This document discusses various methods for analyzing quantitative data, including coding data, creating a codebook, entering data into a grid format for analysis, checking data for accuracy, and using computers and statistical software to analyze data. It covers descriptive statistics for one and two variables, such as frequency distributions, measures of central tendency and variation, scatterplots, cross-tabulations, and measures of association between two variables.
1. Descriptive statistics provide a simple summary of data through measures of central tendency, frequency, and variability.
2. Common measures include the mean, median, mode, standard deviation, and outliers.
3. Inferential statistics allow researchers to make generalizations about populations based on analyses of samples. They include t-tests, ANOVA, correlation, and regression.
This document discusses quantitative data analysis methods. It begins by explaining that collected data must be analyzed using appropriate statistical methods to meet information needs based on the objectives for data collection. Various types of variables, scales of measurement, and descriptive and inferential statistics are defined. Specific statistical tests that can be used to compare groups or determine relationships among variables are also outlined, including parametric tests that assume normal distributions and nonparametric alternatives.
Here are the modes for the three examples:
1. The mode is 3. This value occurs most frequently among the number of errors committed by the typists.
2. The mode is 82. This value occurs most frequently among the number of fruits yielded by the mango trees.
3. The mode is 12 and 15. These values occur most frequently among the students' quiz scores.
This document provides an overview of statistics and statistical tests. It defines descriptive statistics as concerned with data collection, presentation and interpretation, while inferential statistics involves drawing conclusions from statistical analysis. Parametric tests can be applied to normally distributed interval/ratio data, while non-parametric tests do not require normality assumptions. Examples of parametric and non-parametric tests are provided, along with guidelines for applying a two-sample t-test to compare means between two independent groups. Two examples of applying a t-test are given to test differences between groups.
How to choose the right statistics techniques in different situation. This short presentation provide a compact summary on various method of statistics either descriptive and inferential.
for further inquiry please reach me at bodhiyawijaya@gmail.com
This document outlines topics related to statistics that will be covered. It is divided into 6 parts. Part 1 discusses the role of statistics in research, descriptive statistics, sampling procedures, sample size, and inferential statistics. Part 2 covers choice of statistical tests, defining variables, scales of measurements, and number of samples. Parts 3 and 4 discuss parametric and non-parametric tests. Part 5 is about goodness of fit tests. Part 6 covers choosing correct statistical tests and introduction to multiple regression. The document also provides examples and definitions of key statistical concepts like mean, median, mode, range, and different sampling methods.
1. Descriptive statistics provide a simple summary of data through measures of central tendency, frequency, and variability.
2. Common measures include the mean, median, mode, standard deviation, and outliers.
3. Inferential statistics allow researchers to make generalizations about populations based on analyses of samples. They include t-tests, ANOVA, correlation, and regression.
This document discusses quantitative data analysis methods. It begins by explaining that collected data must be analyzed using appropriate statistical methods to meet information needs based on the objectives for data collection. Various types of variables, scales of measurement, and descriptive and inferential statistics are defined. Specific statistical tests that can be used to compare groups or determine relationships among variables are also outlined, including parametric tests that assume normal distributions and nonparametric alternatives.
Here are the modes for the three examples:
1. The mode is 3. This value occurs most frequently among the number of errors committed by the typists.
2. The mode is 82. This value occurs most frequently among the number of fruits yielded by the mango trees.
3. The mode is 12 and 15. These values occur most frequently among the students' quiz scores.
This document provides an overview of statistics and statistical tests. It defines descriptive statistics as concerned with data collection, presentation and interpretation, while inferential statistics involves drawing conclusions from statistical analysis. Parametric tests can be applied to normally distributed interval/ratio data, while non-parametric tests do not require normality assumptions. Examples of parametric and non-parametric tests are provided, along with guidelines for applying a two-sample t-test to compare means between two independent groups. Two examples of applying a t-test are given to test differences between groups.
How to choose the right statistics techniques in different situation. This short presentation provide a compact summary on various method of statistics either descriptive and inferential.
for further inquiry please reach me at bodhiyawijaya@gmail.com
This document outlines topics related to statistics that will be covered. It is divided into 6 parts. Part 1 discusses the role of statistics in research, descriptive statistics, sampling procedures, sample size, and inferential statistics. Part 2 covers choice of statistical tests, defining variables, scales of measurements, and number of samples. Parts 3 and 4 discuss parametric and non-parametric tests. Part 5 is about goodness of fit tests. Part 6 covers choosing correct statistical tests and introduction to multiple regression. The document also provides examples and definitions of key statistical concepts like mean, median, mode, range, and different sampling methods.
Descriptive statistics are used to summarize and describe characteristics of a data set. It includes measures of central tendency like mean, median, and mode, measures of variability like range and standard deviation, and the distribution of data through histograms. Inferential statistics are used to generalize results from a sample to the population it represents through estimation of population parameters and hypothesis testing. Correlation and regression analysis are used to study relationships between two or more variables.
This document provides an overview of descriptive statistics and related concepts. It begins with an introduction to descriptive analysis and then covers various types of variables and levels of measurement. It describes measures of central tendency including mean, median and mode. Measures of dispersion like range, standard deviation and normal distribution are also discussed. The document also covers measures of asymmetry, relationship and concludes with emphasizing the importance of statistical planning in research.
This document discusses descriptive and inferential statistics. Descriptive statistics are used to analyze and represent previously collected data through measures like frequency, range, mean, mode, and standard deviation. Variables can be nominal, ordinal, or interval. Inferential statistics are used to draw conclusions and make predictions based on descriptive statistics. Key concepts in inferential statistics include experiments, probability, population, sampling, and hypothesis testing.
Basics of Educational Statistics (Descriptive statistics)HennaAnsari
The document discusses various statistical concepts related to descriptive data analysis including measures of central tendency, dispersion, and distribution. It defines key terms like mean, median, mode, range, variance, standard deviation, normal curve, skewness, and kurtosis. Examples are provided to demonstrate calculating and applying these concepts. The learning objectives are to understand the purpose of central tendency measures, how to calculate measures like range and quartiles, and explain concepts such as the normal curve, skewness, and kurtosis.
The document provides an overview of quantitative data analysis and various statistical concepts including the normal distribution, z-tests, confidence intervals, and t-tests. It discusses how the normal distribution was developed by de Moivre and Gauss. It then explains the key properties of the normal distribution and how it can be used to describe many natural phenomena. Examples are provided to illustrate how to calculate and interpret confidence intervals and choose the appropriate statistical test.
