Unit 1 lesson 4
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This document discusses different measures of spreadoutness in statistics, including range, standard deviation, z-scores, and standard error of the mean. It explains that range is the simplest measure but has limitations, while standard deviation measures how far scores are from the mean in the data's own units. Z-scores indicate an individual score's distance from the mean in units of standard deviations and allow comparison across data sets with different means and standard deviations. The standard error of the mean represents sampling error and is used to construct confidence intervals.
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This document discusses various statistical measures used to summarize and describe data, including measures of central tendency (mean, median, mode) and measures of dispersion (range, variance, standard deviation). It provides definitions and examples of calculating each measure. Standardized scores like z-scores and t-scores are also introduced as ways to compare performance across different tests or distributions. Exercises are included for readers to practice calculating and interpreting these common descriptive statistics.
analytical representation of data
This document discusses analytical representation of data through descriptive statistics. It begins by showing raw, unorganized data on movie genre ratings. It then demonstrates organizing this data into a frequency distribution table and bar graph to better analyze and describe the data. It also calculates averages for each movie genre. The document then discusses additional descriptive statistics measures like the mean, median, mode, and percentiles to further analyze data through measures of central tendency and dispersion.
O Z Scores 68 O The Normal Curve 73 O Sample and Popul.docx
O Z Scores 68
O The Normal Curve 73
O Sample and Population 83
O Probability 88
O Controversies: Is the Normal Curve
Really So Normal? and Using
Nonrandom Samples 93
• Z Scores, Normal Curves, Samples
and Populations, and Probabilities
in Research Articles 95
O Advanced Topic: Probability Rules
and Conditional Probabilities 96
O Summary 97
• Key Terms 98
O Example Worked-Out Problems 99
O Practice Problems 102
O Using SPSS 105
O Chapter Notes 106
CHAPTER 3
Some Key Ingredients
for Inferential Statistics
Z Scores, the Normal Curve, Sample
versus Population, and Probability
Chapter Outline
IMETII'M'Ir919W1191.7P9MTIPlw
0 rdinarily, psychologists conduct research to test a theoretical principle or the effectiveness of a practical procedure. For example, a psychophysiologist might measure changes in heart rate from before to after solving a difficult problem.
The measurements are then used to test a theory predicting that heart rate should change
following successful problem solving. An applied social psychologist might examine
Before beginning this chapter, be
sure you have mastered the mater-
ial in Chapter 1 on the shapes of
distributions and the material in
Chapter 2 on the mean and stan-
dard deviation.
67
68 Chapter 3
Z score number of standard deviations
that a score is above (or below, if it is
negative) the mean of its distribution; it
is thus an ordinary score transformed so
that it better describes the score's location
in a distribution.
the effectiveness of a program of neighborhood meetings intended to promote water
conservation. Such studies are carried out with a particular group of research partici-
pants. But researchers use inferential statistics to make more general conclusions about
the theoretical principle or procedure being studied. These conclusions go beyond the
particular group of research participants studied.
This chapter and Chapters 4, 5, and 6 introduce inferential statistics. In this
chapter, we consider four topics: Z scores, the normal curve, sample versus popula-
tion, and probability. This chapter prepares the way for the next ones, which are
more demanding conceptually.
Z Scores
In Chapter 2, you learned how to describe a group of scores in terms and the mean
and variation around the mean. In this section you learn how to describe a particular
score in terms of where it fits into the overall group of scores. That is, you learn how
to use the mean and standard deviation to create a Z score; a Z score describes a score
in terms of how much it is above or below the average.
Suppose you are told that a student, Jerome, is asked the question, "To what extent
are you a morning person?" Jerome responds with a 5 on a 7-point scale, where 1 =
not at all and 7 = extremely. Now suppose that we do not know anything about how
other students answer this question. In this situation, it is hard to tell whether Jerome is
more or less of a m.
Measures of central tendency and dispersion
This document discusses various measures of central tendency and dispersion. It defines the mean, median, and mode as measures of central tendency, and describes how to calculate the arithmetic mean, geometric mean, harmonic mean, median, and mode. It also discusses measures of dispersion such as variance and standard deviation, and classifies them as either measures of absolute dispersion or relative dispersion.
