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Contents
Preface
Acknowledgments
About the Author
Chapter 1 Introduction to Statistical Concepts
Learning Objectives
Statistics as Tools in the Research Process
The Role of Statistics in Research
Three Statistical Approaches
Descriptive Statistics
Inferential Statistics
Correlational and Predictive Statistics
Preliminary Concepts
Constants Versus Variables
Classifying Variables
Experimental Classification
Mathematical Classification
Measurement Classification
The Language of Statistics
Variables Versus Constants
Notation
Conducting Research in the Social Sciences
Measurement Methods
Observation
Self-Report
Standardized Tests
Interpreting Research Outcomes: Reliability and Validity
Factors Affecting Internal Validity
Proactive History
Retroactive History
Maturation
Testing
Attrition (Experimental Mortality)
Investigator Bias
Factors
Affecting External Validity
Sampling Bias
The Hawthorne Effect
Designing the Study
Experimental Designs
Correlational Designs
Case Study Designs
Cross-Cultural Research Designs
Evaluation Research Designs
Meta-Analysis
Using Computers in Statistics
Summary of Terms and Concepts
Concept Review Answers
Exercises
Chapter 2
Organizing
and Presenting Data
Learning Objectives
Organizing Raw Data
Presenting Raw Data
Presenting Data in a Table: The Frequency Distribution Forms of Frequency Distributions
Simple Frequency Distributions
Grouped Frequency Distributions
Presenting Data in a Graph
Graphing Univariate Frequency Distributions
Bar Graph
Histogram
Stem-and-Leaf Diagrams
Frequency Polygon
Ogive
Misleading Graphs
The Shape of Univariate Frequency Distributions
Symmetry
Kurtosis
Summary of Terms and Concepts
Concept Review Answers
Exercises
Chapter 3 Describing the Central Tendency of Distributions
Learning Objectives
Three Measures of Central Tendency
Mode
Median
Mean
Calculating Measures of Central Tendency
Mode For Ungrouped Data For Grouped Data
Median For Ungrouped Data For Grouped Data
Mean For Raw Data
For Data in a Simple Frequency Distribution
For Data in a Grouped Frequency Distribution
Interpreting Measures of Central Tendency
Mode
Median
Mean
Shape and Measures of Central Tendency
Symmetrical Distributions
Skewed Distributions
Comparing Measures of Central Tendency
Sensitivity to Score Values
Resistance to Sampling Fluctuation
Misleading With Measures of Average
Summary of Terms and Formulas
Concept Review Answers
Exercises
Chapter 4 Describing the Variability of Distributions
Learning Objectives
Measures of Variability
Range
Semi-Interquartile Range
Variance and Standard Deviation
Calculating Measures of Variability
Range
Semi-Interquartile Range
Variance and Standard Deviation
Defining Formulas
Computational Formulas: Raw Data
Computational Formulas: Data in a Frequency Distribution
Interpreting Measures of Variability
Range
Semi-Interquartile Range
Variance and Standard Deviation
Summary of Terms and Formulas
Concept Review Answers
Exercises
Chapter 5 Describing the Position of Scores in Distributions
Learning Objectives
Percentiles and Percentile Ranks
Percentiles
Percentile Ranks
Calculating Percentiles and Percentile Ranks
Percentiles
Percentile Ranks
The z Score
Calculating z Scores
Properties of a z Distribution
The Mean
The Variance and Standard Deviation
The Shape
Using z to Locate Scores in a Distribution
Summary of Terms and Formulas
Concept Review Answers
Exercises
Chapter 6 Introduction to Inference: The Normal Curve
Learning Objectives
Empirical and Theoretical Frequency Distributions
The Normal Curve
Properties of the Standard Normal Curve
Using the Normal Curve to Solve Problems
Finding Areas Under the Curve
Finding z Scores With the Curve
Working With Empirical Data That Are Normally Distributed
Summary of Terms and Formulas
Concept Review Answers
Exercises
Chapter 7 Introduction to Inference: Probability
Learning Objectives
Simple Probability
Conditional Probability
Probability of Compound Events
Probability of A and B
Probability of A or B
Methods of Counting
Permutations
Combinations
Binomial Probability
Frequency Distributions as Probability Distributions
The Normal Curve as a Probability Distribution
Summary of Formulas
Concept Review Answers
