and the crime level plummets. Let’s
take a look.
Here are some data on the consumption of ice cream and the
crime rate for 10 cities.
Consumption of Ice Cream
Crime Rate
Consumption of ice cream
1.00
.743
Crime rate
1.00
So, the correlation between these two variables, consumption of
ice cream and crime rate, is .743. This is a pretty healthy
relationship, accounting for about 50% of the variance between
the two variables (.7432 = .55 or 55%).
Now, we’ll add a third variable, average outside temperature.
Here are the Pearson correlation coefficients for the set of three
variables.
Consumption of Ice Cream
Crime Rate
Average Outside Temperature
Consumption of ice cream
1.00
.743
.704
Crime rate
1.00
.655
Average outside temperature
47. 1.00
As you can see by these values, there’s a fairly strong
relationship between ice cream consumption and outside
temperature and between crime rate and outside temperature.
We’re interested in the question, “What’s the correlation
between ice cream consumption and crime rate with the effects
of outside temperature removed or partialed out?”
That’s what partial correlation does. It looks at the relationship
between two variables (in this case, consumption of ice cream
and crime rate) as it removes the influence of a third (in this
case, outside temperature).
A third variable that explains the relationship between two
variables can be a mediating variable or a confounding variable.
Those are different types of variables with different definitions,
though, and are easy to confuse. In our example with
correlations, a confounding variable is something like
temperature that affects both our variables of interest and
explains the correlation between them. A mediating variable is a
variable that comes between our two variables of interest and
explains the apparent relationship. For example, if A is
correlated with B and B is correlated with C, A and C would
seem to be related but only because they are both related to B.
B is a mediating variable. Perhaps A affects B and B affects C,
so A and C are correlated.
LIGHTBOARD LECTURE VIDEO
Partial Correlations
When we talk about correlations between two variables, we
almost always think about it by drawing these two overlapping
circles. And we have variable A variable B. And they
somehow are correlated. They overlap in some way. And they
share this information. Sometimes, though, there can be
another variable. Let's call it-- let's see, my computer brain
suggests C. That correlates with both of those. And when these
variables all correlate together, there's all these overlapping
areas. So A, B, and C all measure the same thing to some
degree. A and C all measure this same thing to some degree.
48. And B and C all measure this same thing to some degree.
Sometimes we want to know, though, what would the
relationship between A and B be if we controlled for C?
Would the correlation go up? Would it go down? And you
can even see visually, some of this correlation between A and
B is this part right here that is actually part of C as well. So
statistically, we call this correlation after controlling for
another a partial correlation. And I'm going to show you what
a partial correlation looks like. If we control for a variable, it
means we statistically remove it. It's as if it's not there. It's
as if everyone got And it creates now, between A and B, this
new relationship. And you can look-- literally, it is different.
It's a different type of correlation. It probably would go down,
mathematically. The other thing interesting-- when you
remove a relationship because of a partial correlation, is the
variables themselves are now a different shape because a little
bit of A used to be C. And a little bit of B used to be C. So
when you control for a third variable, you end up with a
different relationship and different variables. One way to
think about controlling for another variable is, instead of
thinking about variables, think about friends. We all have
different friends. Sometimes you're friends with someone
because you share some other friend. So imagine instead,
you've got three friends here-- 1, 2, and 3. You often see 1
and 2 together. But it's because they're with number 3.
They're with friend 3. What would happen if we remove 3, that
1 and 2 are never together unless 3's there? Let's remove all
the times where 3 is also there. Well, 1 and 2 spend a little bit
of time together. But they don't associate as closely. They're
not really close friends with each other. They just seem to be
friends because they both hang out with number 3. And
number 3 has the nice house and has all the fun parties. But if
it's just 1 and 2, they barely like each other.
Using SPSS to Compute Partial Correlations
Let’s use some data and SPSS to illustrate the computation of a
49. partial correlation. Here are the raw data.