Ch 6 DISPERSION.doc
Measures of dispersion describe how spread out or varied the values in a data set are. There are absolute measures like range and interquartile range, and relative measures like coefficient of variation. Range is the difference between the highest and lowest values, while interquartile range describes the middle 50% of values. Mean deviation, variance, and standard deviation are also measures of dispersion that take into account how far values are from the mean or average. Standard error describes the precision of the sample mean as an estimate of the population mean. These measures help determine how representative the central value or mean is of the overall data set.
Guidance and counselling.pptx
The document discusses guidance and counselling in education. It defines guidance as assisting students to manage their lives, make decisions, and solve problems. Counselling helps students learn about themselves and their situations. The purposes of guidance and counselling are to help students develop personally and socially, adjust to challenges, and utilize their abilities. It aims to develop good citizenship and attitudes. Guidance is a continuous process of helping students reach their potential in a way that benefits themselves and society. The median and mean are described as measures to summarize grouped or ungrouped student data.
Practical Language Testing by Fulcher (2010)
This document discusses key concepts in language testing and standardized tests. It covers two testing paradigms: norm-referenced testing which compares test takers to a group, and criterion-referenced testing which evaluates if a criterion is met. The document also defines standardized tests, explores why testing is viewed as a science, and examines concepts like central tendency, dispersion, reliability, and ways to calculate reliability such as using correlations and item analysis.
Worst Practices in Statistical Data Analysis
Scientific integrity, scientific fraud, questionable research practices, Smeesters affair, Geraerts affair, Förster affair: lecture at Willem Heiser farewell symposium.
Identify each of the following as examples of nominal, ordinal, inte.docx
Identify each of the following as examples of nominal, ordinal, interval, or ratio scales of measurement. (4 points each)
A poll of registered voters in Florida asking which candidate they support
The length of time required for a wound to heal when using a new medicine
The number of telephone calls arriving at a switchboard per five-minute period
The distance first-year college football players can kick a ball
Mental health diagnoses present in an elderly population
The rankings of employees on their job performance
(Points : 24)
Question 2.
2.
Two hundred raffle tickets are sold. Your friend has five people in her family who each bought two raffle tickets. What is the probability that someone from her family will win the raffle?
(Points : 4)
Question 3.
3.
Jolie has 45 minutes to do her statistics homework. If the mean is 38 minutes and the standard deviation is 3, calculate Jolie's z score. Once calculated, interpret your findings in terms of Jolie's performance.
(
HINT:
use the normal distribution and the probability that other students performed better or worse.) (Points : 8)
Question 4.
4.
A psychologist measures units of change for a memory test after students are given an opportunity to sleep only four hours. The following change units were obtained: 7, -12, 4, -7, 3, -10. Find the a) mean, b) median, c) mode, d) standard deviation, e) range, and f) variance. (Points : 24)
Question 5.
5.
A student scored 81 on a chemistry test and 75 on a history test. For the chemistry test, the mean was 70 and the standard deviation was 20. For the history test, the mean was 65 and the standard deviation was 8. Did the student do better on the chemistry test or the history test? Explain your answer. (Points : 12)
Question 6.
6.
Suppose you want to figure out what to do with your degree in psychology. You ask some fellow students from your psychology program who recently graduated to find out what they are doing with their degree and how much it pays. What type of sampling is this? What are the limitations of this sampling approach? (Points : 8)
Question 7.
7.
Variables in which the values are categories are known as (Points : 4)
Interval variables
Nominal variables
Ordinal variables
Ratio variables
Question 8.
8.
Before the researcher can conduct a statistical test, the research question must be translated into (Points : 4)
A testable hypothesis
Additional observations
Mathematical symbols
Numbers
Question 9.
9.
The hypothesis stating that there are no differences, effects, or relationships is (Points : 4)
The alternative hypothesis
The baseline hypothesis
The null hypothesis
The reasonable hypothesis
Question 10.
10.
