Explaining Psychological Statistics, 2nd Edition,9780471345824

Explaining Psychological Statistics, 2nd Edition

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Edition: 2nd
ISBN13: 9780471345824
ISBN10: 0471345822
Format: Hardcover
Pub. Date: 2000-11-01
Publisher(s): Wiley
List Price: $130.69

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Summary

This comprehensive graduate-level statistics text is aimed at students with a minimal background in the area or those who are wary of the subject matter. The new edition of this successful text will continue to offer students a lively and engaging introduction to the field, provide comprehensive coverage of the material, and will also include examples and exercises using common statistical software packages (SPSS).

Author Biography

BARRY H. COHEN, PhD, is the Associate Director of the master’s program in psychology at New York University, where he has been teaching statistics for more than fifteen years.

Table of Contents

Preface to the Second Edition: For the Instructor xxv
Preface to the Second Edition: For the Student xxxiii
Acknowledgments xxxvii
Part One Descriptive Statistics 1(123)
Introduction to Psychological Statistics
1(20)
Conceptual Foundation
1(11)
What Is (Are) Statistics?
1(1)
Statistics and Research
2(1)
Variables and Constants
2(1)
Scales of Measurement
3(3)
Continuous versus Discrete Variables
6(1)
Scales versus Variables
7(1)
Parametric versus Nonparametric Statistics
7(1)
Independent versus Dependent Variables
7(1)
Experimental versus Correlational Research
8(1)
Populations versus Samples
9(1)
Statistical Formulas
10(1)
Summary
10(1)
Exercises
11(1)
Basic Statistical Procedures
12(6)
Variables with Subscripts
12(1)
The Summation Sign
12(1)
Properties of the Summation Sign
13(3)
Rounding Off Numbers
16(1)
Summary
17(1)
Exercises
18(1)
Optional Material
18(3)
Double Summations
18(1)
Random Variables and Mathematical Distributions
19(1)
Summary
20(1)
Exercises
20(1)
Frequency Tables, Grapphs, and Distributions
21(28)
Conceptual Foundation
21(11)
Frequency Distributions
21(1)
The Cumulative Frequency Distribution
22(1)
The Relative Frequency and Cumulative Relative Frequency Distributions
23(1)
The Cumulative Percentage Distribution
23(1)
Percentiles
24(1)
Graphs
24(4)
Real versus Theoretical Distributions
28(1)
Summary
29(2)
Exercises
31(1)
Basic Statistical Procedures
32(12)
Grouped Frequency Distributions
32(1)
Apparent versus Real Limits
32(1)
Constructing Class Intervals
33(1)
Choosing the Class Interval Width
33(1)
Choosing the Limits of the Lowest Interval
34(1)
Relative and Cumulative Frequency Distributions
35(1)
Cumulative Percentage Distribution
35(1)
Finding Percentiles and Percentile Ranks by Formula
36(3)
Graphing a Grouped Frequency Distribution
39(1)
Guidelines for Drawing Graphs of Frequency Distributions
40(2)
Summary
42(1)
Exercises
43(1)
Optional Material
44(5)
Stem-and-Leaf Displays
44(3)
Summary
47(1)
Exercises
47(1)
Key Formulas
48(1)
Measures of Central Tendency and Variability
49(40)
Conceptual Foundation
49(18)
Measures of Central Tendency
49(4)
Measures of Variability
53(8)
Skewed Distributions
61(4)
Summary
65(1)
Exercises
66(1)
Basic Statistical Procedures
67(10)
Formulas for the Mean
67(2)
Computational Formulas for the Variance and Standard Deviation
69(2)
Obtaining the Standard Deviation Directly from Your Calculator
71(1)
Properties of the Mean
72(1)
Properties of the Standard Deviation
73(2)
Summary
75(1)
Exercises
76(1)
Optional Material
77(12)
Box-and-Whisker Plots
77(3)
Dealing with Outliers
80(1)
Measuring Skewness
81(2)
Measuring Kurtosis
83(2)
Summary
85(1)
Exercises
86(1)
Key Formulas
86(3)
