Statistical reasoning in psychology and education/
Edward W. Minium, Bruce M. King, Gordon Bear.
- 3rd ed.
- New York: John Wiley and Sons, 1993.
- xiii, 590 p. : ill. ; 26 cm.
1.1 Descriptive Statistics 1.2 Inferential Statistics 1.3 Relationship and Prediction 1.4 Our Concern: Applied Statistics 1.5 The Role of Applied Statistics 1.6 Do Statistics Lie? 1.7 Other Concerns about Statistics Point of Controversy: Are Statistics Necessary? 1.8 Some Tips on Studying Statistics 1.9 Summary CHAPTER 2 PRELIMINARY CONCEPTS 2.1 Random Samples 2.2 Variables and Constants 2.3 Scales of Measurement 2.4 Scales of Measurement and Problems of Statistical Treatment 2.5 Computational Accuracy with Continuous Variables 2.6 Summary CHAPTER 3 FREQUENCY DISTRIBUTIONS, PERCENTIIES, AND PERCENTILE RANKS
Organizing Qualitative Dau Grouped Scores How to Construct a Grouped Frequency Distribution Apparent versus Real Limits
The Relative Frequency Distribution Stem-and-Leaf Displays The Cumulative Frequency Distribution Percentiles and Percentile Ranks Computing Percentiles from Grouped Data 3.10 Computation of Percentile Rank 3.11 Summary CHAPTER 4 GRAPHIC REPRESENTATION OF FREQUENCY DISTRIBUTIONS 4.1 Basic Procedures 4.2 The Histogram 4.3 The Frequency Polygon 4.4 Choosing Between a Histogram and a Polygon 4.5 The Bar Diagram and the Pie Chart 4.6 The Cumulative Percentage Curve 4.7 Factors Affecting the Shape of Graphs 4.8 Characteristics of Frequency Distributions 4.9 Summary CHAPTER 5 CENTRAL TENDENCY 5.1 The Mode 5.2 The Median 5.3 The Arithmetic Mean 5.4 Properties of the Mode 5.5 Properties of the Mean Point of Controversy: Is It Permissible to Calculate the Mean for Psychological and Educational Tests? 5.6 Properties of the Median 5.7 Measures of Central Tendency in Symmetrical and Asymmetrical Distributions 5-8 The Effects of Score Transformations 5.9 Summary CHAPTER 6 VARIABILITY
The Range The Semi-Interquanile Range Deviation Scores Deviational Measures: The Variance Deviational Measures: The Standard Deviation Point of Controversy: Calculating the Sample Variance: Should We Divide by n or (w — 1)? 6.6 Calculation of the Variance and
Standard Deviation: Raw-Score Method Properties of the Range Properties of the Semi-Interquartile Range Properties of the Standard Deviation 6.10 Score Transformations and Measures of Variability 6.11 Standard Scores (z Scores) 6.12 Measures of Variability and the Normal Distribution 6.13 Comparing the Means of Two Distributions 6.14 Summary CHAPTER 7 the_normal curve 7.1 Historical Aspects of the Normal Curve The Nature of the Normal Curve 7.3 Standard Scores and the Normal Curve 7.4 The Standard Normal Curve: Finding Areas When the Score is Known 7.5 The Standard Normal Curve: Finding Scores When the Area is Known
7.6 The Normal Curve as a Model for Real Variables 7.7 The Normal Curve as a Model for Sampling Distributions Point of Controversy: How Normal Is the Normal Curve? 