Statistics for the Behavioral and Social Sciences

by Aron, Arthur; Aron, Elaine N.; Coups, Elliot

• ISBN13: 9780131505087
• ISBN10: 0131505084
• Edition: 3rd
• Format: Paperback
• Copyright: 2008-01-01
• Publisher: Prentice Hall

Summary

This unique book capitalizes on a successful approach of using definitional formulas to emphasize concepts of statistics, rather than rote memorization. This conceptual approach constantly reminds readers of the logic behind what they are learning. Procedures are taught verbally, numerically, and visually, which appeals to a variety of users with different learning styles.Focusing on understanding, the book emphasizes the intuitive, de-emphasizes the mathematical, and explains everything in clear, simple languagewith a large number of practice problems.For those trying to master statistics, as well as reading and understanding research articles.

Table of Contents

Preface to the Instructor	xi
Introduction to the Student	xix
Displaying the Order in a Group of Numbers	1	(28)
The Two Branches of Statistical Methods	2	(1)
Some Basic Concepts	2	(1)
Kinds of Variables	3	(1)
Frequency Tables	4	(4)
Frequency Graphs	8	(5)
Shapes of Frequency Distributions	13	(7)
Math Anxiety, Statistics Anxiety, and You: A Message for Those of You Who Are Truly Worried About This Course	14	(4)
Gender, Ethnicity, and Math Performance	18	(2)
Frequency Tables, Histograms, and Frequency Polygons in Research Articles	20	(1)
Summary	21	(1)
Key Terms	22	(1)
Example Worked-Out Problems	22	(1)
Practice Problems	23	(6)
The Mean, Variance, Standard Deviation, and Z Scores	29	(28)
The Mean	30	(6)
The Variance and the Standard Deviation	36	(6)
Z Scores	42	(7)
The Psychology of Statistics and the Tyranny of the Mean	43	(6)
Mean, Variance, Standard Deviation, and Z Scores in Research Articles	49	(2)
Summary	51	(1)
Key Terms	51	(1)
Example Worked-Out Problems	51	(2)
Practice Problems	53	(4)
Correlation and Prediction	57	(50)
Graphing Correlations: The Scatter Diagram	59	(1)
Patterns of Correlation	60	(7)
The Degree of Linear Correlation: The Correlation Coefficient	67	(8)
Galton: Gentleman Genius	71	(4)
Issues in Interpreting the Correlation Coefficient	75	(3)
Prediction	78	(5)
Multiple Regression and Multiple Correlation	83	(3)
The Correlation Coefficient and the Proportion of Variance Accounted For	86	(1)
Correlation and Prediction in Research Articles	86	(3)
Summary	89	(2)
Key Terms	91	(1)
Exampled Worked-Out Problems	91	(3)
Practice Problems	94	(10)
Chapter Appendix: Hypothesis Tests and Power for the Correlation Coefficient	104	(3)
Some Key Ingredients for Inferential Statistics: The Normal Curve, Probability, and Population Versus Sample	107	(25)
The Normal Distribution	107	(10)
Probability	117	(3)
Sample and Population	120	(5)
Surveys, Polls, and 1948's Costly ``Free Sample''	124	(1)
Normal Curves, Probabilities, Samples, and Populations in Research Articles	125	(1)
Summary	125	(1)
Key Terms	126	(1)
Example Worked-Out Problems	126	(2)
Practice Problems	128	(4)
Introduction to Hypothesis Testing	132	(22)
A Hypothesis-Testing Example	133	(1)
The Core Logic of Hypothesis Testing	134	(1)
The Hypothesis-Testing Process	135	(5)
One-Tailed and Two-Tailed Hypothesis Tests	140	(6)
To Be or Not to Be---But Can Not Being Be? The Problem of Whether and When to Accept the Null Hypothesis	143	(3)
Hypothesis Tests in Research Articles	146	(1)
Summary	147	(1)
Key Terms	147	(1)
Example Worked-Out Problem	147	(2)
Practice Problems	149	(5)
Hypothesis Testing and the Means of Samples	154	(31)
The Distribution of Means	154	(10)
Hypothesis Testing with a Distribution of Means	164	(4)
Estimation and Confidence Intervals	168	(4)
Hypothesis Tests about Means of Samples and Confidence Intervals in Research Articles	172	(3)
More about Polls: Sampling Errors and Errors in Thinking about Samples	173	(2)
Summary	175	(1)
Key Terms	176	(1)
Example Worked-Out Problems	176	(1)
Practice Problems	177	(8)
Making Sense of Statistical Significance: Decision Errors, Effect Size, and Statistical Power	185	(32)
Decision Errors	185	(4)
Effect Size	189	(5)
Statistical Power	194	(5)
Effect Sizes for Relaxation and Meditation: A Restful Meta-Analysis	195	(4)
What Determines the Power of a Study?	199	(7)
The Role of Power When Planning a Study	206	(2)
The Role of Power When Interpreting the Results of a Study	208	(3)
Decision Errors, Effect Size, and Power in Research Articles	211	(1)
Summary	212	(1)
Key Terms	213	(1)
Example Worked-Out Problem	213	(1)
Practice Problems	213	(4)
Introduction to the t Test	217	(39)
The t Test for a Single Sample	218	(10)
William S. Gosset, alias ``Student'': Not a Mathematician, but a Practical Man	219	(9)
The t Test for Dependent Means	228	(11)
Assumptions of the t Test	239	(1)
Effect Size and Power for the t Test for Dependent Means	240	(3)
t Test in Research Articles	243	(2)
Summary	245	(1)
Key Terms	245	(1)
Example Worked-Out Problems	245	(4)
Practice Problems	249	(7)
The t Test for Independent Means	256	(33)
The Distribution of Differences Between Means	257	(6)
Hypothesis Testing with a t Test for Independent Means	263	(9)
Assumptions of the t Test for Independent Means	272	(1)
Effect Size and Power for the t Test for Independent Means	272	(1)
The t Test for Independent Means in Research Articles	272	(5)
Two Women Make a Point about Gender and Statistics	274	(3)
Summary	277	(1)
Key Terms	278	(1)
Example Worked-Out Problems	278	(3)
Practice Problems	281	(8)
Introduction to the Analysis of Variance	289	(44)
Basic Logic of the Analysis of Variance	290	(7)
Sir Ronald Fisher, Caustic Genius at Statistics	296	(1)
Carrying Out an Analysis of Variance	297	(8)
Hypothesis Testing with the Analysis of Variance	305	(1)
Assumptions in the Analysis of Variance	306	(1)
Comparing Each Group to Each Other Group	306	(3)
Effect Size and Power for the Analysis of Variance	309	(3)
Factorial Analysis of Variance	312	(3)
Recognizing and Interpreting Interaction Effects	315	(6)
Analysis of Variance in Research Articles	321	(1)
Summary	321	(1)
Key Terms	322	(1)
Example Worked-Out Problems	323	(1)
Practice Problems	324	(9)
Chi-Square Tests and Strategies When Population Distribution Are Not Normal	333	(44)
Chi-Square Tests	333	(2)
The Chi-Square Statistic and the Chi-Square Test for Goodness of Fit	335	(6)
Karl Pearson: Inventor of Chi-Square and Center of Controversy	336	(5)
The Chi-Square Test for Independence	341	(8)
Assumptions for the Chi-Square Tests	349	(1)
Effect Size and Power for the Chi-Square Tests for Independence	350	(3)
Strategies for Hypothesis Testing When Population Distributions Are Not Normal	353	(3)
Data Transformations	356	(4)
Rank-Order Tests	360	(4)
Chi-Square Tests, Data Transformations, and Rank-Order Tests in Research Articles	364	(2)
Summary	366	(1)
Key Terms	367	(1)
Example Worked-Out Problems	367	(4)
Practice Problems	371	(6)
Making Sense of Advanced Statistical Procedures in Research Articles	377	(36)
Brief Review of Multiple Regression	378	(1)
Hierarchical and Stepwise Multiple Regression	378	(4)
Partial Correlation	382	(1)
Reliability	383	(1)
Factor Analysis	384	(3)
Causal Modeling	387	(4)
Procedures that Compare Groups	391	(1)
Analysis of Covariance (ANCOVA)	392	(1)
Multivariate Analysis of Variance (MANOVA) and Multivariate Analysis of Covariance (MANCOVA)	393	(1)
Overview of Statistical Techniques	394	(1)
The Golden Age of Statistics: Four Guys around London	395	(1)
How to Read Results Involving Unfamiliar Statistical Techniques	395	(1)
Summary	396	(1)
Key Terms	397	(1)
Practice Problems	397	(16)
Appendix: Tables	413	(8)
Answers to Set I Practice Problems	421	(21)
Glossary	442	(7)
Glossary of Symbols	449	(2)
References	451	(6)
Index	457

