Statistics for Psychology

by Aron, Arthur; Aron, Elaine N.

• ISBN13: 9780130358103
• ISBN10: 013035810X
• Edition: 3rd
• Format: Hardcover
• Copyright: 2003-01-01
• Publisher: Prentice Hall

Summary

A book that focuses on the logic behind the concepts of statistics for psychology, using definitional formulas rather than emphasizing rote memorization. Clearly written, each procedure is conveyed both numerically and verbally, with many visual examples to illustrate the text. It takes the reader from basic procedures through analysis of variance (ANOVA), and not only teaches statistics, but also prepares the user to read and understand research articles as well.This book is an introduction to statistics for psychology, covering such topics as order in a group of numbers; mean, variance, standard deviation, and Z scores; correlation; prediction; the normal curve, probability, and population versus sample; hypothesis testing; the t test; analysis of variance; chi-square tests; the general linear model; and making sense of advanced statistical procedures in research articles.For statisticians, psychologists and those involved in psychological research in the behavioral and social sciences.

Table of Contents

Preface to the Instructor	xi
Introduction to the Student	xix
Displaying the Order in a Group Of Numbers	1	(34)
The Two Branches of Statistical Methods	2	(1)
Some Basic Concepts	2	(4)
Box 1-1: Important Trivia for Poetic Statistics Students	5	(1)
Frequency Tables	6	(6)
Box 1-2: Math Anxiety, Statistics Anxiety, and Yon: A Message, for-Those of you Who Are Truly Worried about this Course	10	(2)
Frequency Graphs	12	(6)
Shapes of Frequency Distributions	18	(4)
Controversy: Misleading Graphs	22	(4)
Box 1-3: Gender, Ethnicity, and Math Performance	24	(2)
Frequency Tables, Histograms, and Frequency Polygons in Research Articles	26	(1)
Summary	27	(1)
Key Terms	28	(1)
Example Worked-Out Computational Problems	28	(1)
Practice Problems	29	(6)
The Mean, Variance, Standard Deviation, and Z Scores	35	(34)
The Mean	35	(4)
Other Measures of Central Tendency	39	(4)
The Variance and the Standard Deviation	43	(8)
Z Scores	51	(7)
Box 2-1: The Sheer Joy (Yes, Joy) of Statistical Analysis	52	(6)
Controversy: The Tyranny of the Mean	58	(3)
The Mean and Standard Deviation in Research Articles	61	(1)
Summary	62	(1)
Key Terms	63	(1)
Example Worked-Out Computational Problems	63	(2)
Practice Problems	65	(4)
Correlation	69	(44)
Graphing Correlations: The Scatter Diagram	70	(5)
Patterns of Correlation	75	(5)
The Degree of Linear Correlation: The Correlation Coefficient	80	(8)
Box 3-1: Galton: Gentleman Genius	82	(6)
Correlation and Causality	88	(4)
Box 3-2: Illusory Correlation: When You Know Perfectly Well that If It's Big, It's Fat-and you are Perfectly Wrong	91	(1)
Issues in Interpreting the Correlation Coefficient	92	(3)
Controversy: What Is a Large Correlation?	95	(1)
Correlation in Research Articles	96	(2)
Summary	98	(1)
Key Terms	99	(1)
Example Worked-Out Computational Problems	99	(2)
Practice Problems	101	(8)
Chapter Appendix: Hypothesis Tests and Power for the Correlation Coefficient	109	(4)
Prediction	113	(44)
Predictor and Criterion Variables	114	(1)
Prediction Using Z Scores	114	(3)
Raw-Score Prediction Using the Z-Score Prediction Model	117	(2)
Raw-Score Prediction Using the Direct Raw-Score Prediction Model	119	(6)
The Regression Line	125	(3)
Error and Proportionate Reduction in Error	128	(8)
Multiple Regression	136	(2)
Limitations of Regression	138	(1)
Controversy: Comparing Predictors	139	(1)
Box 4-1: Clinical Versus Statistical Prediction	139	(1)
Prediction in Research Articles	140	(3)
Summary	143	(1)
Key Terms	144	(1)
Example Worked-Out Computational Problems	144	(3)
Practice Problems	147	(10)
Some Key Ingredients for Inferential Statistics: The Normal Curve, Probability, and Population Versus Sample	157	(32)
The Normal Distribution	158	(11)
Box 5-1: De Moivre, the Eccentric Stranger Who Invented the Normal Curve	159	(10)
Probability	169	(4)
Box 5-2: Pascal Begins Probability Theory at the Gambling Table, then Learns to Bet on God	170	(3)
Sample and Population	173	(4)
Box 5-3: Surveys, Polls, and 1948's Costly ``Free Sample''	176	(1)
Controversies: Is the Normal Curve Really Normal?, What Does Probability Really Mean?, and Using Nonrandom Samples	177	(3)
