Statistics for Psychology

by Aron, Arthur; Aron, Elaine N.

• ISBN13: 9780139140785
• ISBN10: 0139140786
• Edition: 2nd
• Format: Hardcover
• Copyright: 1998-09-01
• Publisher: Pearson College Div

Summary

For the first course in Statistics, the Second Edition of Statistics for Psychology capitalizes on a successful approach which presents statistics through definitional formulas to emphasize conceptual understanding, not rote memorization. Presenting statistical methods as a living, growing field of research, the book highlights recent controversies and developments. Thoroughly revised with new content and many new examples, the text takes the student from basic procedures through analysis of variance (ANOVA), and in a unique concluding chapter introduces the general linear model to integrate all of the statistical procedures presented. Better than any other text, Statistics for Psychology not only teaches statistics, but prepares students to read and understand research articles.

Table of Contents

Preface to the Instructor	xiii	(8)
Introduction to the Student	xxi
1 Displaying the Order in a Group of Numbers	1	(29)
The Two Branches of Statistical Methods	2	(1)
Frequency Tables	2	(1)
Box 1-1: Important Trivia for Poetic Statistics Students	3	(2)
How to Make a Frequency Table	5	(2)
Grouped Frequency Tables	7	(4)
Histograms	11	(1)
Box 1-2: Math Anxiety, Statistics Anxiety, and You: A Message for Those of You Who Are Truly Worried About This Course	12	(3)
Frequency Polygons	15	(3)
Shapes of Frequency Distributions	18	(4)
Controversies and Limitations	22	(2)
Box 1-3: Gender, Ethnicity, and Math Performance	24	(1)
Frequency Tables, Histograms, and Frequency Polygons in Research Articles	25	(2)
Summary	27	(1)
Key Terms	28	(1)
Practice Problems	28	(2)
2 The Mean, Variance, Standard Deviation, and Z Scores	30	(32)
The Mean	31	(4)
Alternative Measures of Central Tendency	35	(4)
The Variance and the Standard Deviation	39	(8)
Z Scores	47	(1)
Box 2-1: The Sheer Joy (Yes, Joy) of Statistical Analysis	48	(6)
Controversies and Limitations: The Tyranny of the Mean	54	(2)
The Mean and Standard Deviation As Described in Research Articles	56	(2)
Summary	58	(1)
Key Terms	59	(1)
Practice Problems	59	(1)
Chapter Appendix: Optional Computational Formulas for the Variance and the Standard Deviation	60	(2)
3 Correlation	62	(38)
Independent or Predictor Variables and Dependent Variables	64	(1)
Graphing Correlations: The Scatter Diagram	65	(3)
Patterns of Correlation	68	(4)
Computing an Index of Degree of Linear Correlation: The Pearson Correlation Coefficient	72	(2)
Box 3-1: Galton: Gentleman Genius	74	(5)
Integrating the Steps and Additional Examples	79	(5)
Testing the Statistical Significance of the Correlation of the Correlation Coefficient	84	(1)
Box 3-2: Illusory Correlation: When You Know Perfectly Well That If It's Big, It's Fat--and You Are Perfectly Wrong	85	(1)
Issues in Interpreting the Correlation Coefficient	86	(2)
Controversies and Recent Developments: What Is a Large Correlation?	88	(3)
Correlation Coefficients As Described in Research Articles	91	(1)
Summary	92	(1)
Key Terms	93	(1)
Practice Problems	94	(2)
Chapter Appendix I: Optional Computational Formula for the Correlation Coefficient	96	(2)
Chapter Appendix II: Hypothesis Tests and Power for the Correlation Coefficient	98	(2)
4 Prediction	100	(34)
Terminology of Bivariate Prediction	101	(1)
The Bivariate Prediction Model With Z Scores	102	(2)
Bivariate Prediction Using Raw Scores	104	(2)
The Regression Line	106	(2)