Standardized Scores and the Normal Distribution
89(35)
Conceptual Foundation
89(15)
z Scores
89(2)
Finding a Raw Score from a z Score
91(1)
Sets of z Scores
91(1)
Properties of z Scores
92(1)
Sat, T, and IQ Scores
93(1)
The Normal Distribution
94(2)
Introducing Probability: Smooth Distributions versus Discrete Events
96(1)
Real Distributions versus the Normal Distribution
97(1)
z Scores as a Research Tool
98(1)
Sampling Distribution of the Mean
99(1)
Standard Error of the Mean
100(1)
Sampling Distribution versus Population Distribution
101(1)
Summary
102(1)
Exercises
103(1)
Basic Statistical Procedures
104(11)
Finding Percentile Ranks
104(2)
Finding the Area between Two z Scores
106(1)
Finding the Raw Scores Corresponding to a Given Area
107(1)
Areas in the Middle of a Distribution
108(1)
From Score to Proportion and Proportion to Score
109(1)
Describing Groups
109(4)
Summary
113(1)
Exercises
114(1)
Optional Material
115(9)
The Mathematics of the Normal Distribution
115(1)
The Central Limit Theorem
116(1)
Probability
117(4)
Summary
121(1)
Exercises
122(1)
Key Formulas
123(1)
Part Two One- and Two-Sample Hypothesis Tests 124(117)
Introduction to Hypothesis Testing: The One-Sample z Test
124(30)
Conceptual Foundation
124(13)
Selecting a Group of Subjects
124(1)
The Need for Hypothesis Testing
125(1)
The Logic of Null Hypothesis Testing
126(1)
The Null Hypothesis Distribution
126(1)
The Null Hypothesis Distribution for the One-Sample Case
127(1)
z Scores and the Null Hypothesis Distribution
128(1)
Statistical Decisions
129(1)
The z Score as Test Statistic
130(1)
Type I and Type II Errors
131(1)
The Trade-Off between Type I and Type II Errors
132(1)
One-Tailed versus Two-Tailed Tests
133(2)
Summary
135(1)
Exercises
136(1)
Basic Statistical Procedures
137(12)
State the Hypotheses
137(2)
Select the Statistical Test and the Significance Level
139(1)
Select the Sample and Collect the Data
139(1)
Find the Region of Rejection
139(2)
Calculate the Test Statistic
141(1)
Make the Statistical Decision
142(1)
Interpreting the Results
143(1)
Assumptions Underlying the One-Sample z Test
143(1)
Varieties of the One-Sample Test
144(1)
Why the One-Sample Test Is Rarely Performed
145(1)
Publishing the Results of One-Sample Tests
146(1)
Summary
147(1)
Exercises
148(1)
Optinal Material
149(5)
Summary
152(1)
Exercises
152(1)
Key Formulas
153(1)
Interval Estimation and the t Distribution
154(28)
Conceptual Foundation
154(11)
The Mean of the Null Hypothesis Distribution
155(1)
When the Population Standard Deviation Is Not Known
155(1)
Calculating a Simple Example
156(1)
The t Distribution
156(2)
Degrees of Freedom and the t Distribution
158(1)
Critical Values of the t Distribution
159(1)
Calculating the One-Sample t Test
160(1)
Sample Size and the One-Sample t Test
160(1)
Uses for the One-Sample t Test
161(1)
Cautions Concerning the One-Sample t Test
161(1)
Estimating the Population Mean
162(1)
Summary
163(1)
Exercises
164(1)
Basic Statistical Procedures
165(9)
Select the Sample Size
165(1)
Select the Level of Confidence
165(1)
Select the Random Sample and Collect the Data
165(1)
Calculate the Limits of the Interval
166(4)
Relationship between Interval Estimation and Null Hypothesis Testing
170(1)
Assumptions Underlying the One-Sample t Test and the Confidence Interval for the Population Mean
170(1)
Use of the Confidence Interval for the Population Mean
171(1)
Publishing the Results of One-Sample t Tests
172(1)
Summary
172(1)
Exercises
173(1)
Optional Material
174(8)
The Sampling Distribution of the Variance
175(1)
The Chi-Square Distribution
176(1)
Hypothesis Testing for Sample Variances
176(2)
The t Distribution Revisited
178(1)
Some Properties of Estimators
