PREFACE vii ABOUT THE BOOK AND AUTHORS x 1 INTRODUCTION 1 1.1 Descriptive Statistics, 3 1.2 Inferential Statistics, 3 1.3 Our Concern: Applied Statistics, 4 1.4 Variables and Constants, 5 1.5 Scales of Measurement, 6 1.6 Scales of Measurement and Problems of Statistical Treatment, 8 1.7 Do Statistics Lie?, 9 Point of Controversy: Are Statistical Procedures Necessary?, 11 1.

8 Some Tips on Studying Statistics, 12 1.9 Statistics and Computers, 12 1.10 Summary, 13 2 FREQUENCY DISTRIBUTIONS, PERCENTILES, AND PERCENTILE RANKS 16 2.1 Organizing Qualitative Data, 16 2.2 Grouped Scores, 18 2.3 How to Construct a Grouped Frequency Distribution, 19 2.4 Apparent versus Real Limits, 21 2.5 The Relative Frequency Distribution, 21 2.

6 The Cumulative Frequency Distribution, 22 2.7 Percentiles and Percentile Ranks, 24 2.8 Computing Percentiles from Grouped Data, 25 2.9 Computation of Percentile Rank, 28 2.10 Summary, 28 3 GRAPHIC REPRESENTATION OF FREQUENCY DISTRIBUTIONS 32 3.1 Basic Procedures, 32 3.2 The Histogram, 33 3.3 The Frequency Polygon, 34 3.

4 Choosing between a Histogram and a Polygon, 35 3.5 The Bar Diagram and the Pie Chart, 37 3.6 The Cumulative Percentage Curve, 39 3.7 Factors Affecting the Shape of Graphs, 40 3.8 Shape of Frequency Distributions, 42 3.9 Summary, 43 4 CENTRAL TENDENCY 46 4.1 The Mode, 46 4.2 The Median, 47 4.

3 The Mean, 48 4.4 Properties of the Mode, 49 4.5 Properties of the Mean, 50 Point of Controversy: Is It Permissible to Calculate the Mean for Tests in the Behavioral Sciences?, 51 4.6 Properties of the Median, 52 4.7 Measures of Central Tendency in Symmetrical and Asymmetrical Distributions, 53 4.8 The Effects of Score Transformations, 54 4.9 Summary, 55 5 VARIABILITY AND STANDARD (z) SCORES 58 5.1 The Range and Semi-Interquartile Range, 58 5.

2 Deviation Scores, 60 5.3 Deviational Measures: The Variance, 61 5.4 Deviational Measures: The Standard Deviation, 62 5.5 Calculation of the Variance and Standard Deviation: Raw-Score Method, 63 5.6 Calculation of the Standard Deviation with SPSS, 64 Point of Controversy: Calculating the Sample Variance: Should We Divide by n or (n − 1)?, 67 5.7 Properties of the Range and Semi-Interquartile Range, 68 5.8 Properties of the Standard Deviation, 68 5.9 How Big Is a Standard Deviation?, 69 5.

10 Score Transformations and Measures of Variability, 69 5.11 Standard Scores (z Scores), 70 5.12 A Comparison of z Scores and Percentile Ranks, 73 5.13 Summary, 74 6 STANDARD SCORES AND THE NORMAL CURVE 78 6.1 Historical Aspects of the Normal Curve, 78 6.2 The Nature of the Normal Curve, 81 6.3 Standard Scores and the Normal Curve, 81 6.4 The Standard Normal Curve: Finding Areas When the Score Is Known, 83 6.

5 The Standard Normal Curve: Finding Scores When the Area Is Known, 86 6.6 The Normal Curve as a Model for Real Variables, 88 6.7 The Normal Curve as a Model for Sampling Distributions, 88 Point of Controversy: How Normal Is the Normal Curve?, 89 6.8 Summary, 89 7 CORRELATION 92 7.1 Some History, 93 7.2 Graphing Bivariate Distributions: The Scatter Diagram, 95 7.3 Correlation: A Matter of Direction, 96 7.4 Correlation: A Matter of Degree, 98 7.

5 Understanding the Meaning of Degree of Correlation, 99 7.6 Formulas for Pearson''s Coefficient of Correlation, 100 7.7 Calculating r from Raw Scores, 101 7.8 Calculating r with SPSS, 103 7.9 Spearman''s Rank-Order Correlation Coefficient, 106 7.10 Correlation Does Not Prove Causation, 107 7.11 The Effects of Score Transformations, 110 7.12 Cautions Concerning Correlation Coefficients, 110 7.

13 Summary, 114 8 PREDICTION 118 8.1 The Problem of Prediction, 118 8.2 The Criterion of Best Fit, 120 Point of Controversy: Least-Squares Regression versus the Resistant Line, 121 8.3 The Regression Equation: Standard-Score Form, 122 8.4 The Regression Equation: Raw-Score Form, 123 8.5 Error of Prediction: The Standard Error of Estimate, 125 8.6 An Alternative (and Preferred) Formula for SYX, 127 8.7 Calculating the "Raw-Score" Regression Equation and Standard Error of Estimate with SPSS, 128 8.