Exercises
Chapter 8 Introduction to Inference: The Random Sampling
Distribution
Learning Objectives
Statistical Inference
Descriptive Versus Inferential Statistics
Random Sampling
The Random Sampling Distribution
The Random Sampling Distribution of the Mean
The Mean
The Variance
The Standard Deviation
The Shape: The Central Limit Theorem
Solving Problems With the Random Sampling Distribution of the Mean
The Random Sampling Distribution of the Difference Between Means
The Mean
The Variance
The Standard Deviation
The Shape
Solving Problems With the Random Sampling Distribution of the Difference
The Random Sampling Distribution of a Proportion
The Mean
The Variance
The Standard Deviation
The Shape
Solving Problems With the Random Sampling Distribution of a Proportion
Summary of Terms and Formulas
Concept Review Answers
Exercises
Chapter 9 Inference With the Normal Curve
Learning Objectives
Hypothesis Testing and Interval Estimation
Setting Up Confidence Intervals Using the Normal Distribution
Setting Up the Confidence Interval for a Population Mean
Setting Up the Confidence Interval for the Difference Between Population Means
Setting Up the Confidence Interval for a Population Proportion
Hypothesis Testing With the Normal Curve
Types of Hypotheses
Conceptual Hypotheses
Research Hypotheses
Statistical Hypotheses
The Logic and Procedure for Testing a Hypothesis
Null and Alternative Hypotheses
Testing the Null
Decision Criteria
One-Tailed and Two-Tailed Tests
Testing a Hypothesis About a Population Mean
Testing a Hypothesis About the Difference Between Population Means
Testing a Hypothesis About a Population Proportion
Consequences of Statistical Decisions
Statistical Significance
Type I and Type II Errors
Power
Assumptions Underlying Inference With the Normal Curve
Choosing the Appropriate Test of Significance
Summary of Formulas
Concept Review Answers
Exercises
Chapter 10 Inference With the t Distribution
Learning Objectives
The t Distribution and Unbiased Estimates
Sample Variance
Unbiased Estimate of Population Variance
Relationship between the Normal and the t Distribution
t Ratio for a Sample Mean
Degrees of Freedom When Estimating Parameters
When to Use the t Distribution
Setting Up Confidence Intervals Using the t Distribution
Setting Up the Confidence Interval for a Population Mean
Setting Up the Confidence Interval for the Difference Between Independent Population Means
Hypothesis Testing With the t Distribution
Testing Hypotheses About Population Means
Testing a Hypothesis About the Difference Between Independent Population Means
Assumptions Underlying Inference With the t Distribution
Dependent or Correlated Samples
Within-Participants Designs
Matched-Groups Designs
When to Use Dependent-Groups Designs
t Test for the Difference Between Two Dependent Samples
Power Revisited
Effect Size
Effect Size and Sample Size
Choosing the Appropriate Test of Significance
Summary of Formulas
Concept Review Answers Exercises
Chapter 11 Inference With the F Distribution
Learning Objectives
The F Distribution
Constructing an Empirical F Distribution
Characteristics of the F Distribution
Using the F Distribution
Null and Alternative Hypotheses
One-Way Analysis of Variance
Partitioning the Variance
Calculating the Sums of Squares
Calculating the Mean Squares
Calculating and Interpreting the F Ratio
Running a One-Way Analysis of Variance
Two-Way Analysis of Variance
The Logic of Two-Way Analysis of Variance
Main Effects
The Interaction
Partitioning the Variance
Calculating the Sums of Squares
Calculating the Mean Squares
Calculating and Interpreting the F Ratios
Running a Two-Way Analysis of Variance
Assumptions Underlying Inference With the F Distribution
Inferential Error
Calculating Effect Size
Choosing the Appropriate Test of Significance
Summary of Formulas
Concept Review Answers
Exercises
Chapter 12 Analysis of Variance With Repeated Measures
Learning Objectives
One-Way ANOVA With Repeated Measures
Null and Alternative Hypotheses
Partitioning the Variance
Calculating the Sums of Squares
Calculating the Mean Squares
Calculating the F Ratio
Running a One-Way ANOVA With Repeated Measures
Two-Way ANOVA With Repeated Measures on One Factor
Null and Alternative Hypotheses