City
Ice Cream Consumption
Crime Rate
Average Outside Temperature
1
3.4
62
88
2
5.4
98
89
3
6.7
76
65
4
2.3
45
44
5
5.3
94
89
6
4.4
88
62
7
5.1
90
91
8
2.1
68
50. 33
9
3.2
76
46
10
2.2
35
41
1. Enter the data we are using into SPSS.
2. Click Analyze → Correlate → Partial and you will see the
Partial Correlations dialog box, as shown in Figure 5.10.
3. Move Ice_Cream and Crime_Rate to the Variables: box by
dragging them or double-clicking on each one.
4. Move the variable named Outside_Temp to the Controlling
for: box.
5. Click OK and you will see the SPSS output as shown
in Figure 5.11.
Figure 5.10 ⬢ The Partial Correlations dialog box
Understanding the SPSS Output
As you can see in Figure 5.11, the correlation between ice
cream consumption (Ice_Cream) and crime rate (Crime_Rate)
with the influence or moderation of outside temperature
(Outside_Temp) removed is .525. This is less than the simple
Pearson correlation between ice cream consumption and crime
rate (which is .743), which does not consider the influence of
outside temperature. What seemed to explain 55% of the
variance (and was what we call “significant at the .05 level”),
with the removal of Outside_Temp as a moderating variable,
now explains .5252 = 0.28 = 28% of the variance (and the
relationship is no longer significant).
Figure 5.11 ⬢ The completed partial correlation analysis
Our conclusion? Outside temperature accounted for enough of
the shared variance between the consumption of ice cream and
51. the crime rate for us to conclude that the two-variable
relationship was significant. But, with the removal of the
moderating or confounding variable outside temperature, the
relationship was no longer significant. And we don’t need to
stop selling ice cream to try to reduce crime.
Real-World Stats
This is a fun one and consistent with the increasing interest in
using statistics in various sports in various ways, a discipline
informally named sabermetrics. The term was coined by Bill
James (and his approach is represented in the movie and
book Moneyball).
Stephen Hall and his colleagues examined the link between
teams’ payrolls and the competitiveness of those teams (for both
professional baseball and soccer), and he was one of the first to
look at this from an empirical perspective. In other words, until
these data were published, most people made decisions based on
anecdotal evidence rather than quantitative assessments. Hall
looked at data on team payrolls in American Major League
Baseball and English soccer between 1980 and 2000, and he
used a model that allows for the establishment of causality (and
not just association) by looking at the time sequence of events
to examine the link.
In baseball, payroll and performance both increased
significantly in the 1990s, but there was no evidence that
causality runs in the direction from payroll to performance. In
comparison, for English soccer, the researchers did show that
higher payrolls actually were at least one cause of better
performance. Pretty cool, isn’t it, how association can be
explored to make real-world decisions?
Want to know more? Go online or to the library and find …
Hall, S., Szymanski, S., & Zimbalist, A. S. (2002). Testing
causality between team performance and payroll: The cases of
Major League Baseball and English soccer. Journal of Sports
Economics, 3, 149–168.
Summary
The idea of showing how things are related to one another and
52. what they have in common is a very powerful one, and the
correlation coefficient is a very useful descriptive statistic (one
used in inference as well, as we will show you later). Keep in
mind that correlations express a relationship that is associative
but not necessarily causal, and you’ll be able to understand how
this statistic gives us valuable information about relationships
between variables and how variables change or remain the same
in concert with others. Now it’s time to change speeds just a bit
and wrap up Part II with a focus on reliability and validity. You
need to know about these ideas because you’ll be learning how
to determine what differences in outcomes, such as scores and
other variables, represent.
Time to Practice
1. Use these data to answer Questions 1a and 1b. These data are
saved as Chapter 5 Data Set 2.
a. Compute the Pearson product-moment correlation coefficient
by hand and show all your work.
b. Construct a scatterplot for these 10 pairs of values by hand.