A group of students made the following scores on a 10-item quiz in psychological statistics: {5, 6, 7, 7, 7, 8, 8, 9, 9, 10, 10} What is the mean score? (Points : 4)
6.6.
STATISTICS AND PROBABILITY.pptx
The document discusses various measures of central tendency including the mean, median, and mode. It provides definitions and formulas for calculating each measure. The mean is the average and is calculated by adding all values and dividing by the total number of values. The median is the middle value when values are arranged from lowest to highest. The mode is the value that occurs most frequently in the data set. Examples are provided to demonstrate calculating each measure using both raw and grouped data.
Data and Data Collection in Data Science.ppt
What is Data and methods of Data Collection in Data Science and Technology.
Course Module 9: (Some) Statistics For Managers Who Hate Statistics
Course Module 9: (Some) Statistics For Managers Who Hate StatisticsCenter for Evidence-Based Management
This document provides an overview of key statistical concepts for evidence-based management including:
1) It defines population and sample, and explains how sample size impacts accuracy and preventing type 2 errors.
2) It outlines different variable types and levels of measurement for categorical and continuous data.
3) It describes common statistical models like mean, standard deviation, and confidence intervals; and statistical concepts like hypothesis testing, statistical significance, power, and effect sizes for critically evaluating research.Effects of self talk
This is a presentation reporting the results of a study conducted at The University of New Orleans on the Effects of Self-Talk on the Level of Success in College Students.
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Course Module 9: (Some) Statistics For Managers Who Hate Statistics
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Unit 1 lesson 4
- 1. Unit 1: Background to Inferential Statistics Lesson 4: Measures of Spreadoutness EDER 6010: Statistics for Educational Research Dr. J. Kyle Roberts University of North Texas Next Slide
- 3. Range “ The simplest measure of spreadoutness” The number of units on the scale of measurement that include the highest and lowest values Range = (X Highest – X Lowest ) + 1 X = 1,2,3,4,5 Range = (5 – 1) +1 = 5 X = -1,-2,-3,-4,-5 Range = ((-1) – (-5)) +1 = 4 + 1 = 5 Next Slide
- 4. Problems with Range It only considers two scores: Study 2: X = 1, 2, 3, 4, 5 Range = 5 Study 3: X = 1,1,1,1,1,5,5,5,5,5 Range = 5 Study 4: X = 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,5 Range = 5 Study 1: X = 1, 5 Range = 5 Next Slide
- 5. Standard Deviation “ A measure of spreadoutness in the data’s own metric” Next Slide where: is each person’s individual score is the mean of all scores n is the number of people in the study
- 6. Computing the SD X = 1, 2, 3, 4 SD = 1.29 Next Slide
- 7. “ Average Distance From the Mean” SD = 1.29 SD = 1.29 SD = 1.73 Next Slide 1 2 3 4 8 9 10 11 1 2 3 4
- 9. Z-Scores A measure of spreadoutness for individuals. 2 Studies Study 1 Study 2 Johnny scored 5 points above the mean Susan scored 9 points above the mean Who did better in relationship to their fellow classmates? Next Slide
- 10. Computing Z-Scores How far that person is from the mean Relative to the standard deviation Next Slide
- 11. The 2 Studies Mean = 10 SD = 2 Mean = 10 SD = 9 Z Johnny = +2.5 Z Susan = +1.0 Next Slide Study 1 Study 2 Johnny scored 5 points above the mean Susan scored 9 points above the mean Who did better in relationship to their fellow classmates?
- 12. Relative Rules for Z-Scores 1. Typically ranges from -3.0 to +3.0 2. All Z-scores have a mean of 0 and a SD of 1 Next Slide X 2 3 3 4 5 5 6 Z -1.42 -.71 -.71 .00 .71 .71 1.42
- 13. Standard Error of the Mean “The Standard Deviation of the Sampling Distribution” Standard Deviation of X Number of people in the study Used in the construction of “Confidence Intervals” Next Slide
- 14. Unit 1: Background to Inferential Statistics Lesson 4: Measures of Spreadoutness EDER 6010: Statistics for Educational Research Dr. J. Kyle Roberts University of North Texas