Error and Proportionate Reduction in Error	108	(6)
Another Example of Bivariate Prediction	114	(3)
Extension to Multiple Regression and Correlation	117	(5)
Box 4-1: Clinical Versus Statistical Prediction	122	(3)
Controversies and Limitations	125	(1)
Prediction Models As Described in Research Articles	126	(2)
Summary	128	(1)
Key Terms	129	(1)
Practice Problems	129	(5)
5 Some Key Ingredients for Inferential Statistics: The Normal Curve, Probability, and Population Versus Sample	134	(26)
The Normal Distribution	135	(2)
Box 5-1: DeMoivre, the Eccentric Stranger Who Invented the Normal Curve	137	(6)
Probability	143	(2)
Box 5-2: Pascal Begins Probability Theory at the Gambling Table, Then Learns to Bet on God	145	(2)
Sample and Population	147	(3)
Box 5-3: Surveys, Polls, and 1948's Costly "Free Sample"	150	(1)
Relation of Normal Curve, Probability, and Sample Versus Population	151	(1)
Controversies and Limitations	152	(3)
Normal Curves, Probabilities, Samples, and Populations in Research Articles	155	(1)
Summary	156	(1)
Key Terms	157	(1)
Practice Problems	157	(1)
Chapter Appendix: Probability Rules and Conditional Probabilities	158	(2)
6 Introduction to Hypothesis Testing	160	(24)
A Hypothesis-Testing Example	162	(1)
The Core Logic of Hypothesis Testing	163	(1)
The Hypothesis-Testing Process	163	(7)
Box 6-1: To Be or Not to Be--But Can Not Being Be? The Problem of Whether and When to Accept the Null Hypothesis	170	(2)
One-Tailed and Two-Tailed Hypothesis Tests	172	(5)
Controversies and Limitations	177	(2)
Hypothesis Tests As Reported in Research Articles	179	(1)
Summary	180	(1)
Key Terms	181	(1)
Practice Problems	181	(3)
7 Hypothesis Tests With Means of Samples	184	(28)
The Distribution of Means	185	(1)
Constructing a Distribution of Means	186	(2)
Characteristics of a Distribution of Means	188	(6)
Hypothesis Testing Involving a Distribution of Means	194	(1)
Box 7-1: More About Polls: Sampling Errors and Errors in Thinking About Samples	195	(6)
Estimation and Confidence Intervals	201	(4)
Controversies and Limitations: Confidence Intervals or Significance Tests?	205	(2)
Standard Deviation of the Distribution of Sample Means, Hypothesis Tests About Means of Samples, and Confidence Intervals As Described in Research Articles	207	(2)
Summary	209	(1)
Key Terms	210	(1)
Practice Problems	210	(2)
8 Statistical Power and Effect Size	212	(40)
What Is Statistical Power?	213	(3)
Alpha, Beta, and Power	216	(3)
Calculating Statistical Power	219	(4)
Power Tables	223	(1)
What Determines the Power of a Study?	223	(1)
Effect Size	224	(7)
Sample Size	231	(3)
Box 8-1: The Power of Typical Psychology Experiments	234	(1)
Other Influences on Power	235	(1)
Role of Power When Designing an Experiment	236	(4)
Importance of Power in Evaluating the Results of a Study	240	(2)
Power, Effect Size, and Confidence Intervals	242	(1)
Meta-Analysis	242	(1)
Box 8-2: Effect Sizes for Relaxation and Meditation: A Restful Meta-Analysis	243	(1)
Controversies and Limitations: Statistical Significance Controversy Continued--Effect Size Versus Statistical Significance	244	(2)
Power and Effect Size As Described in Research Articles	246	(2)
Summary	248	(1)
Key Terms	249	(1)
Practice Problems	249	(3)
9 The t Test for Dependent Means	252	(36)
Box 9-1: William S. Gosset, Alias "Student": Not a Mathematician, but a "Practical Man"	254	(1)
Introduction to the t Test: The t Test for a Single Sample	255	(11)
The t Test for Dependent Means	266	(10)
Assumptions of the t Test	276	(1)
Effect Size and Power for the t Test for Dependent Means	276	(4)