Based on the scatterplot, would you predict the correlation to be
direct or indirect? Why?
Number Correct (out of a possible 20)
Attitude (out of a possible 100)
17
94
13
73
12
59
15
80
16
93
14
85
16
66
53. 16
79
18
77
19
91
2. Use these data to answer Questions 2a and 2b. These data are
saved as Chapter 5 Data Set 3.
Speed (to complete a 50-yard swim)
Strength (number of pounds bench-pressed)
21.6
135
23.4
213
26.5
243
25.5
167
20.8
120
19.5
134
20.9
209
18.7
176
29.8
156
28.7
177
a. Using either a calculator or a computer, compute the Pearson
correlation coefficient.
b. Interpret these data using the general range of very weak to
very strong. Also compute the coefficient of determination.
How does the subjective analysis compare with the value of r 2?
3. Rank the following correlation coefficients on strength of
54. their relationship (list the weakest first).
. .71
. +.36
. −.45
. .47
. −.62
· For the following set of scores, calculate the Pearson
correlation coefficient and interpret the outcome. These data are
saved as Chapter 5 Data Set 4.
Achievement Increase Over 12 Months
Classroom Budget Increase Over 12 Months
0.07
0.11
0.03
0.14
0.05
0.13
0.07
0.26
0.02
0.08
0.01
0.03
0.05
0.06
0.04
0.12
0.04
0.11
· For the following set of data, by hand, correlate minutes of
exercise with grade point average (GPA). What do you conclude
given your analysis? These data are saved as Chapter 5 Data Set
5.
Exercise
GPA
25
56. 14
3.66
11
3.91
18
3.80
9
3.89
Time to Practice Video
Chapter 5: Problem 6
Chapter 5, Problem 6 asks you to compute a correlation. They
want to assess how honor students GPAs are correlated with
their hours of studying, and then to answer the question of
why that correlation is so low. So you see listed here are
individual student's GPAs and the average number of hours
that they study. We want to set up our SPSS data file with this
information. When we look here, you'll see the two variables.
And under Variable View, make sure that they're both set up
with scale, since they're both measured on a continuous range.
A GPA can go from can go from When we look here to do,
this we're going to go under Analyze and then Correlate By
Variate. We have two variables, so this would be a by variate
correlation. This is straightforward here. We're going to take
both of them, move it to our variables. You notice down here
it's saying we have the Pearson, which is for by variate
continuous data. We're going to look for a two-tailed
significance. Is it, how are they related to each other? We are
asking it to flag our significant correlations. You always want
to look under Options, but it defaults to what we want. We
could say we want to show the means and standard deviations,
we don't need to do that for this one. So instead, let's hit OK.
And here is our information. When we look at our
significance, it's a We need it to be lower than a And so, the
question is, why is this correlation of a so low? Well, if we
look back at our data itself, it's going to give us an
understanding. Of these are really high GPAs. When there's
57. very little variability, you're typically not going to get a strong
correlation because there's not much change. Even though
there seems to be a range of how they studied, in terms of
hours, it didn't have a big effect on their GPA because they're
all really high. And this is how you answer Chapter 5, Problem
6.
1. The coefficient of determination between two variables is
.64. Answer the following questions:
a. What is the Pearson correlation coefficient?
b. How strong is the relationship?
c. How much of the variance in the relationship between these
two variables is unaccounted for?
2. Here is a set of three variables for each of 20 participants in
a study on recovery from a head injury. Create a simple matrix
that shows the correlations between each variable. You can do
this by hand (and plan on being here for a while) or use SPSS or
any other application. These data are saved as Chapter 5 Data
Set 6.
Age at Injury
Level of Treatment
12-Month Treatment Score
25
1
78
16
2
66
8
2
78
23
3
89
31
4
87
59. 53
2
69
11
3
79
33
2
69
3. Look at Table 5.4. What type of correlation coefficient would
you use to examine the relationship between biological sex
(defined in this study as having only two categories: male or
female) and political affiliation? How about family
configuration (two-parent or single-parent) and high school
GPA? Explain why you selected the answers you did.