8 Error in Estimating Y from X, 130 8.9 Cautions Concerning Estimation of Predictive Error, 132 8.10 Prediction Does Not Prove Causation, 133 8.11 Summary, 133 9 INTERPRETIVE ASPECTS OF CORRELATION AND REGRESSION 136 9.1 Factors Influencing r: Degree of Variability in Each Variable, 136 9.2 Interpretation of r: The Regression Equation I, 137 9.3 Interpretation of r: The Regression Equation II, 139 9.4 Interpretation of r : Proportion of Variation in Y Not Associated with Variation in X, 140 9.

5 Interpretation of r: Proportion of Variance in Y Associated with Variation in X, 142 9.6 Interpretation of r: Proportion of Correct Placements, 144 9.7 Summary, 145 10 PROBABILITY 147 10.1 Defining Probability, 148 10.2 A Mathematical Model of Probability, 149 10.3 Two Theorems in Probability, 150 10.4 An Example of a Probability Distribution: The Binomial, 151 10.5 Applying the Binomial, 153 10.

6 Probability and Odds, 155 10.7 Are Amazing Coincidences Really That Amazing?, 155 10.8 Summary, 156 11 RANDOM SAMPLING AND SAMPLING DISTRIBUTIONS 160 11.1 Random Sampling, 161 11.2 Using a Table of Random Numbers, 163 11.3 The Random Sampling Distribution of the Mean: An Introduction, 164 11.4 Characteristics of the Random Sampling Distribution of the Mean, 166 11.5 Using the Sampling Distribution of X to Determine the Probability for Different Ranges of Values of X, 168 11.

6 Random Sampling without Replacement, 173 11.7 Summary, 173 12 INTRODUCTION TO STATISTICAL INFERENCE: TESTING HYPOTHESES ABOUT A SINGLE MEAN (z) 175 12.1 Testing a Hypothesis about a Single Mean, 176 12.2 The Null and Alternative Hypotheses, 176 12.3 When Do We Retain and When Do We Reject the Null Hypothesis?, 178 12.4 Review of the Procedure for Hypothesis Testing, 178 12.5 Dr. Brown''s Problem: Conclusion, 178 12.

6 The Statistical Decision, 180 12.7 Choice of HA: One-Tailed and Two-Tailed Tests, 182 12.8 Review of Assumptions in Testing Hypotheses about a Single Mean, 183 Point of Controversy: The Single-Subject Research Design, 184 12.9 Summary, 185 13 TESTING HYPOTHESES ABOUT A SINGLE MEAN WHEN IS UNKNOWN (t) 187 13.1 Estimating the Standard Error of the Mean When Is Unknown, 187 13.2 The t Distribution, 189 13.3 Characteristics of Student''s Distribution of t, 191 13.4 Degrees of Freedom and Student''s Distribution of t, 192 13.

5 An Example: Has the Violent Content of Television Programs Increased?, 193 13.6 Calculating t from Raw Scores, 196 13.7 Calculating t with SPSS, 198 13.8 Levels of Significance versus p-Values, 200 13.9 Summary, 202 14 INTERPRETING THE RESULTS OF HYPOTHESIS TESTING: EFFECT SIZE, TYPE I AND TYPE II ERRORS, AND POWER 205 14.1 A Statistically Significant Difference versus a Practically Important Difference, 205 Point of Controversy: The Failure to Publish "Nonsignificant" Results, 206 14.2 Effect Size, 207 14.3 Errors in Hypothesis Testing, 210 14.

4 The Power of a Test, 212 14.5 Factors Affecting Power: Difference between the True Population Mean and the Hypothesized Mean (Size of Effect), 212 14.6 Factors Affecting Power: Sample Size, 213 14.7 Factors Affecting Power: Variability of the Measure, 214 14.8 Factors Affecting Power: Level of Significance (), 214 14.9 Factors Affecting Power: One-Tailed versus Two-Tailed Tests, 214 14.10 Calculating the Power of a Test, 216 Point of Controversy: Meta-Analysis, 217 14.11 Estimating Power and Sample Size for Tests of Hypotheses about Means, 218 14.

12 Problems in Selecting a Random Sample and in Drawing Conclusions, 220 14.13 Summary, 221 15 TESTING HYPOTHESES ABOUT THE DIFFERENCE BETWEEN TWO INDEPENDENT GROUPS 224 15.1 The Null and Alternative Hypotheses, 224 15.2 The Random Sampling Distribution of the Difference between Two Sample Means, 225 15.3 Properties of the Sampling Distribution of the Difference between Means, 228 15.4 Determining a Formula for t, 228 15.5 Testing the Hypothesis of No Difference between Two Independent Means: The Dyslexic Children Experiment, 231 15.6 Use of a One-Tailed Test, 234 15.

7 Calculation of t with SPSS, 234 15.8 Sample Size in Inference about Two Means, 237 15.9 Effect Size, 237 15.10 Estimating Power and Sample Size for Tests of Hypotheses about the Difference between Two Independent Means, 241 15.11 Assumptions Associated with Inference about the Difference between Two Independent Means, 242 15.12 The Random-Sampling Model versus the Random-Assignment Model, 243 15.13 Random Sampling and Random Assignment as Experimental Controls, 244 15.14 Summary, 245 16 TESTING FOR A DIFFERENCE BETWEEN TWO DEPENDENT (CORRELATED) GROU.