Statistical Applications for the Behavioral Sciences

by Laurence G. Grimm (Univ. of Illinois-Chicago)

• ISBN13: 9780471509820
• ISBN10: 0471509825
• Format: Hardcover
• Copyright: 1993-02-01
• Publisher: Wiley

Summary

Explains the conceptual foundations of statistical analyses (particularly inferential statistics), emphasizing the research context. Teaches students how to ''work the formulas'' by presenting cleary defined steps for dealing with statistical problems. Covers chi-square and other nonparametric tests, one/two-way and repeated-measures ANOVA, data analytic procedures such as linear correlation and regression. Boxed features highlight the topics under discussion using published and unpublished research and contain biographical sketches of luminaries in the field of statistics. Each chapter concludes with an extended summary, the relevant formulas and numerous work problems.

Table of Contents

PART 1: BASIC CONCEPTS OF RESEARCH AND DESCRIPTIVE STATISTICS	1	(120)
Basic Concepts in Research	3	(21)
Why Study Research Design in Conjunction with Statistics?	3	(2)
An Overview of the Research Process	5	(2)
Basic Concepts in the Conduct of Research	7	(17)
Feeling Good and Helping Others A Study with a Confound	16	(4)
Summary	20	(1)
Work Problems	20	(4)
Scales of Measurement and Data Display	24	(23)
Measurement and Its Scales	24	(3)
Discrete Variables, Continuous Variables, and the Real Limits of Numbers	27	(4)
Some Notes on the History of Statistics	30	(1)
Using Tables to Organize Data	31	(4)
Using Graphs to Display Data	35	(6)
Using a Graph to Provide a Visual Display of Data	40	(1)
The Shape of Things to Come	41	(6)
Summary	44	(1)
Work Problems	45	(2)
Measures of Central Tendency	47	(22)
Describing a Distribution of Scores	47	(1)
Populations and Samples	48	(1)
The Rounding Rule	49	(1)
The Mean	49	(5)
The Median	54	(4)
The Mode	58	(1)
How the Shape of Distributions Affects Measures of Central Tendency	59	(2)
When to Use the Mean, Median, and Mode	61	(1)
Experimental Research and the Mean: A Glimpse of Things to Come	62	(7)
Learning to Control Your Heart Rate	63	(2)
Summary	65	(1)
Key Formulas for Chapter 3	66	(1)
Work Problems	66	(3)
Measures of Variability	69	(23)
The Importance of Measures of Variability	69	(1)
Range	70	(3)
Mean Deviation	73	(2)
The Variance	75	(6)
The Substantive Importance of the Variance	81	(1)
The Standard Deviation	81	(2)
The Origins of the Standard Deviation	83	(1)
Simple Transformations and Their Effect on the Mean and Variance	83	(1)
Deciding Which Measure of Variability to Use	84	(8)
Summary	86	(1)
Key Formulas for Chapter 4	87	(1)
Work Problems	88	(4)
The Normal Curve and Transformation: Percentiles, z Scores and T Scores	92	(29)
Percentile Rank	91	(8)
The Normal Distributions	99	(4)
Abraham De Moivre	101	(2)
Standard Scores: z Scores and T Scores	103	(18)
With z Scores You Can Compare Apples and Oranges	115	(1)
Summary	115	(1)
Key Formulas for Chapter 5	116	(1)
Work Problems	116	(5)
PART 2: INFERENTIAL STATISTICS: PARAMETRIC TESTS	121	(306)
Hypothesis Testing and Sampling Distributions	123	(17)
Inferential Statistics	123	(1)
Two Kinds of Inferential Procedures	124	(6)
Sampling Distributions	130	(10)
Population and Sample Distributions A Sampling Distribution of Means Summary	137	(1)
Key Formulas for Chapter 6	138	(1)
Work Problems	138	(2)