4. When two variables are correlated (such as strength and
running speed), they are associated with one another. Explain
how, even if there is a correlation between the two, one might
not cause the other.
5. Provide three examples of an association between two
variables where a causal relationship makes perfect sense
conceptually.
6. Why can’t correlations be used as a tool to prove a causal
relationship between variables rather than just an association?
7. When would you use partial correlation?
Student Study Site
Get the tools you need to sharpen your study skills!
Visit edge.sagepub.com/salkindfrey7e to access practice
quizzes, eFlashcards, original and curated videos, data sets, and
more!6 AN INTRODUCTION TO UNDERSTANDING
RELIABILITY AND VALIDITY JUST THE TRUTH6: MEDIA
LIBRARY
Premium VideosLightboard Lecture Video
· Reliability
60. · ValidityTime to Practice Video
· Chapter 6: Problem 5
Difficulty Scale
(not so hard)WHAT YOU WILL LEARN IN THIS CHAPTER
· Defining reliability and validity and understanding why they
are important
· This is a stats class! What’s up with this measurement stuff?
· Understanding how the quality of tests is evaluated
· Computing and interpreting various types of reliability
coefficients
· Computing and interpreting various types of validity
coefficientsAN INTRODUCTION TO RELIABILITY AND
VALIDITY
Ask any parent, teacher, pediatrician, or almost anyone in your
neighborhood what the five top concerns are about today’s
children, and there is sure to be a group who identifies obesity
as one of those concerns. Sandy Slater and her colleagues
developed and tested the reliability and validity of a self-
reported questionnaire on home, school, and neighborhood
physical activity environments for youth located in low-income
urban minority neighborhoods and rural areas. In particular, the
researchers looked at such variables as information on the
presence of electronic and play equipment in youth participants’
bedrooms and homes and outdoor play equipment at schools.
They also looked at what people close to the children thought
about being active. A total of 205 parent–child pairs completed
a 160-item take-home survey on two different occasions, a
perfect model for establishing test–retest reliability. The
researchers found that the measure had good reliability and
validity. The researchers hoped that this survey could be used to
help identify opportunities and develop strategies to encourage
underserved youth to be more physically active.
Want to know more? Go online or to the library and find …
Slater, S., Full, K., Fitzgibbon, M., & Uskali, A. (2015, June 4).
Test–retest reliability and validity results of the Youth Physical
Activity Supports Questionnaire. SAGE Open, 5(2).
61. doi:10.1177/2158244015586809
What’s Up With This Measurement Stuff?
An excellent question and one that you should be asking. After
all, you enrolled in a stats class, and up to now, that’s been the
focus of the material that has been covered. Now it looks like
you’re faced with a topic that belongs in a tests and
measurements class. So, what’s this material doing in a stats
book?
Well, much of what we have covered so far in Statistics for
People Who (Think They) Hate Statistics has to do with the
collection and description of data. Now we are about to begin
the journey toward analyzing and interpreting data. But before
we begin learning those skills, we want to make sure that the
data are what you think they are—that the data represent what it
is you want to know about. In other words, if you’re studying
poverty, you want to make sure that the measure you use to
assess poverty works and that it works time after time. Or, if
you are studying aggression in middle-aged males, you want to
make sure that whatever tool you use to assess aggression works
and that it works time after time.
More really good news: Should you continue in your education
and want to take a class on tests and measurements, this
introductory chapter will give you a real jump on understanding
the scope of the area and what topics you’ll be studying.