Normal Curves, Probabilities, Samples, and Populations in Research Articles	180	(1)
Summary	181	(1)
Key Terms	182	(1)
Example Worked-Out Computational Problems	182	(2)
Practice Problems	184	(3)
Chapter Appendix: Probability Rules and Conditional Probabilities	187	(2)
Introduction to Hypothesis Testing	189	(28)
A Hypothesis-Testing Example	190	(1)
The Core Logic of Hypothesis Testing	191	(1)
The Hypothesis-Testing Process	191	(8)
One-Tailed and Two-Tailed Hypothesis Tests	199	(5)
Controversy: Should Significance Tests Be Banned?	204	(3)
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	206	(1)
Hypothesis Tests in Research Articles	207	(1)
Summary	208	(1)
Key Terms	209	(1)
Example Worked-Out Computational Problems	209	(1)
Practice Problems	210	(7)
Hypothesis Tests With Means of Samples	217	(36)
The Distribution of Means	217	(9)
Hypothesis Testing with a Distribution of Means	226	(7)
Box 7-1: More about Polls: Sampling Errors and Errors in Thinking about Samples	227	(6)
Estimation, Standard Errors, and Confidence Intervals	233	(5)
Controversy: Confidence Intervals or Significance Tests?	238	(2)
Hypothesis Tests about Means of Samples, Standard Errors, and Confidence Intervals in Research Articles	240	(2)
Summary	242	(1)
Key Terms	243	(1)
Example Worked-Out Computational Problems	244	(1)
Practice Problems	245	(8)
Making Sense of Statistical Significance: Effect Size, Decision Error, and Statistical Power	253	(46)
Effect Size	254	(7)
Box 8-1: Effect Sizes for Relaxation and Meditation: A Restful Meta-Analysis	259	(2)
Decision Errors	261	(3)
Statistical Power	264	(7)
What Determines the Power of a Study?	271	(12)
Box 8-2: The Power of Typical Psychology Experiments	279	(4)
The Role of Power When Planning a Study	283	(1)
The Importance of Power When Evaluating the Results of a Study	284	(3)
Controversy: Statistical Significance Controversy Continued-Effect Size Versus Statistical Significance	287	(2)
Effect Size, Decision Errors, and Power in Research Articles	289	(2)
Summary	291	(1)
Key Terms	292	(1)
Example Worked-Out Computational Problems	292	(1)
Practice Problems	293	(6)
Introduction to the t Test	299	(42)
The t Test For a Single Sample	300	(12)
Box 9-1: William S. Gosset, Alias ``Student'': Not a Mathematician, but a Practical Man	301	(11)
The t Test for Dependent Means	312	(10)
Assumptions	322	(1)
Effect Size and Power for the t Test for Dependent Means	323	(3)
Controversy: Advantages and Disadvantages of Repeated-Measures Designs	326	(1)
Box 9-2: The Power of Studies Using Difference Scores: How the Lanarkshire Milk Experiment Could Have Been Milked for More	327	(1)
t Tests in Research Articles	327	(2)
Summary	329	(1)
Key Terms	329	(1)
Example Worked-Out Computational Problems	329	(2)
Practice Problems	331	(10)
The t Test For Independent Means	341	(36)
The Distribution of Differences between Means	342	(7)
Hypothesis Testing With a t Test for Independent Means	349	(7)
Assumptions of the t Test for Independent Means	356	(3)
Box 10-1: Monte Carlo Methods: When Mathematics Becomes Just an Experiment and Statistics Depend on a Game of Chance	357	(2)
Effect Size and Power for the t Test for Independent Means	359	(3)
Controversy: The Problem of Too Many t Tests	362	(2)
The t Test for Independent Means in Research Articles	364	(2)
Summary	366	(1)
Key Terms	366	(1)
Example Worked-Out Computational Problems	366	(3)
Practice Problems	369	(8)
Introduction to the Analysis Of Variance	377	(40)
Basic Logic of the Analysis of Variance	378	(8)
Box 11-1: Sir Ronald Fisher, Caustic Genius of Statistics	384	(2)
Carrying Out an Analysis of Variance	386	(8)
Hypothesis Testing with the Analysis of Variance	394	(4)
Assumptions in the Analysis of Variance	398	(2)
Planned Comparisons	400	(4)
Controversy: Omnibus Tests versus Planned Comparisons	404	(1)
Analyses of Variance in Research Articles	405	(1)
Summary	406	(1)
Key Terms	407	(1)
Example Worked-Out Computational Problems	407	(2)
Practice Problems	409	(8)
The Structural Model in the Analysis Of Variance	417	(34)
Principles of the Structural Model	418	(5)
Box 12-1: Analysis of Variance as a Way of Thinking About the World	421	(2)
Using the Structural Model to Figure an Analysis of Variance	423	(5)
Assumptions in the Analysis of Variance with Unequal Sample Sizes	428	(3)
Post-Hoc Comparisons	431	(2)
Effect Size and Power for the Analysis of Variance	433	(4)