UNIVARIATE & BIVARIATE ANALYSIS
UNIVARIATE BIVARIATE & MULTIVARIATE
UNIVARIATE ANALYSIS
-One variable analysed at a time
BIVARIATE ANALYSIS
-Two variable analysed at a time
MULTIVARIATE ANALYSIS
-More than two variables analysed at a time
TYPES OF ANALYSIS
DESCRIPTIVE ANALYSIS
INFERENTIAL ANALYSIS
DESCRIPTIVE ANALYSIS
Transformation of raw data
Facilitate easy understanding and interpretation
Deals with summary measures relating to sample data
Eg-what is the average age of the sample?
INFERENTIAL ANALYSIS
Carried out after descriptive analysis
Inferences drawn on population parameters based on sample results
Generalizes results to the population based on sample results
Eg-is the average age of population different from 35?
DESCRIPTIVE ANALYSIS OF UNIVARIATE DATA
1. Prepare frequency distribution of each variable
Missing Data
Situation where certain questions are left unanswered
Analysis of multiple responses
Measures of central tendency
3 measures of central tendency
1.Mean
2.Median
3.Mode
MEAN
Arithmetic average of a variable
Appropriate for interval and ratio scale data
x
MEDIAN
Calculates the middle value of the data
Computed for ratio, interval or ordinal scale.
Data needs to be arranged in ascending or descending order
MODE
Point of maximum frequency
Should not be computed for ordinal or interval data unless grouped.
Widely used in business
MEASURE OF DISPERSION
Measures of central tendency do not explain distribution of variables
4 measures of dispersion
1.Range
2.Variance and standard deviation
3.Coefficient of variation
4.Relative and absolute frequencies
DESCRIPTIVE ANALYSIS OF BIVARIATE DATA
There are three types of measure used.
1.Cross tabulation
2.Spearmans rank correlation coefficient
3.Pearsons linear correlation coefficient
Cross Tabulation
Responses of two questions are combined
Spearman’s rank order correlation coefficient.
Used in case of ordinal data
Basics of Educational Statistics (Inferential statistics)HennaAnsari
This document provides information about inferential statistics presented by Dr. Hina Jalal. It defines inferential statistics as using data from a sample to make inferences about the larger population from which the sample was taken. It discusses key areas of inferential statistics like estimating population parameters and testing hypotheses. It also explains the importance of inferential statistics in research for making conclusions from samples, comparing models, and enabling inferences about populations based on sample data. Flow charts are presented for selecting common statistical tests for comparisons, correlations, and regression.
This document provides an overview of various statistical analysis techniques used in inferential statistics, including t-tests, ANOVA, ANCOVA, chi-square, regression analysis, and interpreting null hypotheses. It defines key terms like alpha levels, effect sizes, and interpreting graphs. The overall purpose is to explain common statistical methods for analyzing data and determining the probability that results occurred by chance or were statistically significant.
Here are the steps to find the quartiles for this data set:
1. Order the data from lowest to highest: 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 5, 5, 6, 7
2. The number of observations is 16. To find the quartiles, we split the data into 4 equal parts.
3. n/4 = 16/4 = 4
4. Q1 is the median of the lower half of the data, which is the 4th observation: 2
5. Q2 is the median of all the data, which is also the 8th observation: 3
6. Q3 is the median of the upper half
The document discusses various measures used to describe the dispersion or variability in a data set. It defines dispersion as the extent to which values in a distribution differ from the average. Several measures of dispersion are described, including range, interquartile range, mean deviation, and standard deviation. The document also discusses measures of relative standing like percentiles and quartiles, and how they can locate the position of observations within a data set. The learning objectives are to understand how to describe variability, compare distributions, describe relative standing, and understand the shape of distributions using these measures.
Descriptive statistics are used to summarize and describe characteristics of a data set. They include measures of central tendency like the mean, median, and mode as well as measures of variability such as range, standard deviation, and variance. Descriptive statistics help analyze and understand patterns in data through tables, charts, and summaries without drawing inferences about the underlying population.
This document discusses quantitative data analysis and statistical measures. It describes levels of quantitative description, types of data analysis including descriptive and inferential analysis, and statistical measures used in descriptive analysis such as measures of central tendency, spread, relative position, and relationship. Specific statistical measures are defined, like mean, median, mode, range, variance, standard deviation, percentile scores, correlation coefficients, and when they are appropriate to use. Computational data analysis tools like IBM SPSS Statistics are also mentioned.
Tools and Techniques - Statistics: descriptive statistics Ramachandra Barik
Tools and Techniques - Statistics: descriptive statistics - See more at: http://www.pcronline.com/eurointervention/67th_issue/volume-9/number-8/167/tools-and-techniques-statistics-descriptive-statistics.html#sthash.rtzcQ3ah.dpuf
This document discusses descriptive statistics and numerical measures used to describe data sets. It introduces measures of central tendency including the mean, median, and mode. The mean is the average value calculated by summing all values and dividing by the number of values. The median is the middle value when values are arranged in order. The mode is the most frequently occurring value. The document also discusses measures of dispersion like range and standard deviation which describe how spread out the data is. Examples are provided to demonstrate calculating the mean, median and other descriptive statistics.
This document discusses different measures of central tendency including the mean, median, and mode. It provides definitions and examples of how to calculate each measure. The mean is the average and is calculated by adding all values and dividing by the total number. The median is the middle value when values are arranged from lowest to highest. The mode is the most frequent value. The appropriate measure depends on the type of data and distribution. The mean is generally preferred but the median is better for skewed or open-ended distributions.
This document discusses various measures of central tendency including:
- Arithmetic mean, which is the most widely used measure. It is defined as the sum of all values divided by the number of values.
- Geometric mean, which gives more weight to smaller values. It is used to average rates of change.
- Median, which is the middle value when data is arranged from lowest to highest. Half of the data will be above and below the median.
- Mode, which is the most frequently occurring value in the data set. It indicates the most typical or probable value.
The document also discusses choosing an appropriate measure based on the data characteristics and purpose of the analysis. Quartiles, deciles, and
This document provides an overview of basic statistical concepts for bio science students. It defines measures of central tendency including mean, median, and mode. It also discusses measures of dispersion like range and standard deviation. Common probability distributions such as binomial, Poisson, and normal distributions are explained. Hypothesis testing concepts like p-values and types of statistical tests for different types of data like t-tests for continuous variables and chi-square tests for categorical data are summarized along with examples.
- The document discusses implementing task-based language teaching through a 12-week project where students work in groups to conduct surveys, analyze the data, and present their findings. It involves choosing topics, designing questionnaires, collecting data through interviews, analyzing trends, and making presentations. The project aims to provide authentic language practice and intrinsically motivating activities. It allows students to take responsibility for their own language learning.