Box 9-2: The Power of Studies Using Difference Scores: How the Lanarkshire Milk Experiment Could Have Been Milked for More	280	(1)
Controversies and Limitations	280	(1)
t Tests As Described in Research Articles	281	(2)
Summary	283	(1)
Key Terms	284	(1)
Practice Problems	284	(3)
Chapter Appendix: Optional Computational Formulas for the t Test for Dependent Means	287	(1)
10 The t Test for Independent Means	288	(30)
Basic Strategy of the t Test for Independent Means: The Distribution of Differences Between Means	289	(6)
Steps of Hypothesis Testing With a t Test for Independent Means	295	(9)
Assumptions of the t Test for Independent Means	304	(1)
Effect Size and Power for the t Test for Independent Means	305	(1)
Box 10-1: Monte Carlo Methods, or When Mathematics Becomes Just an Experiment and Statistics Depend on a Game of Chance	306	(3)
Controversies and Limitations	309	(1)
The t Test for Independent Means As Described in Research Articles	310	(3)
Summary	313	(1)
Key Terms	314	(1)
Practice Problems	314	(2)
Chapter Appendix: Optional Computational Formulas for the t Test for Independent Means	316	(2)
11 Introduction to the Analysis of Variance	318	(30)
Basic Logic of the Analysis of Variance	320	(6)
Box 11-1: Sir Ronald Fisher, Caustic Genius of Statistics	326	(2)
Carrying Out an Analysis of Variance	328	(7)
Hypothesis Testing With the Analysis of Variance	335	(2)
Assumptions in the Analysis of Variance	337	(1)
Effect Size and Power for the Analysis of Variance	338	(4)
Controversies and Limitations: Random Assignment Versus Systematic Selection	342	(1)
Analyses of Variance As Described in Research Articles	343	(1)
Summary	344	(1)
Key Terms	345	(1)
Practice Problems	345	(3)
12 The Structural Model in the Analysis of Variance	348	(28)
Principles of the Structural Model	350	(3)
Box 12-1: Analysis of Variance As a Way of Thinking About the World	353	(1)
Using the Structural Model to Conduct an Analysis of Variance	354	(1)
Analysis of Variance Tables	355	(1)
Analysis of Variance With Unequal-Sized Groups	356	(6)
Summary of Procedures for Computing an Analysis of Variance Using the Structural Model	362	(1)
Multiple Comparisons	362	(3)
Assumptions in the Analysis of Variance With Unequal Sample Sizes	365	(1)
Effect Size and Power	366	(2)
Controversies, Limitations, and Recent Developments	368	(1)
Structural Model Analysis of Variance and Multiple Comparisons As Described in Research Articles	369	(2)
Summary	371	(1)
Key Terms	371	(1)
Practice Problems	372	(3)
Chapter Appendix I: Optional Computational Formulas for the Sums of Squares in a One-Way Analysis of Variance	375	(1)
13 Factorial Analysis of Variance	376	(50)
Basic Logic of Factorial Designs and Interaction Effects	377	(12)
Basic Logic of the Two-Way Analysis of Variance	389	(2)
Box 13-1: Personality and Situational Influences on Behavior: An Interaction Effect	391	(16)
Power and Effect Size in the Factorial Analysis of Variance	407	(4)
Extensions and Special Cases of the Factorial Analysis of Variance	411	(1)
Controversies, Limitations, and Recent Developments	412	(3)
Factorial Analysis of Variance Results As Reported in Research Articles	415	(1)
Summary	416	(1)
Key Terms	417	(1)
Practice Problems	417	(4)
Chapter Appendix I: Optional Computational Formulas for the Two-Way Analysis of Variance	421	(2)
Chapter Appendix II: One-Way Repeated-Measures Analysis of Variance	423	(3)
14 Chi-Square Tests	426	(32)
The Chi-Square Statistic and the Chi-Square Test for Goodness of Fit	428	(1)
Box 14-1: Karl Pearson, Inventor of Chi-Square and Center of Controversy	429	(8)