178(1)
Summary
179(1)
Exercises
179(1)
Key Formulas
180(2)
The t Test for Two Independent Sample Means
182(32)
Conceptual Foundation
182(11)
Null Hypothesis Distribution for the Differences of Two Sample Means
183(1)
Standard Error of the Difference
184(1)
Formula for Comparing the Means of Two Samples
185(1)
Null Hypothesis for the Two-Sample Case
186(1)
The z Test for Two Large Samples
187(1)
Separate-Variances t Test
187(1)
The Pooled-Variances Estimate
188(1)
The Pooled-Variances t Test
189(1)
Formula for Equal Sample Sizes
189(1)
Calculating the Two-Sample t Test
190(1)
Interpreting the Calculated t
190(1)
Limitations of Statistical Conclusions
191(1)
Summary
192(1)
Exercises
192(1)
Basic Statistical Procedures
193(13)
State the Hypotheses
194(1)
Select the Statistical Test and the Significance Level
194(1)
Select the Samples and Collect the Data
195(1)
Find the Region of Rejection
195(1)
Calculate the Test Statistic
196(1)
Make the Statistical Decision
197(1)
Interpreting the Results
197(1)
Confidence Intervals for the Difference between Two Population Means
198(2)
Assumptions of the t Test for Two Independent Samples
200(2)
When to Use the Two-Sample t Test
202(1)
When to Construct Confidence Intervals
203(1)
Publishing the Results of the Two-Sample t Test
203(1)
Summary
204(1)
Exercises
205(1)
Optional Material
206(8)
Zero Differences between Sample Means
206(1)
Adding Variances to Find the Variance of the Difference
206(1)
When to Use the Separate-Variances t Test
207(3)
Heterogeneity of Variance as an Experimental Result
210(1)
Summary
210(1)
Exercises
211(1)
Key Formulas
212(2)
Statistical Power and Effect Size
214(27)
Conceptual Foundation
214(11)
The Alternative Hypothesis Distribution
214(2)
The Expected t Value (Delta)
216(2)
The Effect Size
218(1)
Power Analysis
219(1)
The Interpretation of t Values
220(1)
Estimating Effect Size
221(2)
Manipulating Power
223(1)
Summary
223(1)
Exercises
224(1)
Basic Statistical Procedures
225(7)
Using Power Tables
225(1)
The Relationship between Alpha and Power
226(1)
Power Analysis with Fixed Sample Sizes
227(1)
Sample Size Determination
228(2)
The Power of a One-Sample Test
230(1)
Summary
230(1)
Exercises
231(1)
Optional Material
232(9)
The Case of Unequal Sample Sizes
232(1)
The Case against Null Hypothesis Testing: The Null Is Never True
233(1)
The Limited Case for NHST
233(1)
The General Case for NHST: Screening Out Small Effect Sizes
234(2)
Supplementing the Null Hypothesis Test
236(2)
Summary
238(1)
Exercises
239(1)
Key Formulas
239(2)
Part Three Hypothesis Tests Involving Two Measures on Each Subject 241(83)
Linear Correlation
241(31)
Conceptual Foundation
241(12)
Perfect Correlation
241(1)
Negative Correlation
242(1)
The Correlation Coefficient
242(2)
Linear Transformations
244(1)
Graphing the Correlation
244(2)
Dealing with Curvilinear Relationships
246(1)
Problems in Generalizing from Sample Correlations
247(2)
Correlation Does Not Imply Causation
249(1)
True Experiments Involving Correlation
250(1)
Summary
250(1)
Exercises
251(2)
Basic Statistical Procedures
253(11)
The Covariance
253(1)
The Unbiased Covariance
254(1)
An Example of Calculating Pearson's r
254(1)
Alternative Formulas
255(1)
Which Formula to Use
256(1)
Testing Pearson's r for Significance
256(2)
Understanding the Degrees of Freedom
258(1)
Assumptions Associated with Pearson's r
258(2)
Uses of the Pearson Correlation Coefficient
260(1)
Publishing the Results of Correlational Studies
261(1)
Summary
261(1)
Exercises
262(2)
Optional Material
264(8)
The Power Associated with Correlational Tests
264(2)
Fisher Z Transformation
266(1)
The Confidence Interval for p
266(1)