Descriptive statistics summarize and describe data through measures like central tendency (mean, median, mode) and variability (range, standard deviation). There are different scales of measurement for variables, including nominal (categories without order), ordinal (ranked order), interval (equal intervals between ranks), and ratio (absolute zero point). Graphs like histograms, bar graphs, and scatterplots can visually portray relationships in the data.
This document is a paper submitted by Solanki Pratiksha M. about language learning strategies as discussed in the book by Rebecca L. Oxford. It discusses six main categories of language learning strategies: cognitive strategies, mnemonic strategies, metacognitive strategies, compensatory strategies, affective strategies, and social strategies. It also addresses influences on strategy choice and current and future trends in strategies research.
Descriptive statistics are used to summarize and describe characteristics of a data set. It includes measures of central tendency like mean, median, and mode, measures of variability like range and standard deviation, and the distribution of data through histograms. Inferential statistics are used to generalize results from a sample to the population it represents through estimation of population parameters and hypothesis testing. Correlation and regression analysis are used to study relationships between two or more variables.
This document provides an overview of descriptive statistics and related concepts. It begins with an introduction to descriptive analysis and then covers various types of variables and levels of measurement. It describes measures of central tendency including mean, median and mode. Measures of dispersion like range, standard deviation and normal distribution are also discussed. The document also covers measures of asymmetry, relationship and concludes with emphasizing the importance of statistical planning in research.
This document discusses descriptive and inferential statistics. Descriptive statistics are used to analyze and represent previously collected data through measures like frequency, range, mean, mode, and standard deviation. Variables can be nominal, ordinal, or interval. Inferential statistics are used to draw conclusions and make predictions based on descriptive statistics. Key concepts in inferential statistics include experiments, probability, population, sampling, and hypothesis testing.
Basics of Educational Statistics (Descriptive statistics)HennaAnsari
The document discusses various statistical concepts related to descriptive data analysis including measures of central tendency, dispersion, and distribution. It defines key terms like mean, median, mode, range, variance, standard deviation, normal curve, skewness, and kurtosis. Examples are provided to demonstrate calculating and applying these concepts. The learning objectives are to understand the purpose of central tendency measures, how to calculate measures like range and quartiles, and explain concepts such as the normal curve, skewness, and kurtosis.
The document provides an overview of quantitative data analysis and various statistical concepts including the normal distribution, z-tests, confidence intervals, and t-tests. It discusses how the normal distribution was developed by de Moivre and Gauss. It then explains the key properties of the normal distribution and how it can be used to describe many natural phenomena. Examples are provided to illustrate how to calculate and interpret confidence intervals and choose the appropriate statistical test.
UNIVARIATE & BIVARIATE ANALYSIS
UNIVARIATE BIVARIATE & MULTIVARIATE
UNIVARIATE ANALYSIS
-One variable analysed at a time
BIVARIATE ANALYSIS
-Two variable analysed at a time
MULTIVARIATE ANALYSIS
-More than two variables analysed at a time
TYPES OF ANALYSIS
DESCRIPTIVE ANALYSIS
INFERENTIAL ANALYSIS
DESCRIPTIVE ANALYSIS
Transformation of raw data
Facilitate easy understanding and interpretation
Deals with summary measures relating to sample data
Eg-what is the average age of the sample?
INFERENTIAL ANALYSIS
Carried out after descriptive analysis
Inferences drawn on population parameters based on sample results
Generalizes results to the population based on sample results
Eg-is the average age of population different from 35?
DESCRIPTIVE ANALYSIS OF UNIVARIATE DATA
1. Prepare frequency distribution of each variable
Missing Data
Situation where certain questions are left unanswered
Analysis of multiple responses
Measures of central tendency
3 measures of central tendency
1.Mean
2.Median
3.Mode
MEAN
Arithmetic average of a variable
Appropriate for interval and ratio scale data
x
MEDIAN
Calculates the middle value of the data
Computed for ratio, interval or ordinal scale.
Data needs to be arranged in ascending or descending order
MODE
Point of maximum frequency
Should not be computed for ordinal or interval data unless grouped.
Widely used in business
MEASURE OF DISPERSION
Measures of central tendency do not explain distribution of variables
4 measures of dispersion
1.Range
2.Variance and standard deviation
3.Coefficient of variation
4.Relative and absolute frequencies
DESCRIPTIVE ANALYSIS OF BIVARIATE DATA
There are three types of measure used.
1.Cross tabulation
2.Spearmans rank correlation coefficient
3.Pearsons linear correlation coefficient
Cross Tabulation
Responses of two questions are combined
Spearman’s rank order correlation coefficient.
Used in case of ordinal data
Basics of Educational Statistics (Inferential statistics)HennaAnsari
This document provides information about inferential statistics presented by Dr. Hina Jalal. It defines inferential statistics as using data from a sample to make inferences about the larger population from which the sample was taken. It discusses key areas of inferential statistics like estimating population parameters and testing hypotheses. It also explains the importance of inferential statistics in research for making conclusions from samples, comparing models, and enabling inferences about populations based on sample data. Flow charts are presented for selecting common statistical tests for comparisons, correlations, and regression.
This document provides an overview of various statistical analysis techniques used in inferential statistics, including t-tests, ANOVA, ANCOVA, chi-square, regression analysis, and interpreting null hypotheses. It defines key terms like alpha levels, effect sizes, and interpreting graphs. The overall purpose is to explain common statistical methods for analyzing data and determining the probability that results occurred by chance or were statistically significant.
Here are the steps to find the quartiles for this data set:
1. Order the data from lowest to highest: 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 5, 5, 6, 7
2. The number of observations is 16. To find the quartiles, we split the data into 4 equal parts.
3. n/4 = 16/4 = 4
4. Q1 is the median of the lower half of the data, which is the 4th observation: 2
5. Q2 is the median of all the data, which is also the 8th observation: 3
6. Q3 is the median of the upper half
The document discusses various measures used to describe the dispersion or variability in a data set. It defines dispersion as the extent to which values in a distribution differ from the average. Several measures of dispersion are described, including range, interquartile range, mean deviation, and standard deviation. The document also discusses measures of relative standing like percentiles and quartiles, and how they can locate the position of observations within a data set. The learning objectives are to understand how to describe variability, compare distributions, describe relative standing, and understand the shape of distributions using these measures.
Descriptive statistics are used to summarize and describe characteristics of a data set. They include measures of central tendency like the mean, median, and mode as well as measures of variability such as range, standard deviation, and variance. Descriptive statistics help analyze and understand patterns in data through tables, charts, and summaries without drawing inferences about the underlying population.
This document discusses quantitative data analysis and statistical measures. It describes levels of quantitative description, types of data analysis including descriptive and inferential analysis, and statistical measures used in descriptive analysis such as measures of central tendency, spread, relative position, and relationship. Specific statistical measures are defined, like mean, median, mode, range, variance, standard deviation, percentile scores, correlation coefficients, and when they are appropriate to use. Computational data analysis tools like IBM SPSS Statistics are also mentioned.