Excerpts

TO THE INSTRUCTOR 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 40 years of experience teaching, researching, and writing. We believe that this book is as different from the conventional lot of statistics books as Paris is from Calcutta, yet still comfortable and stimulating to the long-suffering community of statistics instructors. The approach embodied in this text has been developed during our combined 40 years 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 undergraduate years, 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 understand statistics that I read about in my field." In this third edition of thisBrief Coursewe have tried to maintain those things about the book that have been especially appreciated, while reworking the text 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 some comments. we made in the first edition about how this book from the beginning has been quite different from other statistics texts. WHAT WE HAVE DONE DIFFERENTLY We continue to do what the best of the newer books are already doing well: emphasizing the intuitive, deemphasizing the mathematical, and explaining everything in direct, simple language. But what we have done differs from these other books in 10 key respects. 1.The definitional formulas are brought to center stagebecause they provide a concise symbolic summary of the logic of each particular procedure. All our explanations, examples, practice problems, and test bank items are based on these definitional formulas. (The amount of data to be processed in our practice problems and test items are reduced appropriately to keep computations manageable.) Why this approach? To date, statistics texts have failed to adjust to technologic reality. What is important is not that the students learn to calculate a correlation coefficient with a large data set--computers can do that for them. What is important is that students work problems in a way that they remain constantly aware of the underlying logic of what they are doing. Consider the population variance--the average of the squared deviations from the mean. This concept is immediately clear from the definitional formula (once the student is used to the symbols) Teaching computational formulas today is an anachronism. Researchers do their statistics on computers now. At the same time, the use of statistical software makes the understanding of the basic principles, as they are symbolically expressed in the definitional formula, more important than ever. Students still need to work lots of problems by hand to learn the material. But they need to work them using the definitional formulas that reinforce the concepts, not using the computational formulas that obscure them. Those formulas once made some sense as time-savers for researchers who had to work with large data sets by hand, but they were always poor teaching tools. (Because some instructors may feel naked without them, we still provide the computational formulas, usually in a brief footnote, at the point in the chapter where they would traditionally have been introduced.) 2.Each procedure is taught both verbally and numerically--and usually visually as well. In fact, when we introduceevery

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