Partitioning the Variance
Calculating the Sums of Squares
Calculating the Mean Squares
Calculating and Interpreting the F Ratios
Running a Two-Way ANOVA With Repeated Measures on One Factor
Interpreting a Two-Way ANOVA With Repeated Measures
Assumptions Underlying ANOVA With Repeated Measures
Choosing the Appropriate Test of Significance
Summary of Formulas
Concept Review Answers
Exercises
Chapter 13 Multiple Comparison Procedures
Learning Objectives
Controlling the Error Rate
A Priori (Planned) Comparisons
A Posteriori or Post Hoc Comparisons
The Scheffé Method
Constructing the Comparison
The Standard Error of the Comparison
Evaluating the Comparison for Significance
Running a Scheffé Test
The Tukey Method
Running a Tukey Test
Summary of Terms and Formulas
Concept Review Answers
Exercises
Chapter 14 Inference With the Chi-Square Distribution
Learning Objectives
The Chi-Square Distribution
Constructing the Sampling Distribution of Chi-Square
Characteristics of the Chi-Square Distribution
Using the Chi-Square Distribution
The Chi-Square Test for Goodness of Fit
Null and Alternative Hypotheses
Calculating Chi-Square
Interpreting Chi-Square
The Chi-Square Test for Independence
Null and Alternative Hypotheses
Determining Expected Frequencies
Calculating Chi-Square
Interpreting Chi-Square
Assumptions Underlying Inference With the Chi-Square Distribution
Choosing the Appropriate Test of Significance
Summary of Terms and Formulas
Concept Review Answers
Exercises
Chapter 15 Additional Nonparametric Techniques
Learning Objectives
The Mann-Whitney U Test
Null and Alternative Hypotheses
The U Statistic
Running the Mann-Whitney U Test
Running the Mann-Whitney U Test for Large Sample Sizes
The Wilcoxon Signed-Ranks Test
Null and Alternative Hypotheses
The T Statistic
Running the Wilcoxon Signed-Ranks Test
Running the Wilcoxon Signed-Ranks Test for Large Sample Sizes
The Kruskal-Wallis Test
Null and Alternative Hypotheses
The H Statistic
Running the Kruskal-Wallis Test
The Friedman Test
Null and Alternative Hypotheses
The Chi-Square Statistic
Running the Friedman Test
Choosing the Appropriate Test of Significance
Summary of Terms and Formulas
Exercises
Chapter 16 Correlational Techniques
Learning Objectives
Correlation as a Descriptive Technique
Constructing Bivariate Frequency Distributions
Graphing Bivariate Frequency Distributions: The Scattergram
Quantifying the Bivariate Relationship
Pearson’s Product-Moment Coefficient of Correlation
Calculating the Pearson Coefficient of Correlation
Data in Raw-Score Form
Data in Deviation-Score Form
Data in z-Score Form
Factors Influencing the Correlation Coefficient
Linearity of Regression
Homoscedasticity
Discontinuous Distributions
Interpreting the Coefficient of Correlation
Correlation as an Inferential Technique
Null and Alternative Hypotheses
Testing the Significance of the Correlation
Assumptions Underlying Inference About Correlations
The Spearman Rank-Order Correlation Test
Null and Alternative Hypotheses
The Rho Statistic
Running the Spearman Rank-Order Correlation Test
Summary of Terms and Formulas
Concept Review Answers
Exercises
Chapter 17 Predictive Techniques
Learning Objectives
The Regression Line
Criterion of Best Fit
The Regression Equation
Calculating the Slope
Calculating the Y Intercept
Laying Down the Regression Line
Using the Regression Equation for Prediction
Error of Prediction: The Standard Error of Estimate
Interpreting the Correlation in Terms of Explained Variance
Calculating Effect Size: Coefficient of Determination
Regression on the Mean
Multiple Regression Analysis
The Multiple Correlation Coefficient
Using Multiple Correlation for Prediction
Partial Correlation
Summary of Terms and Formulas
Concept Review Answers
Exercises
Chapter 18 Choosing the Appropriate Test of Significance
Learning Objectives
Nonparametric Versus Parametric Analysis
Choosing the Appropriate Parametric Test of Significance
Choosing the Appropriate Nonparametric Test of Significance
Testing for Identical Rank-Order Populations
Testing for Differences Between Obtained and Expected Frequencies
Exercises
Appendix A: Toolbox
Appendix B: Statistical Tables
Answers to Exercises
Glossary of Terms
References
Index