Tools and Techniques - Statistics: descriptive statistics Ramachandra Barik
Tools and Techniques - Statistics: descriptive statistics - See more at: http://www.pcronline.com/eurointervention/67th_issue/volume-9/number-8/167/tools-and-techniques-statistics-descriptive-statistics.html#sthash.rtzcQ3ah.dpuf
This document discusses descriptive statistics and numerical measures used to describe data sets. It introduces measures of central tendency including the mean, median, and mode. The mean is the average value calculated by summing all values and dividing by the number of values. The median is the middle value when values are arranged in order. The mode is the most frequently occurring value. The document also discusses measures of dispersion like range and standard deviation which describe how spread out the data is. Examples are provided to demonstrate calculating the mean, median and other descriptive statistics.
This document discusses different measures of central tendency including the mean, median, and mode. It provides definitions and examples of how to calculate each measure. The mean is the average and is calculated by adding all values and dividing by the total number. The median is the middle value when values are arranged from lowest to highest. The mode is the most frequent value. The appropriate measure depends on the type of data and distribution. The mean is generally preferred but the median is better for skewed or open-ended distributions.
This document discusses various measures of central tendency including:
- Arithmetic mean, which is the most widely used measure. It is defined as the sum of all values divided by the number of values.
- Geometric mean, which gives more weight to smaller values. It is used to average rates of change.
- Median, which is the middle value when data is arranged from lowest to highest. Half of the data will be above and below the median.
- Mode, which is the most frequently occurring value in the data set. It indicates the most typical or probable value.
The document also discusses choosing an appropriate measure based on the data characteristics and purpose of the analysis. Quartiles, deciles, and
This document provides an overview of basic statistical concepts for bio science students. It defines measures of central tendency including mean, median, and mode. It also discusses measures of dispersion like range and standard deviation. Common probability distributions such as binomial, Poisson, and normal distributions are explained. Hypothesis testing concepts like p-values and types of statistical tests for different types of data like t-tests for continuous variables and chi-square tests for categorical data are summarized along with examples.
- The document discusses implementing task-based language teaching through a 12-week project where students work in groups to conduct surveys, analyze the data, and present their findings. It involves choosing topics, designing questionnaires, collecting data through interviews, analyzing trends, and making presentations. The project aims to provide authentic language practice and intrinsically motivating activities. It allows students to take responsibility for their own language learning.
Descriptive statistics summarize and describe data through measures like central tendency (mean, median, mode) and variability (range, standard deviation). There are different scales of measurement for variables, including nominal (categories without order), ordinal (ranked order), interval (equal intervals between ranks), and ratio (absolute zero point). Graphs like histograms, bar graphs, and scatterplots can visually portray relationships in the data.
This document is a paper submitted by Solanki Pratiksha M. about language learning strategies as discussed in the book by Rebecca L. Oxford. It discusses six main categories of language learning strategies: cognitive strategies, mnemonic strategies, metacognitive strategies, compensatory strategies, affective strategies, and social strategies. It also addresses influences on strategy choice and current and future trends in strategies research.
The document discusses validity and reliability in research. It defines reliability as the consistency of scores from one administration of an instrument to another, and validity as the appropriateness of inferences made from research findings. The document outlines different types of validity evidence including content, criterion, and construct validity. It also discusses threats to internal validity such as subject characteristics, loss of subjects, and location that could influence research outcomes. Methods for achieving validity and reliability are presented, including minimizing threats in experimental research designs.
The document discusses reliability and validity in research tools. It defines reliability as consistency of data collection and validity as measuring what is intended. It discusses different types of reliability - stability over time, equivalence of alternate forms, and internal consistency. It also discusses different types of validity - content, criterion, and construct validity. Factors like threats to groups, regression, time, and respondents' history can affect validity. Reliability ensures consistency while validity determines accuracy of what is measured.
The document discusses various methods for teaching grammar in English language teaching (ELT), including the deductive and inductive methods. It also covers grammar presentation, practice, and exercises. Some key points made include: the deductive method can teach grammar in isolation while the inductive method has students discover rules through language use; grammar practice should involve mechanical and meaningful components; exercises should include recognition, drill, creative, and test activities; and form, meaning and use should all be considered when teaching grammar.
This document discusses different theories and conceptions of teaching. It describes the shift from a focus on methods in the 20th century to a more complex view of language pedagogy in the 21st century. It outlines three main conceptions of teaching: 1) science-research conceptions which view teaching as applying principles from research, 2) theory-philosophy conceptions which are based on educational theories, and 3) art-craft conceptions which treat each teaching situation uniquely based on its characteristics. The document advocates for an approach to teaching that involves diagnosis of learners' needs, treatment through appropriate activities and techniques, and assessment to evaluate learning.
This document discusses the different types of validity in psychological testing: face validity, content validity, criterion validity (including predictive and concurrent validity), and discriminant validity. It provides examples for each type of validity. Criterion validity refers to how a test correlates with other measures of the same construct. Discriminant validity shows a test does not correlate with measures of different constructs. Validity is determined through empirical evidence over many studies, and is not an all-or-none concept. Factors like history, maturation, testing, and selection can threaten a test's validity if not controlled.
The document discusses various approaches and methods for teaching language, including:
- Communicative Language Teaching (CLT) which takes ideas from multiple methods and focuses on communication.
- Grammar-Translation which teaches grammar rules and translation exercises to read literature.
- Direct Method which uses only the target language and teaches concrete vocabulary through objects.
- Audio-Lingualism which teaches grammar inductively and relies on behaviorism and drills.
- Task-Based Learning which uses tasks to accomplish concrete goals and teaches necessary language.
The document discusses key qualities of measurement devices: validity, reliability, practicality, and backwash effect. It defines each quality and provides examples. Validity refers to what a test measures, and includes content, construct, criterion-related, concurrent, and predictive validity. Reliability is how consistent measurements are, including equivalency, stability, internal, and inter-rater reliability. Practicality means a test is easy to construct, administer, score and interpret. Backwash effect is a test's influence on teaching and learning.
Quantitative and qualitative research methods differ in important ways. Quantitative research uses statistical analysis of numeric data from standardized instruments, while qualitative research relies on descriptive analysis of text or image data collected from a small number of individuals. The two approaches also differ in how the research problem is identified, how literature is reviewed, how data is collected and analyzed, and how findings are reported. Common quantitative designs include experimental, correlational, and survey designs, while qualitative designs include grounded theory, ethnographic, narrative, and action research designs. The best approach depends on matching the research questions and goals.