Controversy: The Independence Assumption and the Unit of Analysis Question	437	(2)
Structural Model Analysis of Variance and Post-Hoc Comparisons in Research Articles	439	(1)
Summary	439	(2)
Key Terms	441	(1)
Example Worked-Out Computational Problems	441	(3)
Practice Problems	444	(7)
Factorial Analysis of Variance	451	(56)
Basic Logic of Factorial Designs and Interaction Effects	452	(4)
Recognizing and Interpreting Interaction Effects	456	(7)
Basic Logic of the Two-Way Analysis of Variance	463	(4)
Box 13-1: Personality and Situational Influences on Behavior: An Interaction Effect	466	(1)
Figuring a Two-Way Analysis of Variance	467	(13)
Power and Effect Size in the Factorial Analysis of Variance	480	(3)
Extensions and Special Cases of the Factorial Analysis of Variance	483	(2)
Controversy: Unequal Cell Sizes and Dichotomizing Numeric Variables	485	(2)
Factorial Analysis of Variance Results in Research Articles	487	(2)
Summary	489	(1)
Key Terms	490	(1)
Example Worked-Out Computational Problems	490	(3)
Practice Problems	493	(14)
Chi-Square Tests	507	(36)
The Chi-Square Statistic and the Chi-Square Test for Goodness of Fit	509	(8)
Box 14-1: Karl Pearson, Inventor of Chi-Square and Center of Controversy	510	(7)
The Chi-Square Test for Independence	517	(9)
Assumptions for Chi-Square Tests	526	(1)
Effect Size and Power for Chi-Square Tests for Independence	526	(4)
Controversy: The Minimum Expected Frequency	530	(1)
Chi-Square Tests in Research Articles	531	(1)
Summary	532	(1)
Key Terms	532	(1)
Example Worked-Out Computational Problems	533	(3)
Practice Problems	536	(7)
Strategies When Population Distributions Are Not Normal: Data Transformations and Rank-Order Tests	543	(26)
Assumptions in the Standard Hypothesis-Testing Procedures	544	(1)
Data Transformations	545	(5)
Rank-Order Tests	550	(5)
Comparison of Methods	555	(1)
Controversy: Computer Intensive Methods	556	(3)
Data Transformations and Rank-Order Tests in Research Articles	559	(2)
Box 15-1: Where Do Random Numbers Come Front?	560	(1)
Summary	561	(1)
Key Terms	561	(1)
Example Worked-Out Computational Problems	562	(1)
Practice Problems	562	(7)
Integrating What You Have Learned: The General Linear Model	569	(30)
The Relationships Between Major Statistical Methods	569	(1)
Review of the Principles of Multiple Regression	570	(1)
The General Linear Model	571	(2)
The General Linear Model and Multiple Regression	573	(1)
Bivariate Regression and Correlation as Special Cases of Multiple Regression	573	(1)
The t Test as a Special Case of the Analysis of Variance	574	(4)
Box 76-1: The Golden Age of Statistics: Four Guys around London	575	(3)
The t Test as a Special Case of the Significance Test for the Correlation Coefficient	578	(5)
The Analysis of Variance as a Special Case of the Significance Test of the Multiple Regression	583	(5)
Choice of Statistical Tests	588	(3)
Box 16-2: Two Women Make a Point about Gender and Statistics	589	(2)
Controversy: Whay is Causality?	591	(1)
Summary	592	(1)
Key Terms	593	(1)
Practice Problems	594	(5)
Making Sense of Advanced Statistical Procedures in Research Articles	599	(40)
Brief Review of Multiple Regression	600	(1)
Hierarchial and Stepwise Multiple Regression	600	(5)
Partial Correlation	605	(1)
Reliability	606	(2)
Factor Analysis	608	(2)
Causal Modeling	610	(5)
Procedures that Compare Groups and Independent and Dependent Variables	615	(1)
Analysis of Covariance (ANCOVA)	616	(1)
Multivariate Analysis of Variance (MANOVA) and Multivariate Analysis of Covariance (MANCOVA)	617	(1)
Overview of Statistical Techniques	618	(1)
Controversy: Should Statistics Be Controversial?	619	(3)
Box 17-1: The Forced Partnership of Fisher and Pearson	620	(2)
How to Read Results Using Unfamiliar Statistical Techniques	622	(1)
Summary	623	(1)
Key Terms	624	(1)
Practice Problems	624	(15)
Appendix A Tables	639	(8)
Table A-1 Normal Curve Areas: Percentage of the Normal Curve between the Mean and the Z Scores Shown	639	(3)
Table A-2 Cutoff Scores for the t Distribution	642	(1)
Table A-3 Cutoff Scores for the F Distribution	643	(3)
Table A-4 Cutoff Scores for the Chi-Square Distribution	646	(1)
Table A-5 Index to Power Tables and Tables Giving Number of Participants Needed for 80% Power	646	(1)
Answers To Set I Practice Problems	647	(30)
Glossary	677	(8)
Glossary of Symbols	685	(2)
References	687	(10)
Index	697