7.8 Summary CHAPTER 8 DERIVED SCORES 8.1 The Need for Derived Scores 8.2 Standard Scores 8.3 Translating Raw Scores to Standard Scores 8.4 Standard Scores as Linear Transformations of Raw Scores 8.5 Percentile Scores 8.6 Comparability of Scores 8.7 Normalized Standard Scores 8.8 Combining Measures from Different Distributions 8.9 Summary CHAPTER 9 CORRELATION 9.1 Some History 9.2 Graphing Bivariate Distributions: The Scatter Diagram 9.3 Correlation: A Matter of Direction 9.4 Correlation: A Matter of Degree 9.5 Understanding the Meaning of Degree of Correlation 9.6 Formulas for Pearson's Coefficient of Correlation ~ 9.7 Calculating rlrom Raw Scores 9.8 Correlation Does Not Establish Causation 9 9 The Effects of Score Transformations 9.10 Cautions Concerning Correlation Coefficients 9.11 Other Ways to Measure Association 9.12 Summary CHAPTER 10 PREDICTION : 10.1 The Problem of Prediction 10.2 The Criterion of Best Fit Point of Controversy: Least-Squares Regression versus the Resistant Line 10.3 The Regression Equation: Standard-Score Form 10.4 The Regression Equation: Raw-Score Form 10.5 Error of Prediction: The Standard Error of Estimate 10.6 An Alternative (and Preferred) Formula for 5^ 10.7 Error in Estimating Tfrom X 10.8 Cautions Concerning Estimation of Predictive Error 10.9 Summary CHAPTER 11 INTERPRETIVE ASPECTS OF CORRELATION AND REGRESSION 11.1 Factors Influencing r: Range of Talent 11.2 The Correlation Coefficient in Discontinuous Distributions 11.3 Factors Influencing r: Heterogeneity of Samples 11.4 Interpretation of r: The Regression Equation I 11.5 Interpretation of r: The Regression Equation II 11.6 Regression Problems in Research 11.7 An Apparent Paradox in Regression 11.8 Interpretation of r: Proportion of Variation in Y Not Associated with Variation in X 11.9 Interpretation of r: Proportion of Variance in Y Associated with Variance in X 11.10 Interpretation of r: Proportion of Correct Placements 11.11 Summary CHAPTER 12 PROBABILITY 12.1 Defining Probability 12.2 A Mathematical Model of Probability 12.3 Two Theorems in Probability 12.4 An Example of a Probability Distribution: The Binomial 12.5 Applying the Binomial 12.6 The Frequency Distribution (and Normal Curve) as a Probability Distribution 12.7 Are Amazing Coincidences Really that Amazing? 12.8 Summary CHAPTER 13 THE BASIS OF STATISTICAL INFERENCE 13.1 A Problem in Inference: Testing Hypotheses 13.2 A Problem in Inference: Estimation 13.3 Basic Issues in Inference 13.4 Random Sampling 13.5 Using a Table of Random Numbers 13.6 The Random Sampling Distribution of the Mean: An Introduction 13.7 Characteristics of the Random Sampling Distribution of the Mean 13.8 Putting the Sampling Distribution of the Mean to Use 13.9 Summary CHAPTER 14 TESTING HYPOTHESES ABOUT SINGLE MEANS {z and t) 14.1 Testing a Hypothesis About a Single Mean 14.2 When Do We Retain and When Do We Reject the Hypothesis? 14.3 Generality of the Procedure for Hypothesis Testing 14.4 Dr. Frost's Problem: Conclusion 14.5 Review of Assumptions in Inference about a Single Mean 14.6 Estimating the Standard Error of the Mean When a is Unknown 14.7 The t Distribution 14.8 Characteristics of Student's Distribution of t 14.9 Degrees of Freedom and Student's Distribution of t 14.10 Using Student's Distribution of t 14.11 An Example: Professor Dyett's Question 14.12 Computing / from Raw Scores 14.13 Directional and Nondirectional Alternative Hypotheses 14.14 Reading Research Reports in Behavioral Science Point of Controversy: The Bootstrap Method of Statistical Inference 14.15 Problems in Selecting a Random Sample and in Drawing Conclusions 14.16 Summary CHAPTER 15 FURTHER CONSIDERATIONS IN HYPOTHESIS TESTING 15.1 Statement of the Hypothesis 15.2 