Testing the Significance of a Single Mean: The Single-Sample z and t Tests	140	(27)
The Research Context	140	(2)
Using the Sampling Distribution of Means for the Single-Sample z Test	142	(8)
The Implications of Rejecting the Null Hypothesis	150	(1)
Type I and Type II Errors	151	(2)
Is a Significant Finding ``Significant''?	153	(1)
The Statistical Test for the Mean of a Population When is Unknown: The t Distributions	154	(13)
Visual Illusions and Immaculate Perception	160	(2)
Summary	162	(1)
Key Formulas for Chapter 7	162	(1)
Work Problems	163	(4)
Directional and Nondirectional Testing of the Difference Between Two Means: The Independent-Samples t Test	167	(31)
The Research Context	167	(3)
William Gossett	169	(1)
The Independent-Samples t test	170	(14)
Can Epileptic Seizures Be Controlled by Relaxation Training?	183	(1)
Directional Tests of Significance	184	(14)
Summary	189	(1)
Key Formulas for Chapter 8	190	(1)
Work Problems	191	(7)
Testing the Difference Between Two Means: The Dependent-Samples t Test	198	(19)
The Research Context	198	(3)
The Sampling Distribution for the Dependent-Samples t Test	201	(4)
The t Distribution for Dependent-Samples	205	(3)
Comparing the Independent- and Dependent-Samples t Tests	208	(1)
The One-Tailed Test Revisited	209	(1)
An Example of the Questionable Use of a One-Tailed Dependent-Samples t Test	210	(1)
Assumptions of the Dependent-Samples t Test	210	(2)
The First Applications of the t Test	211	(1)
Summary	212	(1)
Key Formulas for Chapter 9	212	(1)
Work Problems	212	(5)
Confidence Intervals and Hypothesis Testing	217	(24)
The Research Context	217	(2)
Confidence Intervals When Q is Known	219	(2)
Sampling Distributions and Confidence Intervals	221	(2)
The Probabilistic Nature of Confidence Intervals	223	(1)
Confidence Intervals When Q is Unknown	224	(3)
Using Confidence Intervals for Hypothesis Testing	227	(14)
Where Did the Passion Go?	228	(4)
Premarital Cohabitation: A New America Institution	232	(2)
Summary	234	(1)
Key Formulas for Chapter 10	235	(1)
Work Problems	236	(5)
Power Analysis and Hypothesis Testing	241	(16)
Decision Making While Hypothesis Testing	242	(1)
Why Study Power?	243	(1)
The Size of the Treatment Effect and Power	244	(3)
Using the Power Table	247	(2)
The Bigger the Treatment Effect the Greater the Power	249	(1)
Determining the Effect Size: The Achilles Heel of the Power Analysis	250	(1)
Determining Sample Size for a Single-Sample Test	251	(2)
Failing to Reject the Null Hypothesis: Can a Power Analysis Help?	253	(4)
Psychopathy and Frontal Lobe Damage	254	(1)
Summary	255	(1)
Key Formulas for Chapter 11	255	(1)
Work Problems	256	(1)
One-Way Analysis of Variance	257	(34)
The Research Context	258	(1)
Sir Ronald Fisher	259	(1)
The Conceptual Basis of ANOVA: Sources of Variation	259	(10)
Computing the F Ratio in ANOVA	269	(6)
Testing for Statistical Significance	275	(2)
The ANOVA Summary Table	277	(1)
Reporting the Results of the ANOVA	278	(2)
Initiation Rites and Club Loyalty	278	(2)
An Example of ANOVA with Unequal Numbers of Subjects	280	(1)
Strength of Association	280	(3)
Locating the Source of Significance: The Protected t Test	283	(8)
Summary	285	(1)
Key Formulas for Chapter 12	285	(1)
Work Problems	286	(5)
Two-Way Analysis of Variance	291	(45)
The Research Context	291	(12)
The Logic of the Two-Way ANOVA	303	(2)