Excerpts

The heart of this book was written over a summer in a small apartment near the Place Saint Ferdinand, having been outlined in nearby cafes and on walks in the Bois de Boulogne. It is based on our 35 years of experience teaching, researching, and writing. We believe that the book we wrote is as different from the conventional lot of statistics texts as Paris is from Calcutta, yet still comfortable and stimulating to the long-suffering community of statistics instructors. Our approach was developed over three decades of successful teaching--successful not only in the sense that students have consistently rated the course (a statistics course, remember) as a highlight of their major, but also in the sense that students come back to us later saying, "I was light-years ahead of my fellow graduate students because of your course," or "Even though I don't do research, your course has really helped me read the journals in my field." The response to the first and second edition has been overwhelming. We have received hundreds of thank-you e-mails and letters from instructors (and from students themselves!) from all over the English-speaking world. Of course, we were also delighted by the enthusiastic review inContemporary Psychology(Bourgeois, 1997). In this third edition we have tried to maintain those things that have been especially appreciated, while reworking the book to take into account the feedback we have received, our own experiences, and advances and changes in the field. We have also added new pedagogical features to make the book even more accessible for students. However, before turning to the third edition, we want to reiterate what we said in the first edition about how this book from the beginning has been quite different from other statistics texts. A BRIEF HISTORY OF THE STATISTICS TEXT GENRE In the 1950s and 1960s statistics texts were dry, daunting, mathematical tomes that quickly left most students behind. In the 1970s, there was a revolution--in swept the intuitive approach, with much less emphasis on derivations, proofs, and mathematical foundations. The approach worked. Students became less afraid of statistics courses and found the material more accessible, even if not quite clear. The intuitive trend continued in the 1980s, adding in the 1990s some nicely straightforward writing. A few texts have now also begun to encourage students to use the computer to do statistical analyses. However, discussions of intuitive understandings are becoming briefer and briefer. The standard is a cursory overview of the key idea and sometimes the associated definitional formula for each technique. Then come the procedures and examples for actually doing the computation, using another "computational" formula. Even with all this streamlining, or perhaps because of it, at the end of the course most students cannot give a clear explanation of the logic behind the techniques they have learned. A few months later they can rarely carry out the procedures either. Most important, the three main purposes of the introductory statistics course ark, not accomplished: Students are not able to make sense of the results of psychology research articles, they are poorly prepared for further courses in statistics (where instructors must inevitably spend half the semester reteaching the introductory course), and the exposure to deep thinking that is supposed to justify the course's meeting general education requirements in the quantitative area has not occurred. WHAT WE HAVE DONE DIFFERENTLY We continue to do what the best of the newer books are already doing well: emphasizing the intuitive, de-emphasizing the mathematical, and explaining everything in direct, simple language. But what we have done differs from these other books in 11 key respects. 1.The definitional formulas are brought to center stagebecause they provide a con