Choice of H,,: One-Tailed and Two-Tailed Tests 15.3 The Criterion for Rejecting or Retaining Hq 15.4 The Statistical Decision 15.5 A Statistically Significant Difference Versus a Practically Important Difference 15.6 Errors in Hypothesis Testing 15.7 Levels of Significance Versus p-Values 15.8 Summary Point of Controversy: Dichotomous Significance-testing Decisions CHAPTER 16 TESTING HYPOTHESES ABOUT THE DIFFERENCE BETWEEN TWO INDEPENDENT MEANS 16.1 The Random Sampling Distribution of the Difference Between Two Sample Means 16.2 An Illustration of the Sampling Distribution of the Difference Between Means 16.3 Properties of the Sampling Distribution of the Difference Between Means 16.4 Determining a Formula for t 16.5 Testing the Hypothesis of No Difference Between Two Independent Means: The Dyslexic Children Experiment 16.6 The Conduct of a One-Tailed Test 16.7 Sample Size in Inference about Two Means 16.8 Assumptions Associated with Inference about the Difference Between Two Independent Means 16.9 The Random-Sampling Model Versus the Random Assignment Model 16.10 Random Sampling and Random Assignment as Experimental Controls 16.11 The Experiment Versus the In Situ Study 16.12 Summary CHAPTER 17 TESTING HYPOTHESES DIFFERENCE BETWEEN DEPENDENT MEANS 17.1 Determining a Formula for t ABOUT THE TWO 17.2 Degrees of Freedom for Tests of No Difference Between Dependent Means 17.3 Testing a Hypothesis about Two Dependent Means 17.4 An Alternative Approach to the Problem of Two Dependent Means 17.5 Advantages of the DependentSamples Design 17.6 Hazards of the Dependent-Samples Design 17.7 Summary CHAPTER 18 ESTIMATION OF /i AND l^x- 18.1 Two Ways of Making Estimates 18.2 Interval Estimates of Hx 18.3 Interval Estimates of iix~I^y 18.4 Evaluating an Interval Estimate 18.5 Sample Size Required for Estimates of Hx2^nd Hx- fir 18.6 The Relation Between Interval Estimation and Hypothesis Testing 18.7 The Merits of Interval Estimation 18.8 Summary CHAPTER 19 POWER AND MEASURE OF EFFECT SIZE 19-1 Type I Error and Type II Error 19.2 The Power of a Test Point of Controversy: Failure to Publish "Nonsignificant" Results
Factors Affecting Power: Discrepancy Between the True Population Mean and the Hypothesized Mean (Size of Effect) Factors Affecting Power: Sample Size Factors Affecting Power: Variability of the Measure and Dependent Samples Factors Affecting Power: Level of Significance (a) Factors Affecting Power: One-Tailed Versus Two-Tailed Tests Summary of Factors Affecting Power Calculating the Power of a Test 19.10 Effect Size 19.11 Estimating Power and Sample Size for Tests of Hypotheses about Means 19.12 Some Implications of Power Curves 19.13 Reporting Inferential Statistics Point of Controversy: Meta-Analysis 19.14 Summary CHAPTER 20 ONE-WAY ANALYSIS OF VARIANCE (AND SOME ALTERNATIVES) 20.1 The Null Hypothesis 20.2 The Logic of One Way Analysis of Variance: Variation Within and Between Groups 20.3 Partition of Sums of Squares 20.4 Degrees of Freedom 20.5 Variance Estimates and the F" Ratio 20.6 The Summary Table 20.7 An Example 20.8 Raw Score Formulas for Analysis of Variance 20.9 Comparison of t and F 20.10 Assumptions Associated with ANOVA 20.11 ANOVA and Power 20.12 Post Hoc Comparisons 20.13 An Alternative to the FTest: Planned Comparisons 20.14 How to Construct Planned Comparisons 20.15 