Qualitative and quantitative methods of researchJordan Cruz
The document compares and contrasts qualitative and quantitative research methods. It discusses that qualitative research aims to understand social interactions through smaller, non-randomly selected samples, while quantitative research seeks to test hypotheses and make predictions using larger, randomly selected samples and specific variables. It also outlines the different types of data collected, forms of analysis, roles of researchers, and final reporting structures between the two methods.
B409 W11 Sas Collaborative Stats Guide V4.2marshalkalra
This document provides an overview of numerical summaries and variation within data. It defines key terms like mean, median, mode, range, standard deviation, and variance. It also discusses sources of variation within data like process inputs and conditions versus random temporary events. The document demonstrates how to use SAS software to analyze a cars dataset and create reports and bar charts to describe the data and identify trends and variation.
This document discusses measures of variation used to assess how far data points are from the average or mean. It defines key terms like range, variance, and standard deviation. Variance measures the mathematical dispersion of data relative to the mean, while standard deviation gives a value in the original units of measurement, making it easier to interpret. Formulas are provided for calculating sample variance and standard deviation versus population variance and standard deviation. Chebyshev's Theorem is introduced, stating that a certain minimum percentage of data must fall within a specified number of standard deviations of the mean. An example applies these concepts.
This document discusses computing statistics for single-variable data. It describes six common statistics: three measures of central tendency (mean, median, mode), two measures of spread (variance and standard deviation), and one measure of symmetry (skewness). Formulas are provided for calculating each statistic. Examples are given for computing statistics for both discrete and continuous data sets.
This document discusses statistical procedures and their applications. It defines key statistical terminology like population, sample, parameter, and variable. It describes the two main types of statistics - descriptive and inferential statistics. Descriptive statistics summarize and describe data through measures of central tendency (mean, median, mode), dispersion, frequency, and position. The mean is the average value, the median is the middle value, and the mode is the most frequent value in a data set. Descriptive statistics help understand the characteristics of a sample or small population.
Data Science - Part III - EDA & Model SelectionDerek Kane
This lecture introduces the concept of EDA, understanding, and working with data for machine learning and predictive analysis. The lecture is designed for anyone who wants to understand how to work with data and does not get into the mathematics. We will discuss how to utilize summary statistics, diagnostic plots, data transformations, variable selection techniques including principal component analysis, and finally get into the concept of model selection.
This document provides an introduction to statistics. It discusses what statistics is, the two main branches of statistics (descriptive and inferential), and the different types of data. It then describes several key measures used in statistics, including measures of central tendency (mean, median, mode) and measures of dispersion (range, mean deviation, standard deviation). The mean is the average value, the median is the middle value, and the mode is the most frequent value. The range is the difference between highest and lowest values, the mean deviation is the average distance from the mean, and the standard deviation measures how spread out values are from the mean. Examples are provided to demonstrate how to calculate each measure.
The document discusses different types of variables in research:
1. Independent variables are factors that are manipulated by researchers to determine their effect on dependent variables.
2. Dependent variables are factors that are observed and measured to determine the effect of independent variables.
3. Moderating variables modify the relationship between independent and dependent variables.
4. Control variables are controlled by researchers to neutralize their potential effects on the relationship between independent and dependent variables.
5. Intervening variables theoretically affect phenomena but cannot be directly observed or manipulated.
It also discusses different types of data (qualitative, quantitative), measures of central tendency (mean, median, mode), and measures of variability (
This document discusses descriptive statistics concepts including measures of center (mean, median, mode), measures of variation (range, standard deviation, variance), and properties of distributions (symmetric, skewed). Frequency tables are presented as a method to summarize data, including guidelines for construction and different types (relative frequency and cumulative frequency). Common notation and formulas are provided.
This document discusses various statistical measures used to summarize and analyze data. It covers measures of central tendency (mean, median, mode), measures of variability (range, variance, standard deviation), measures of the shape of a distribution (skewness and kurtosis), and methods for comparing multiple groups (pooled mean and variance). It also discusses concepts like outliers, box plots, z-scores, correlations, and Pearson's correlation coefficient. The document provides definitions, formulas, and examples to explain each statistical measure.
Statistics is the science of collecting and analyzing quantitative data. There are two main types of data: qualitative data which describes characteristics, and quantitative data which is measured numerically. Quantitative data is often displayed graphically, with error bars indicating the precision of the measurements based on the accuracy of the tools used. The standard deviation is a statistic that measures how tightly the data points are clustered around the mean, with a smaller standard deviation indicating more precise results.
This document provides an overview of descriptive statistics techniques for summarizing categorical and quantitative data. It discusses frequency distributions, measures of central tendency (mean, median, mode), measures of variability (range, variance, standard deviation), and methods for visualizing data through charts, graphs, and other displays. The goal of descriptive statistics is to organize and describe the characteristics of data through counts, averages, and other summaries.
After data is collected, it must be processed which includes verifying, organizing, transforming, and extracting the data for analysis. There are several steps to processing data including categorizing it based on the study objectives, coding it numerically or alphabetically, and tabulating and analyzing it using appropriate statistical tools. Statistics help remove researcher bias by interpreting data statistically rather than subjectively. Descriptive statistics are used to describe basic features of data like counts and percentages while inferential statistics are used to infer properties of a population from a sample.
This document discusses various measures of dispersion used in statistics including range, quartile deviation, mean deviation, and standard deviation. It provides definitions and formulas for calculating each measure, as well as examples of calculating the measures for both ungrouped and grouped quantitative data. The key measures discussed are the range, which is the difference between the maximum and minimum values; quartile deviation, which is the difference between the third and first quartiles; mean deviation, which is the mean of the absolute deviations from the mean; and standard deviation, which is the square root of the mean of the squared deviations from the arithmetic mean.
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- Two instructors who will teach 8 classes, with 3 take-home assignments and a final exam.
- Default and contributed datasets that students can use, focusing on nominal, ordinal, interval, and ratio variables.
- Optional late topics like microarray analysis, pattern recognition, and time series analysis.
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- Possible special topics like machine learning, time series analysis, and others.
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- Optional late topics like microarray analysis, pattern recognition, and time series analysis.
- A taxonomy of statistics, covering statistical description, presentation of data through graphs and numbers, and measures of center and variability.
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2. DEALING WITH DATA
CODING DATA systematically reorganizing raw data into
a format that is machine-readable (i.e. easy to analyze
using computers)
Coding can be a clerical task when the data are recorded
as numbers on well-organized recording sheets, but it is
very difficult when, for example, a researcher wants to
code answers to open-ended survey questions into
numbers in a process similar to latent content analysis.
3. DEALING WITH DATA
Researchers uses coding system and a codebook for
data coding:
Coding system set of rules stating that certain numbers are
assigned to variable attributes.
example: a researcher codes males as 1 and females as 2.
