Preface
About the Authors
1 Introduction to Statistics and Frequency Distributions
How to Be Successful in This Course |
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Math Skills Required in This Course |
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Why Do You Have to Take Statistics? |
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Statistics and the Helping Professions |
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Hypothesis Testing, Effect Size, and Confidence Intervals |
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Testing Causal Hypotheses |
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Independent and Dependent Variables |
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Discrete Versus Continuous Variables |
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Frequency Distribution Tables |
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2 Central Tendency
3 Variability
Steps in Computing a Population’s Standard Deviation |
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4 z Scores
Using X to Find Important “Cut Lines” |
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z Scores and the Standard Normal Curve |
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Example 1: Positive z Score |
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Example 2: Negative z Score |
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Example 3: Proportion Between Two z Scores |
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5 The Distribution of Sample Means and z for a Sample Mean
Sampling and Sampling Error |
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Distribution of Sample Means |
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Example: Computing and Interpreting the z for a Sample Mean |
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Exact Probabilities Versus Probability Estimates |
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Overview of the Activities |
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6 Hypothesis Testing With z Scores
Introduction to Hypothesis Testing |
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Hypothesis Testing With z for a Sample Mean Example (One-Tailed) |
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What Does It Mean to Describe Something as “Statistically Significant”? |
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Errors in Hypothesis Testing |
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Why Statisticians “Fail to Reject the Null” Rather Than “Accept the Null” |
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Why Scientists Say “This Research Suggests” Rather Than “This Research Proves” |
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Overview of the Activities |
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7 Single-Sample t Test
One-Tailed Single-Sample t Test Example |
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Two-Tailed Single-Sample t Test Example |
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8 Estimation With Confidence Intervals
Three Statistical Procedures With Three Distinct Purposes |
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Logic of Confidence Intervals |
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Computing a Confidence Interval for a Population Mean |
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Computing Confidence Intervals for a Mean Difference |
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Reporting Confidence Intervals in APA Style |
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Confidence Intervals for Effect Sizes |
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Interpretations of Confidence Intervals |
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9 Related Samples t Test
Repeated/Related Samples t Test |
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Logic of the Single-Sample and Repeated/Related Samples t Tests |
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Related Samples t (Two-Tailed) Example |
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Related Samples t (One-Tailed) Example |
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Statistical Results, Experimental Design, and Scientific Conclusions |
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Overview of the Activities |
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10 Independent Samples t Test
Conceptual Formula for the Independent Samples t |
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Two-Tailed Independent t Test Example |
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One-Tailed Independent t Test Example |
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Overview of the Activities |
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11 One-Way Independent Samples ANOVA
Independent Samples ANOVA |
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An Additional Note on ANOVAs: Family-Wise Error and Alpha Inflation |
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Overview of the Activities |
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12 Two-Factor ANOVA or Two-Way ANOVA
Purpose of the Two-Way ANOVA |
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Describing Factorial Designs |
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Logic of the Two-Way ANOVA |
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Example of a Two-Way ANOVA |
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Overview of the Activities |
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13 Correlation and Regression
When to Use Correlations and What They Can Tell You |
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Direction and Strength of Correlation Coefficients |
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Spearman’s (rs) Correlations |
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Using Scatterplots Prior to Correlation Coefficients |
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Alternative Use for Correlation |
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Correlation and Causation |
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Hypothesis Testing With Correlation |
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Two-Tailed Pearson’s Correlation Example |
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One-Tailed Pearson’s Correlation Example |
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What If You Need to Do a Spearman’s Correlation? |
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Overview of the Activities |
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14 Goodness of Fit and Independence Chi-Square Statistics
Logic of the Chi-Square Test |
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Comparing the Goodness-of-Fit Chi-Square and the Chi-Square for Independence |
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Goodness-of-Fit Chi-Square Example |
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Chi-Square for Independence |
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Overview of the Activities |
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Appendices
Appendix A
Unit Normal Table (z Table) |
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Appendix B
One-Tailed Probabilities t Table |
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Two-Tailed Probabilities t Table |
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Appendix C
Appendix D
The Studentized Range Statistic (q) Table |
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Appendix E
One-Tailed Pearson’s Correlation Table |
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Two-Tailed Pearson’s Correlation Table |
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Appendix F
Spearman’s Correlation Table |
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Appendix G
Appendix H
Critical Values for Chi-Square |
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Appendix I
Computing SSs for Factorial ANOVA |
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Appendix J
Choosing Correct Test Statistics |
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Index