Definitional and Computational Formulas for the Two-Way ANOVA	305	(12)
Testing the Statistical Significance of the F Ratios	317	(4)
Do Firearms Create Aggression?	319	(2)
Strength of Association	321	(1)
Multiple Comparisons	321	(4)
Interpreting the Factors in a Two-Way ANOVA	325	(11)
Summary	325	(1)
Key Formulas for Chapter 13	326	(2)
Work Problems	328	(8)
Repeated-Measures Analysis of Variance	336	(25)
The Research Context	337	(2)
The Logic of the Repeated-Measures ANOVA	339	(3)
The Formulas for the Repeated-Measures ANOVA	342	(8)
Testing the Statistical Significance of the F Ratio	350	(1)
Interpreting the Findings	350	(1)
The ANOVA Summary Table	351	(1)
Multiple Comparisons	351	(3)
The Inverted U Relation Between Arousal and Task Performance	353	(1)
Strength of Association	354	(1)
Assumptions of the Repeated-Measures ANOVA	354	(7)
Summary	355	(1)
Key Formulas for Chapter 14	356	(1)
Work Problems	357	(4)
Linear Correlation	361	(35)
The Research Context	361	(1)
The Correlation Coefficient and Scatter Diagrams	362	(15)
Karl Pearson	364	(13)
Testing the Significance of the Pearson r	377	(5)
Maternal Cognitions and Aggressive Children	381	(1)
Factors That Can Create Misleading Correlation Coefficients	382	(14)
Summary	387	(2)
Key Formulas for Chapter 15	389	(1)
Work Problems	389	(7)
Linear Regression	396	(31)
The Research Context	396	(1)
Overview of Regression	397	(3)
Establishing the Regression Line	400	(13)
Sir Francis Galton	411	(2)
Putting It All Together: A Worked Problem	413	(5)
Why is a Prediction Equation Called a Regression Equation?	417	(1)
The Coefficient of Determination in the Context of Prediction	418	(1)
The Pitfalls of Linear Regression	419	(8)
Summary	421	(1)
Key Formulas for Chapter 16	422	(2)
Work Problems	424	(3)
PART 3: INFERENTIAL STATISTICS: NONPARAMETRIC TESTS	427	(64)
The Chi-Square Test	429	(27)
The Research Context	430	(1)
The Chi-Square Test for One-Way Designs: The Goodness-of Fit Test	431	(6)
The Chi-Square Distribution and Degrees of Freedom	437	(3)
Two-Way Designs: The Chi-Square Test for Independence	440	(7)
The Chi-Square Test for a 2 x 2 Contingency Table	447	(1)
What is Beautiful is Good	447	(1)
Which Cells Are Major Contributors to a Significant Chi-Square Test?	448	(2)
Using the Chi-Square Test with Quantitative Variables	450	(1)
Assumptions of the Chi-Square Test	450	(6)
Summary	451	(1)
Key Formulas for Chapter 17	451	(1)
Work Problems	452	(4)
Other Nonparametric Tests	456	(35)
The Research Context	456	(1)
The Use of Ranked Data in Research	457	(1)
The Spearman Rank Correlation Coefficient	458	(7)
The Point-Biserial Correlation Coefficient	465	(5)
The Mann-Whitney U Test	470	(6)
The Wilcoxon Signed-Ranks Test	476	(5)
Do Infants Notice the Difference Between Lip Movements and Speech Sounds?	480	(1)
Using Nonparametric Tests	481	(10)
Summary	482	(1)
Key Formulas for Chapter 18	483	(1)
Work Problems	484	(7)
Appendixes	491	(80)
A. Some Basic Concepts of Probability	491	(11)
B. Statistical Tables	502	(15)
1. z Table	502	(4)
2. t Table	506	(1)
3. Power Table (Finding Power)	507	(1)
4. Power Table (Finding Delta)	508	(1)
5. F Table	508	(3)
6. Pearson r Table	511	(1)
7. Spearman rs Table	512	(1)
8. Chi-Square Table	513	(1)
9. Mann-Whitney U Table	514	(2)
10. Wilcoxon Signed-Ranks Table	516	(1)
C. Answers to Problems	517	(54)
Glossary	571	(6)
References	577	(9)
Index	586