Codebook a document describing the coding system and
the location of data for variables in a format that computers
can use.
4. DEALING WITH DATA
Precoding placing the code categories on the
questionnaire.
If a researcher does not precode, his first step after
collecting data is to create a codebook. He also gives
each case an identification number to keep track of the
cases. Next he transfers the information from each
questionnaire into a format that computers can read.
5. ENTERING DATA
Most computer programs designed for data analysis
need the data in a grid format.
In the grid, each row represents a respondent, subject, or
case DATA RECORDS because each is a record of
data for a single case
Column or sets of columns represents specific variables.
6. CLEANING DATA
Accuracy is extremely important when coding data.
Errors made in coding can cause misleading results.
Highly recommended to recheck all coding.
Coding can be verified in two ways:
Possible code cleaning (wild code checking)
involves checking the categories of all variables for impossible
codes
Contingency cleaning (consistency checking)
involves cross-classifying two variables and looking for
logically impossible combinations.
7. COMPUTERS AND SOCIAL RESEARCH
Researchers use computers to perform specialized tasks
more efficiently and effectively.
Example: organize data, calculate statistics, write reports
8. COMPUTERS AND SOCIAL RESEARCH
Computer began as mechanical devices for sorting cards
that had holes punched into them.
Each hole were punched in specific locations and
represented information about a variable.
These machines organized vast amounts of information
more quickly, reliably, and efficiently than the paper-and-
pencil methods.
IBM CARDS thin cardboard cards that had 80
columns and 12 rows, or 960 spaces for information.
9. COMPUTERS AND SOCIAL RESEARCH
COMPUTER TERMINAL is a simple typewriter-like
device connected to a mainframe computer, which
people use to type data and instructions directly into the
computer.
MICROCOMPUTERS have replaced mainframes for
many tasks, to more people, and have stimulated new
uses form computers.
Three basic parts:
Monitor (CRT or VDT)
Keyboard
CPU (Central Processing Unit)
10. COMPUTERS AND SOCIAL RESEARCH
Information can get into a microcomputer in 4 ways:
Some is built into the computer memory itself
User can type it on the keyboard
It can come across a telephone line and into the computer
through a modem
It can be stored on floppy disks, or data travellers which
computers can read.
11. HOW COMPUTERS HELP THE RESEARCHER
Purpose of the computer: to write reports, to organize
large amounts of data, and to compute statistical
measures.
Computers help researchers perform tasks faster and
with greater accuracy than by hand.
Without the appropriate computer, a researcher cannot
analyze data from a large-scale research project or
calculate complicated statistics.
SPSS statistical package for the social sciences is a
statistical software most social researchers use that is
specifically designed for analyzing quantitative social
science data.
12. STATISTICS
a branch of applied mathematics used to manipulate and
summarize the features of numbers.
Descriptive statistics describe numerical data. They can
be categorized by the number of variables involved:
Univariate
Bivariate
Multivariate
13. RESULTS WITH ONE VARIABLE (UNIVARIATE)
Frequency Distributions
Measures of Central Tendency
Measures of Variation
14. RESULTS WITH ONE VARIABLE
Univariate describes one variable. The easiest way to
describe the numerical data of one variable is through
frequency distribution.
FREQUENCY DISTRIBUTION can be used with
nominal-, ordinal-, interval-, or ratio-level data and takes
many forms.
Example: A data having 400 respondents can be
summarized on the gender of the respondents with a raw
count or a percentage frequency distribution.
15. GENDER COUNT OF RESPONDENTS
RAW COUNT FREQUENCY PERCENTAGE FREQUENCY
DISTRIBUTION
Distribution
Gender Frequency Gender Frequency
Male 100 Male 25%
Female 300 Female 75%
Total 400 Total 100%
BAR CHART
Females
Column2
Column1
Males frequency distribution
0 20 40 60 80
16. RESULTS WITH ONE VARIABLE
Common types of graphic representations:
Histogram
Bar chart
Pie chart
For interval- or ratio-level data researcher groups the
information into categories; grouped categories should be
mutually exclusive
Interval- or ratio-level data are often plotted in a
frequency polygon.
17. RESULTS WITH ONE VARIABLE
MEASURES OF CENTRAL TENDENCY
Mean arithmetic average
most widely used measure of central tendency
can be used only with interval- or ratio-level data.
Median middle point
50th percentile, or the point at which half the cases
are above it and half below it
can be used with ordinal-, interval-, or ratio-level
data (not nominal-level)
Mode easiest to use and can be used with nominal, ordinal
, interval, or ratio data
most common or frequently occurring number
18. RESULTS WITH ONE VARIABLE
If the frequency distribution forms a NORMAL or BELL-
SHAPED CURVE, the three measures of central
tendency equal each other
number of cases
mean , median, mode
Lowest values of variables highest
19. RESULTS WITH ONE VARIABLE
SKEWED DISTRIBUTION measures of central
tendency are not equal
mode
median
mean
mode
median
mean
20. RESULTS WITH ONE VARIABLE
If most cases have lower scores with a few extreme high
scores, the mean will be the highest, the median in the
middle, and the mode the lowest.
If most cases have higher scores with a few extreme low
scores, the mean will be the lowest, the median in the
middle, and the mode the highest.
In general, the median is best for skewed
distributions, although the mean is used in most other
statistics.
21. RESULTS WITH ONE VARIABLE
MEASURES OF VARIATION one- number summary
of a distribution
Three basic ways:
Range
Percentile
Standard deviation
22. RESULTS WITH ONE VARIABLE
RANGE simplest
largest and smallest score
for ordinal-, interval-, and ratio-level
PERCENTILES tell the score at a specific place within
the distribution
for ordinal-, interval-, and ratio-level
STANDARD DEVIATION most difficult to compute
measure of dispersion; yet is also the most
comprehensive and widely used.
interval or ratio level
based on the mean and gives an “average
distance” between all scores and the mean
23. RESULTS WITH ONE VARIABLE
STEPS IN COMPUTING THE STANDARD DEVIATION
1. Compute the mean.
2. Subtract the mean from each score.
3. Square the resulting difference for each score.
4. Total up the squared differences to get the sum of
squares.
5. Divide the sum of squares by the number of cases to get
the variance.
6. Take the square root of the variance, which is the
standard deviation.
24. RESULTS WITH ONE VARIABLE
Standard deviation and the mean are used to create z-
scores.
Z-scores let a researcher compare two or more
distribution or groups.
also called a standardized score, expresses
points or scores on a frequency distribution in terms of a
number of standard deviations from the mean. Scores
are in terms of their relative position within a
distribution, not as absolute values.