And to make sure that the entire process of collecting data and
making sense out of them works, you first have to make sure
that what you use to collect data works as well. The
fundamental questions that are answered in this chapter are
“How do I know that the test, scale, instrument, and so on. I use
produces scores that aren’t random but actually represent an
individual’s typical performance?” (that’s reliability) and “How
do I know that the test, scale, instrument, and so on. I use
measures what it is supposed to?” (that’s validity).
Anyone who does research will tell you about the importance of
establishing the reliability and validity of your measurement
62. tool, whether it’s a simple observational instrument of consumer
behavior or one that measures a complex psychological
construct such as depression. However, there’s another very
good reason. If the tools that you use to collect data are
unreliable or invalid, then the results of any test or any
hypothesis, and the conclusions you may reach based on those
results, are necessarily inconclusive. If you are not sure that the
test does what it is supposed to and that it does so consistently
without randomness in its scores, how do you know that the
nonsignificant results you got aren’t a function of the lousy test
tools rather than an actual reflection of reality? Want a clean
test of your hypothesis? Make reliability and validity an
important part of your research.
You may have noticed a new term at the beginning of this
chapter—dependent variable. In an experiment, this is the
outcome variable, or what the researcher looks at to see whether
any change has occurred as a function of the treatment that has
taken place. And guess what? The treatment has a name as
well—the independent variable. For example, if a researcher
examined the effect of different reading programs on
comprehension, the independent variable would be the reading
program, and the dependent or outcome variable would be
reading comprehension score. The term dependent variable is
used for the outcome variable because the hypothesis suggests
that it depends on, or is affected by, the independent variable.
Although these terms will not be used often throughout the
remainder of this book, you should have some familiarity with
them.RELIABILITY: DOING IT AGAIN UNTIL YOU GET IT
RIGHT
Reliability is pretty easy to understand and figure out. It’s
simply whether a test, or whatever you use as a measurement
tool, measures something consistently. If you administer a test
of personality type before a special treatment occurs, will the
administration of that same test 4 months later be reliable?
That, my friend, is one type of reliability—the degree to which
scores are consistent for one person measured twice. There are
63. other types of reliability, each of which we will get to after we
define reliability just a bit more.
Test Scores: Truth or Dare?
When you take a test in this class, you get a score, such as 89
(good for you) or 65 (back to the books!). That test score
consists of several elements, including the observed score (or
what you actually get on the test, such as 89 or 65) and a true
score (the typical score you would get if you took the same test
an infinite number of times). We can’t directly measure true
score (because we don’t have the time or energy to give
someone the same test an infinite number of times), but we can
estimate it.
Why aren’t true scores and observed scores the same? Well,
they can be if the test (and the accompanying observed score) is
a perfect (and we mean absolutely perfect) reflection of what’s
being measured.
But the bread sometimes falls on the buttered side, and
Murphy’s law tells us that the world is not perfect. So, what you
see as an observed score may come close to the true score, but
rarely are they the same. Rather, the difference as you see is the
amount of error that is introduced.
Notice that reliability is not the same as validity; it does not
reflect whether you are measuring what you want to. Here’s
why. True score has nothing to do with whether the construct of
interest is really being reflected. Rather, true score is
the mean score an individual would get if he or she took a test
an infinite number of times, and it represents the theoretical
typical level of performance on a given test. Now, one would
hope that the typical level of performance would reflect the
construct of interest, but that’s another question (a question of
validity). The distinction here is that a test is reliable if it
consistently produces whatever score a person would get on
average, regardless of what the test is measuring. In fact, a
perfectly reliable test might not produce a score that has
anything to do with the construct of interest, such as “what you
64. really know.”LIGHTBOARD LECTURE VIDEOReliability
So one of the qualities of a good test is that it's reliable. And
a lot of times when you learn stuff, you hear about validity
and reliability. And you think it's all the same thing. Well,
validity is whether the score matches the thing that supposed
to be measured. We're not talking about that. Reliability is
different. Reliability refers to whether the score you just got
on a test is the typical score you would have gotten on that
test, not whether it matches the level of the trait you're trying
to measure. That's validity. But if you took the test again
tomorrow, would you get the same score if you took it
yesterday? If you'd had a better breakfast, would your score
be any different? That's what reliability is all about. And we
can think about reliability as the purpose of a test is for you
to get the score that represents your typical level of
performance. If you took a test an infinite number of times
and you averaged all those scores-- you alone-- that average is
the typical level of performance you would get. So every
time someone takes a test, when you take a test, you get some
score on it. And if this middle bullseye is your typical level
of performance, the test score you would get if you took the
test infinite number of times and averaged it, that's the score
you typically get. And if you get that score, then it's a reliable
test. And if that's true for everybody, it's a reliable test. But
there's some randomness. There's always randomness. That's
the problem with social sciences. There's all this randomness
in human behavior. And so the score you get won't be your
exact typical level of performance. It will not be right here
on the bullseye. It might be out here somewhere. It might be
further out here. I mean, the further away it is from your
average performance, the less reliable that test is. So good
tests need to produce scores that aren't random. They need to
give you the typical score you would get on that test.