Testing a Null Hypothesis Other Than p = 0
267(1)
Testing the Difference of Two Independent Sample r's
268(1)
Summary
269(1)
Exercises
269(1)
Key Formulas
270(2)
Linear Regression
272(29)
Conceptual Foundation
272(11)
Perfect Predictions
272(1)
Predicting with z Scores
273(1)
Calculating an Example
273(1)
Regression toward the Mean
274(1)
Graphing Regression in Terms of z Scores
274(1)
The Raw-Score Regression Formula
275(1)
The Slope and the Y Intercept
276(1)
Predictions Based on Raw Scores
277(1)
Interpreting the Y Intercept
278(1)
Quantifying the Errors around the Regression Line
278(1)
The Variance of the Estimate
279(1)
Explained and Unexplained Variance
280(1)
The Coefficient of Determination
280(1)
The Coefficient of Nondetermination
281(1)
Calculating the Variance of the Estimate
281(1)
Summary
281(1)
Exercises
282(1)
Basic Statistical Procedures
283(10)
Life Insurance Rates
283(1)
Regression in Terms of Sample Statistics
283(1)
Finding the Regression Equation
284(1)
Making Predictions
284(1)
Using Sample Statistics to Estimate the Variance of the Estimate
285(1)
Standard Error of the Estimate
286(1)
Confidence Intervals for Predictions
286(1)
An Example of a Confidence Interval
287(1)
Assumptions Underlying Linear Regression
288(1)
Regressing X on Y
288(1)
Raw Score Formulas
289(1)
When to Use Linear Regression
289(2)
Summary
291(1)
Exercises
292(1)
Optional Material
293(8)
The Point-Biserial Correlation Coefficient
293(1)
Calculating rpb
294(1)
Deriving rpb from a t Value
295(1)
Interpreting rpb
296(1)
Strength of Association in the Population (Omega Squared)
296(1)
Biserial r
297(1)
Summary
298(1)
Exercises
298(1)
Key Formulas
299(2)
The Matched t Test
301(23)
Conceptual Foundation
301(9)
Before-After Design
301(1)
The Direct-Difference Method
302(1)
The Matched t Test as a Function of Linear Correlation
303(2)
Reduction in Degrees of Freedom
305(1)
Drawback of the Before-After Design
305(1)
Other Repeated-Measures Designs
305(1)
Matched-Pairs Design
306(1)
Correlated or Dependent Samples
307(1)
When Not to Use the Matched t Test
307(1)
Summary
308(1)
Exercises
309(1)
Basic Statistical Procedures
310(10)
State the Hypotheses
310(1)
Select the Statistical Test and the Significance Level
310(1)
Select the Samples and Collect the Data
310(1)
Find the Region of Rejection
311(1)
Calculate the Test Statistic
312(1)
Make the Statistical Decision
312(1)
Using the Correlation Formula for the Matched t Test
312(1)
Raw-Score Formula for the Matched t Test
313(1)
The Confidence Interval for the Difference of Two Population Means
314(1)
Assumptions of the Matched t Test
315(1)
The Varieties of Designs Calling for the Matched t Test
315(2)
Publishing the Results of a Matched t Test
317(1)
Summary
317(1)
Exercises
318(2)
Optional Material
320(4)
Summary
322(1)
Exercises
322(1)
Key Formulas
323(1)
Part Four Analysis of Variance without Repeated Measures 324(111)
One-Way Independent ANOVA
324(38)
Conceptual Foundation
324(12)
Transforming the t Test into ANOVA
325(1)
Expanding the Denominator
326(1)
Expanding the Numerator
326(1)
The F Ratio
327(1)
The F Ratio As a Ratio of Two Population Variance Estimates
327(1)
Degrees of Freedom and the F Distribution
328(1)
The Shape of the F Distribution
329(1)
ANOVA As a One-Tailed Test
329(1)
Using Tables of F Values
330(1)
An Example with Three Equal-Sized Groups
330(1)
Calculating a Simple ANOVA
331(1)
Interpreting the F Ratio
332(1)
Advantages of the One-Way ANOVA
333(1)
Summary
334(1)
Exercises
334(2)
Basic Statistical Procedures
336(14)
An ANOVA Example with Unequal Sample Sizes
336(1)
State the Hypotheses
336(1)
Select the Statistical Test and the Significance Level
336(1)
Select the Samples and Collect the Data