An Alternative for Comparing One Control Group with Several Experimental Groups: Dunnett's Test Point of Controversy: Analysis of Variance Versus A Priori Coraparisons 20.16 Analysis of Variance for Repeated Measures 20.17 Summary CHAPTER 21 FACTORIAL ANALYSIS OF VARIANCE: THE TWO-FACTOR DESIGN 21.1 Main Effects 21.2 Interaction 21.3 The Importance of Interaction 21.4 Partition of the Sum of Squares for Two-way ANOVA 21.5 Degrees of Freedom 21.6 Variance Estimates and F Tests 21.7 Studying the Outcome of Two-Way Analysis of Variance 21.8 Planned Comparisons 21.9 Assumptions of the Two-Factor Design and the Problem of Unequal Numbers of Scores 21.10 Mixed Two-Factor Within-Subjects Design 21.11 Summary CHAPTER 22 INFERENCE ABOUT PEARSON CORRELATION COEFFICIENTS 22.1 The Random Sampling Distribution of r 22.2 Testing the Hypothesis that /? = 0 22.3 Fisher's z' Transformation 22.4 Estimating p 22.5 Testing the Hypothesis of No Difference Between and P2. Independent Samples 22.6 A Note About Assumptions 22.7 Summary CHAPTER 23 _CHL:SQ1IARE AND INFERENCE ABOUT FREQUENCIES 23.1 A Problem in Discrepancy Between Expected and Observed Frequencies 23.2 Chi-Square as a Measure of Discrepancy Between Expected and Observed Frequencies 23.3 The Logic of the Chi-Square Test 23.4 Interpretation of the Outcome of a Chi-Square Test 23.5 Different Hypothesized Proportions in the Test for Goodness of Fit 23.6 Assumptions in the Use of the Theoretical Distribution of Chi-Square 23.7 Hypothesis Testing When df= 1 23.8 Two Variables; Contingency Tables and the Hypothesis of Independence 23.9 Finding Expected Frequencies in a Contingency Table 23.10 Calculation of and Determination of Significance in a Contingency Table Point of Controversy: Yates' Correction for Continuity 23.11 Interval Estimates About Proportions 23.12 Other Applications of Chi-Square 2313 Summary CHAPTER 24 SOME (ALMOST) ASSUMPTION-FREE TESTS 24.1 Randomization Tests 24.2 How to Place Scores in Rank Order 24.3 Test of Location for Two Independent Groups: The Mann- Whitney UTest Point of Controversy: A Comparison of the t test and Mann-Whitney 17 Test with Real-World Distributions 24.4 Test of Location Among Several Independent Groups: The Kruskal- Wallis Test 24.5 Test of Location for Two Dependent Groups: The Sign Test 24.6 Test of Location for Two Dependent Groups: The Wilcoxon Signed- Ranks Test 24.7 Spearman's Rank-Order Correlation Coefficient Point of Controversy: Objectivity and Subjectivity in Inferential Statistics 24.8 Summary EPILOGUE; THE REALM OF STATISTICS APPENDIX A REVIEW Of BASIC MATHEMATICS APPENDIX B SUMMATION RULES APPENDIX C LIST OF SYMBOLS APPENDIX D ANSWERS TO ODD-NUMBERED PROBLEMS APPENDIX E STATISTICAL ANALYSIS BY COMPUTER APPENDIX F STATISTICAL TABLES
Areas Under the Normal Curve Corresponding to Given Values of z The Binomial Distribution Random Numbers Student's t Distribution The F Distribution The Studentized Range Statistic Dunnett's Test: Distribution of t Statistic in Comparing Several Treatment Means with One Control Values of the Correlation Coefficient Required for Different Levels of Significance When H^. p = 0 Values of Fisher's z' for Values of r The Distribution Critical One-Tail Values of for the Mann-Whitney C/Test Critical Values for the Smaller of W+ or W- for the Wilcoxon Signed-Ranks Tests