Chi-Square Test for Independence	437	(10)
Assumptions for Chi-Square Tests	447	(1)
Effect Size and Power for Chi-Square Tests for Independence	447	(4)
Controversies and Limitations	451	(1)
Chi-Square Tests As Reported in Research Articles	452	(1)
Summary	453	(1)
Key Terms	454	(1)
Practice Problems	454	(4)
15 Strategies When Population Distributions Are Not Normal: Data Transformations, Rank-Order Tests, and Computer-Intensive Methods	458	(30)
Assumptions in the Standard Hypothesis-Testing Procedures	459	(2)
Data Transformations	461	(9)
Rank-Order Tests	470	(4)
Computer-Intensive Methods	474	(5)
Comparison of Methods	479	(1)
Box 15-1: Where Do Random Numbers Come From?	480	(2)
Controversies	482	(1)
Procedures Used When Populations Appear Nonnormal As Described in Research Articles	482	(2)
Summary	484	(1)
Key Terms	485	(1)
Practice Problems	485	(3)
16 Integrating What You Have Learned: The General Linear Model	488	(30)
The Relationships Among Major Statistical Methods	489	(1)
Review of the Principles of Multiple Regression and Correlation	490	(2)
Introduction to the General Linear Model	492	(1)
The General Linear Model and Multiple Regression/Correlation	493	(1)
Bivariate Regression and Correlation As Special Cases of Multiple Regression/Correlation	493	(1)
The t Test As a Special Case of the Analysis of Variance	493	(2)
Box 16-1: The Golden Age of Statistics: Four Guys Around London	495	(3)
The t Test As a Special Case of the Significance Test for the Correlation Coefficient	498	(5)
The Analysis of Variance As a Special Case of the Significance Test of the Multiple Correlation Coefficient	503	(6)
Box 16-2: Two Women Make a Point About Gender and Statistics	509	(1)
Choice of Statistical Tests	510	(2)
Assumptions and the General Linear Model	512	(1)
Controversies and Limitations	512	(2)
Summary	514	(1)
Key Terms	515	(1)
Practice Problems	515	(3)
17 Making Sense of Advanced Statistical Procedures in Research Articles	518	(33)
Brief Review of Multiple Regression and Correlation	520	(1)
Hierarchial and Stepwise Multiple Regression	521	(3)
Partial Correlation	524	(2)
Reliability	526	(2)
Factor Analysis	528	(2)
Causal Modeling	530	(4)
Analysis of Covariance (ANCOVA)	534	(1)
Multivariate Analysis of Variance (MANOVA) and Multivariate Analysis of Covariance (MANCOVA)	535	(2)
Overview of Statistical Techniques	537	(1)
Box 17-1: The Forced Marriage of Fisher and Neyman-Pearson	538	(1)
Controversy: Should Statistics Be Controversial?	538	(2)
How to Read Results in Research Articles Involving Unfamiliar Statistical Techniques	540	(2)
Summary	542	(1)
Key Terms	543	(1)
Practice Problems	543	(8)
Appendix A Overview of the Logic and Language of Psychology Research	551	(12)
The Traditionally Ideal Research Approach	552	(1)
Equivalence of Participants in Experimental and Control Groups	553	(5)
Equivalence of Circumstances for Experimental and Control Groups	558	(1)
Representativeness of the Sample	559	(1)
Measurement	560	(2)
Key Terms	562	(1)
Appendix B Tables	563	(8)
Table B-1 Normal Curve Areas: Percentage of the Normal Curve Between the Mean and the Z Scores Shown	563	(3)
Table B-2 Cutoff Scores for the t Distribution	566	(1)
Table B-3 Cutoff Scores for the F Distribution	567	(3)
Table B-4 Cutoff Scores for the Chi-Square Distribution	570	(1)
Table B-5 Index to Power Tables and Tables Giving Number of Participants Needed for 80% Power	570	(1)
Answers to Set I Practice Problems	571	(40)
Glossary	611	(10)
Glossary of Symbols	621	(2)
References	623	(8)
Index	631