336(1)
Find the Region of Rejection
337(1)
Calculate the Test Statistic
337(2)
Make the Statistical Decision
339(1)
Interpreting Significant Results
339(1)
The Sums of Squares Approach
340(1)
Raw-Score Formulas
340(2)
Assumptions of the One-Way ANOVA for Independent Groups
342(1)
Varieties of the One-Way ANOVA
343(2)
Publishing the Results of a One-Way ANOVA
345(2)
Summary
347(1)
Exercises
348(2)
Optional Material
350(12)
Testing Homogeneity of Variance
350(1)
Effect Size and Proportion of Variance Accounted For
351(3)
The Power of ANOVA
354(3)
Summary
357(1)
Exercises
358(1)
Key Formulas
359(3)
Multiple Comparisons
362(29)
Conceptual Foundation
362(11)
The Number of Possible t Tests
362(1)
Experimentwise Alpha
363(1)
Complex Comparisons
364(1)
Planned Comparisons
364(1)
Fisher's Protected t Tests
364(2)
Complete versus Partial Null Hypotheses
366(1)
Tukey's HSD Test
367(1)
The Studentized Range Statistic
367(1)
Advantages and Disadvantages of Tukey's Test
368(1)
Other Procedures for Post Hoc Pairwise Comparisons
369(2)
The Advantage of Planning Ahead
371(1)
Summary
371(1)
Exercises
372(1)
Basic Statistical Procedures
373(10)
Calculating Protected t Tests
373(1)
Calculating Fisher's LSD
374(1)
Calculating Tukey's HSD
374(1)
Interpreting the Results of the LSD and HSD Procedures
375(1)
Assumptions of the Fisher and Tukey Procedures
376(1)
Bonferroni t, or Dunn's Test
376(1)
Complex Comparisons
377(3)
Scheffe's Test
380(1)
Which Post Hoc Comparison Procedure Should You Use?
380(1)
Summary
381(1)
Exercises
382(1)
Optional Material
383(8)
The Harmonic Mean
383(1)
Orthogonal Contrasts
384(1)
Planned (a Priori) Comparisons
385(3)
Summary
388(1)
Exercises
388(1)
Key Formulas
389(2)
Two-Way ANOVA
391(44)
Conceptual Foundation
391(16)
Calculating a Simple One-Way ANOVA
391(1)
Adding a Second Factor
392(1)
Regrouping the Sums of Squares
393(1)
New Terminology
393(1)
Calculating the Two-Way ANOVA
394(1)
Calculating MSw
395(1)
Calculating MSbet for the Drug Treatment Factor
395(1)
Calculating MSbet for the Gender Factor
395(1)
Graphing the Cell Means
396(1)
The Case of Zero Interaction
397(1)
General Linear Model
398(1)
Calculating the Variability Due to Interaction
399(1)
Types of Interactions
399(3)
Separating Interactions from Cell Means
402(1)
The F Ratio in a Two-Way ANOVA
403(1)
Advantages of the Two-Way Design
404(1)
Summary
405(1)
Exercises
406(1)
Basic Statistical Procedures
407(14)
State the Null Hypothesis
407(1)
Select the Statistical Test and the Significance Level
408(1)
Select the Samples and Collect the Data
408(1)
Find the Regions of Rejection
408(1)
Calculate the Test Statistics
408(5)
Make the Statistical Decisions
413(1)
The Summary Table for a Two-Way ANOVA
413(1)
Interpreting the Results
413(1)
Assumptions of the Two-Way ANOVA for Independent Groups
414(1)
Advantages of the Two-Way ANOVA with Two Experimental Factors
415(1)
Advantages of the Two-Way ANOVA with One Grouping Factor
416(1)
Advantages of the Two-Way ANOVA with Two Grouping Factors
417(1)
Publishing the Results of a Two-Way ANOVA
417(1)
Summary
418(1)
Exercises
419(2)
Optional Material
421(14)
Post Hoc Comparisons for the Two-Way ANOVA
421(4)
Planned Comparisons
425(2)
Estimating Effect Sizes
427(1)
The Two-Way ANOVA for Unbalanced Designs
428(3)
Summary
431(1)
Exercises
432(1)
Key Formulas
433(2)
Part Five Analysis of Variance with Repeated Measures 435(72)
Repeated Measures ANOVA
435(37)
Conceptual Foundation
435(11)
Calculation of an Independent-Groups ANOVA
435(1)
The One-Way RM ANOVA as a Two-Way Independent ANOVA
436(1)
Calculating the SS Components of the RM ANOVA
437(1)
Comparing the Independent ANOVA with the RM ANOVA