Observed Score = True Score + Error Score
Error? Yes—in all its glory. For example, let’s suppose for a
65. moment that someone gets an 89 on a stats test, but his or her
true score (which we never really know but only theorize about)
is 80. That means the 9-point difference (that’s the error score)
is due to error, or the reason why individual test scores vary
from being 100% true.
What might be the source of such error? Well, perhaps the room
in which the test was taken was so warm that it caused some
students to fall asleep. That would certainly have an impact on a
test score. Or perhaps the item formats on the test are worded in
a way that people inconsistently interpret them in a random
way. Ditto. Both of these examples would reflect characteristics
of the instrument or conditions of the testing situation rather
than qualities of the trait being measured, right?
Our job is to reduce those errors as much as possible by having,
for example, good test-taking conditions and choosing item
formats that support consistent responses. Reduce this sort of
error and you increase the reliability, because the observed
score more closely matches the true score.
The less random error, the more reliable—it’s that
simple.DIFFERENT TYPES OF RELIABILITY
There are several types of reliability, and we’ll cover the four
most important and most often used in this section. All of these
types of reliability look at how much randomness there is in the
scores by seeing if a test correlates with itself. They are all
summarized in Table 6.1.
Test–Retest Reliability
Test–retest reliability is used when you want to examine
whether a test is reliable over time.
For example, let’s say that you are developing a test that will
examine preferences for different types of vocational programs.
You may administer the test in September and then readminister
the same test (and it’s important for it to be the same test) again
in June. Then, the two sets of scores (remember, the same
people took it twice) are correlated (just like we did in Chapter
5), and you have a measure of reliability. Test–retest reliability
66. is a must when you are examining differences or changes over
time, because you want those changes to be real and not
random.
Table 6.1 ⬢ Different Types of Reliability, When They Are
Used, How They Are Computed, and What They Mean
Type of Reliability
When You Use It
How You Do It
An Example of What You Can Say When You’re Done
Test–retest reliability
When you want to know whether a test is reliable over time
Correlate the scores from a test given at Time 1 with the same
test given at Time 2.
The Bonzo test of identity formation for adolescents is reliable
over time.
Parallel forms reliability
When you want to know if different forms of a test are reliable
or equivalent
Correlate the scores from one form of the test with the scores
from a second form of the same test of the same content (but not
the exact same test).
The two forms of the Regular Guy test are equivalent to one
another and have shown parallel forms reliability.
Internal consistency reliability
When you want to know if there is consistency in scores across
the items within a test
Correlate the items on the test with each other. The most
common way to do this is with a summary index
called coefficient alpha.
All of the items on the SMART Test of Creativity are related to
each other.
Interrater reliability
When you want to know whether there is consistency among
different people who score the same test
Examine the percentage of times that two different raters agree.
The interrater reliability for the Best-Dressed Football Player