25. EXAMPLE OF COMPUTING THE STANDARD DEVIATION
[8 RESPONDENTS, VARIABLE = YEARS OF SCHOOLING]
score score- mean squared (score-mean)
15 2.5 6.25
12 -0.5 .25
12 -0.5 .25
10 -2.5 6.25
16 3.5 12.25
18 5.5 30.25
8 -4.5 20.25
9 -3.5 12.25
Mean = 12.5 sum of squares = 88
Variance = sum of squares = 88 = 11
no. of cases 8
Standard deviation = square root of variance = √11 = 3.317 years
26. Symbols: Formula:
X = score of case Standard deviation
√ ∑(x-x )2
∑ = sigma for sum N
N = number of cases
X = mean
27. RESULTS WITH TWO VARIABLES (BIVARIATE)
The Scattergram
Cross-tabulation/ Percentaged Table
Measures of Association
28. RESULTS WITH TWO VARIABLES
Bavariate statistics let a researcher consider two
variables together and describe the relationship between
variables
Statistical relationships are based on two ideas:
Covariation things that are associated
Example: life expectancy and income
Independence no association or relationship between two
variables
Example: number of siblings and life expectancy
29. RESULTS WITH TWO VARIABLES
SCATTERGRAM a graph on which a researcher plots
each case or observation, where each axis represents
the value of one variable.
used for interval- or ratio-level data; rarely for ordinal;
never for nominal
independent variable = horizontal axis (x)
dependent variable = vertical axis (y)
30. RESULTS WITH TWO VARIABLES
Three aspects of a bivariate relationship in a scattergram:
Form
Independence random scatter with no pattern, or a straight line that
is parallel to one of the axis
Linear straight line that can be visualized in the middle of a maze of
cases running from one corner to another
Curvilinear centre of a maze of cases could form a U curve, right
side up or upside down, or an S curve
Direction
Positive and negative
Precision
Amount of spread in the points on the graph
High level occurs when the points hug the line that summarizes the
relationships
Low level occurs when the points are widely spread around the line
31. RESULTS WITH TWO VARIABLES
PERCENTAGED TABLES presents the same
information as a scattergram in a more condensed form
Cross-tabulation cases are organized in the table on
the basis of two variables at the same time.
Bavariate tables usually contain percentages.
32. RESULTS WITH TWO VARIABLES
CONSTRUCTING PERCENTAGE TABLES
1. Raw data
2. Compound frequency distribution (CFD)
Figure all possible combinations of variable categories
Make a mark next to the combination category into which each
case falls
Add up the marks for the number of cases in a combination
category
3. Set up the parts of a table (labeling rows and columns)
4. Each number from the CFD is placed in a cell in the
table that corresponds to the combination of variable
categories.
33. THE PARTS OF A TABLE
Title
Label row and column variable and give a name to each
of the variable categories.
Marginals totals of the columns and rows
Body of the table
Cell of a table
If there is missing information (cases in which a
respondent refused to answer, ended interview, said “I
don’t know”, etc.), report the number of missing cases
near the table to account for all original cases
For percentaged tables, provide the number of cases or
N on which percentages are computed in parentheses
near the total of 100%. This makes it possible to go back
and forth from a percentaged table to a raw count table
and vice versa.
34. RAW COUNT TABLE
AGE GROUP BY ATTITUDE ABOUT CHANGING THE DRINKING AGE
Age group
Attitude Under 30 30-45 46-60 61 and total
older
Agree 20 10 4 3 37
No opinion 3 (4) 10 10 2 25
Disagree 3 5 21 10 39
_____ _____ _____ _____ _____
Total 26 25 35 15 101
Missing =8
cases (6)
35. COLUMN PERCENTAGED TABLE
AGE GROUP BY ATTITUDE ABOUT CHANGING THE DRINKING AGE
Age group
Attitude Under 30 30-45 46-60 61 and Total
older
Agree 76.9 % 40% 11.14% 20% 36.6%
No opinion 11.5 % 40 % 28.6 % 13.3 % 24.8%
Disagree 11.5% 20% 60% 66.7% 38.6%
_____ ______ ______ ______ _____
Total 99.9% 100% 100% 100% 100%
(N) (26) (25) (35) (15) (101)
Missing =8
cases
36. ROW PERCENTAGED TABLE
AGE GROUP BY ATTITUDE ABOUT CHANGING THE DRINKING AGE
Age group
Attitude Under 30 30-45 46-60 61 and Total (N)
older
Agree 54.1% 27% 10.8% 8.1% 100 (37)
No 12% 40% 40% 8% 100 (25)
opinion
Disagree 7.7% 12.8% 53.8% 25.6% 99.9 (39)
_____ ______ _____ _____ _____
Total 25.7% 24.8% 34.7% 14.9% 100.1 (101)
Missing =8
cases
37. RESULTS WITH TWO VARIABLES
Three ways to percentage a table:
By row
By column
For the total
First two are most often used; last rare
Which is best?
Either can be appropriate.
38. RESULTS WITH TWO VARIABLES
MEASURES OF ASSOCIATION single number that
expresses the strength, and often the direction, of a
relationship; condenses information about a bivariate
relationship into a single number
Many measures are called by letters of the greek
alphabet (lambda, gamma, tau, chi (squared), and rho).
The emphasis is on interpreting the measures, not on
their calculation.
39. SUMMARY OF MEASURES OF ASSOCIATION
Measure Greek Type of data High Independence
symbol association
Lambda λ Nominal 1.0 0
Gamma γ Ordinal +1.0, -1.0 0
Tau τ Ordinal +1.0, -1.0 0
(Kendall’s)
Rho ρ Interval, ratio +1.0, -1.0 0
Chi-squared χ2 Nominal, Infinity 0
ordinal
40. MORE THAN TWO VARIABLES (MULTIVARIATE)
Trivariate percentaged tables
Multiple regression analysis
41. MORE THAN TWO VARIABLES
STATISTICAL CONTROL control variables
Researcher controls for alternative explanations in
multivariate analysis by introducing a third variable.
Example: Bavariate table showing that taller teens like
baseball more than shorter ones
May be spurious since male teens are taller than
females, and males tend to like baseball more than
females.
To test whether the relationship is due to sex, a
researcher must control for gender
42. MORE THAN TWO VARIABLES
TRIAVARIATE PERCENTAGED TABLES
Trivariate tables has a bivariate table of the independent
and dependent variable for each category of the control
variable. partials
Number of partials depends on the number of categories
in the control variable.
Trivariate tables have 3 limitations:
Difficult to interpret if a control variable has more than 4
categories.
Control variables can be at any level of measurement, but
interval or ratio control variables must be grouped, and how
cases are grouped can affect the interpretations of effects.
Total number of cases is a limiting factor because the cases
are divided among cells in partial.
43. MORE THAN TWO VARIABLES
P Number of cells in the partials
C number of cells in the bivariate relationship
N number of categories in the control variable
P=CxN
Example: Control variable having 3 categories, and a
bivariate table having 12 cells.
P= 12 x 3 = 36 cells
An average of 5 cases per cell is recommended, so the
researcher will need 5 x 6 = 180 cases at minimum
44. COMPOUND FREQUENCY DISTRIBUTION FOR TRIVARIATE TABLE
Males Females
Age Attitude No. of cases Age Attitude No. of cases
Under 30 Agree 10 Under 30 Agree 10
Under 30 No option 1 Under 30 No option 2
Under 30 Disagree 2 Under 30 Disagree 1
30-45 Agree 5 30-45 Agree 5
30-45 No option 5 30-45 No option 5
30-45 Disagree 2 30-45 Disagree 3
46-60 Agree 2 46-60 Agree 2
46-60 No option 5 46-60 No option 5
46-60 Disagree 11 46-60 Disagree 10
61 and older Agree 3 61 and older Agree 0
61 and older No option 0 61 and older No option 2
61 and older Disagree 5____ 61 and older Disagree 5______
subtotal 51 subtotal 50
Missing on either variable 4____ Missing on either variable 4______
No. of males 55 No. of females 54
45. PARTIAL TABLE FOR MALES
Attitude Under 30 30-45 46-60 61 and older Total
Agree 10 5 2 3 20
No option 1 5 5 0 11
Disagree 2 2 11 5 20
Total 13 12 18 8 51
Missing =4
cases
PARTIAL TABLE FOR FEMALES
Attitude Under 30 30-45 46-60 61 and older Total
Agree 10 5 2 0 17
No option 2 5 5 2 14
Disagree 1 3 10 5 19
Total 13 13 17 7
Missing =4
cases
46. MORE THAN TWO VARIABLES
Elaboration paradigm system for reading percentaged
trivariate tables
describes the pattern that emerges when a control
variable is introduced
Four terms describe how the partial tables compare to
the initial bivariate table, or how the original bivariate
relationship changes after the control variable is
considered.
47. SUMMARY OF THE ELABORATION PARADIGM
Pattern name Pattern seen when comparing partials to the
original bivariate table
Replication Same relationship in both partials as in bivariate table
Specification Bivariate relationship seen in one of the partial tables
Interpretation Bivariate relationship weakens greatly or disappears in
the partial tables (control variable intervening)
Explanation Bivariate relationship weakens greatly or disappears in
the partial tables (control variable before independent)
Suppressor variable No bivariate relationship, relationship appears in partial
tables only
48. EXAMPLES OF ELABORATION PATTERNS
REPLICATION
Bivariate table Partials
Control = low Control = high
Low High Low High Low High
Low 85% 15% Low 84% 16% 86% 14%
High 15% 85% High 16$ 84% 14% 86%
INTERPRETATION OR EXPLANATION
Bivariate table Partials
Control = low Control = high
Low High Low High Low High
Low 85% 15% Low 45% 55% 55% 45%
High 15% 85% High 55% 45% 45% 55%
49. EXAMPLES OF ELABORATION PATTERNS
SPECIFICATION
Bivariate table Partials
Control = low Control = high
Low High Low High Low High
Low 85% 15% Low 95% 5% 50% 50%
High 15% 85% High 5% 95% 50% 50%
SUPPRESSOR VARIABLE
Bivariate table Partials
Control = low Control = high
Low High Low High Low High
Low 54% 46% Low 84% 16% 14% 86%
High 46% 54% High 16% 84% 86% 14%
50. MORE THAN TWO VARIABLES
Replication pattern easiest to understand; when the
partials replicate or reproduce the same relationship that
existed in the bivariate table before considering the
control variable
control variable has no effect
Specification pattern occurs when one partial replicates
the initial bivariate relationship, but other partials do not.
researcher can specify the category of the control
variable in which the initial relationship persists
Example: college grades and automobiles
51. MORE THAN TWO VARIABLES
Interpretation pattern describes the situation in which
the control variable intervenes between the original
independent and dependent variable.
Explanation pattern looks the same as interpretation;
difference is the temporal order of the control variable
control variable comes before the independent
variable in the initial bivariate relationship
Suppressor variable pattern occurs when the bivariate
tables suggest independence but a relationship appears
in one or both of the partials
52. MORE THAN TWO VARIABLES
MULTIPLE REGRESSION statistical technique which
is quickly computed by an appropriate statistics software
Regression results measure the direction and size of the
effect of each variable on a dependent variable. The
effect is measured precisely and given a numerical
value.
The effect on the dependent variable is measured by a
standardized coefficient or the Greek letter beta (β). It is
equal to the ρ correlation coefficient.
53. MORE THAN TWO VARIABLES
Researchers use the beta regression coefficient to
determine whether control variables have an effect.
Example: the bivariate correlation between X and Y is
0.75. Researcher statistically considers four control
variables. If the beta remains at 0.75, then the four
control variables have no effect. However, if the beta for
X and Y gets smaller, it indicates that the control
variables have an effect.
54. INFERENTIAL STATISTICS
use probability theory to test hypotheses formally, permit
inferences from a sample to a population, and test
whether descriptive results are likely to be due to random
factors or to a real relationship.
are a more powerful type of statistics than descriptive
statistics
rely on principles from probability sampling, where a
researcher uses a random process to select a subset of
cases from the entire population.
used when researchers conduct various statistical test
(e.g. t-test or an F-test)
55. INFERENTIAL STATISTICS
Statistical significance results are not likely to be due
to chance factors
indicates the probability of finding a relationship in the
sample where there is none in the population
uses probability theory and specific statistical tests to
tell a researcher whether the results are likely to be
produced by random error in random sampling
56. INFERENTIAL STATISTICS
Levels of significance (usually .05, .01, or .001) is a way
of talking about the likelihood that the results are due to
chance factors –that is, a relationship appears in the
sample when there is none in the population.
If a researcher says that results are significant at the .05
level, this means:
Results like these are due to a chance factors only 5 in 100
times
There is a 95% chance that the sample results are not due to
chance factors alone, but reflect the population accurately
The odds of such results based on chance alone are .05 or 5%
One can be 95% confident that the results are due to a real
relationship in the population, not chance factors
57. INFERENTIAL STATISTICS
Type I error occurs when the researcher says that a
relationship exists when in fact none exists
falsely rejecting a null hypothesis
Type II error occurs when a researcher says that a
relationship does not exist when in fact it does.
falsely accepting a null hypothesis
True situation in the world
What the researcher says No relationship Causal relationship
No relationship No error Type II error
Causal relationship Type I error No error