438(1)
The Advantage of the RM ANOVA
439(1)
Picturing the Subject by Treatment Interaction
440(1)
Comparing the RM ANOVA to a Matched t Test
440(2)
Dealing with Order Effects
442(1)
Differential Carryover Effects
443(1)
The Randomized-Blocks Design
443(1)
Summary
444(1)
Exercises
445(1)
Basic Statistical Procedures
446(18)
State the Hypotheses
446(1)
Select the Statistical Test and the Significance Level
447(1)
Select the Samples and Collect the Data
447(1)
Find the Region of Rejection
447(1)
Calculate the Test Statistic
447(1)
Make the Statistical Decision
448(1)
Interpreting the Results
449(1)
The Residual Component
449(2)
Assumptions of the RM ANOVA
451(2)
Dealing with a Lack of Sphericity
453(3)
Post Hoc Comparisons
456(1)
Varieties of Repeated-Measures and Randomized-Blocks Designs
457(1)
Publishing the Results of an RM ANOVA
458(2)
Summary
460(1)
Exercises
461(3)
Optional Material
464(8)
Power of the RM ANOVA
464(1)
Counterbalancing
464(3)
Intraclass Correlation
467(2)
Summary
469(1)
Exercises
470(1)
Key Formulas
471(1)
Two-Way Mixed Design ANOVA
472(35)
Conceptual Foundation
472(10)
The One-Way RM ANOVA Revisited
472(2)
Converting the One-Way RM ANOVA to a Mixed Design ANOVA
474(3)
Two-Way Interaction in the Mixed Design ANOVA
477(1)
Summarizing the Mixed Design ANOVA
478(1)
Interpreting the Results
479(1)
The Varieties of Mixed Designs
479(2)
Summary
481(1)
Exercises
482(1)
Basic Statistical procedures
482(15)
State the Hypotheses
483(1)
Select the Statistical Test and the Significance Level
483(1)
Select the Samples and Collect the Data
483(1)
Find the Regions of Rejection
484(1)
Calculate the Test Statistics
485(2)
Make the Statistical Decisions
487(1)
Interpreting the Results
488(1)
Publishing the Results of a Mixed ANOVA
489(1)
Assumptions of the Mixed Design ANOVA
489(2)
Dealing with a Lack of Sphericity in Mixed Designs
491(1)
A Special Case: The Before-After Mixed Design
491(1)
Post Hoc Comparisons
492(1)
An Excerpt from the Psychological Literature
493(1)
Summary
494(1)
Exercises
495(2)
Optional Material
497(10)
Post Hoc Comparisons When the Two Factors Interact
497(2)
Planned and Complex Comparisons
499(1)
Removing Error Variance from Counterbalanced Designs
500(3)
Summary
503(1)
Exercises
504(1)
Key Formulas
505(2)
Part Six Multiple Regression and Its Connection to ANOVA 507(104)
Multiple Regression
507(56)
Conceptual Foundation
507(20)
Uncorrelated Predictors
508(1)
The Standardized Regression Equation
509(1)
More Than Two Mutually Uncorrelated Predictors
509(1)
The Sign of Correlations
510(1)
Two Correlated Predictors
510(1)
The Beta Weights
511(2)
Completely Redundant Predictors
513(1)
Partial Regression Slopes
513(2)
Degrees of Freedom
515(1)
Semipartial Correlations
515(1)
Calculating the Semipartial Correlation
516(1)
Suppressor Variables
517(1)
Complementary Variables
518(1)
The Raw-Score Prediction Formula
519(1)
Partial Correlation
520(2)
Finding the Best Prediction Equation
522(1)
Hierarchical (Theory-Based) Regression
523(1)
Summary
524(1)
Exercises
525(2)
Basic Statistical Procedures
527(21)
The Significance Test for Multiple R
527(1)
Tests for the Significance of Individual Predictors
528(1)
Forward Selection
529(2)
Backward Elimination
531(1)
Stepwise Regression
532(1)
The Misuse of Stepwise Regression
533(1)
Problems Associated with Having Many Predictors
533(4)
Too Few Predictors
537(1)
Minimal Sample Size
537(1)
Basic Assumptions of Multiple Regression
537(3)
Regression with Dichotomous Predictors
540(1)
Multiple Regression as a Research Tool
541(3)
Publishing the Results of Multiple Regression
544(1)
Summary
545(1)
Exercises
546(2)
Optional Material
548(15)
Dealing with Curvilinear Relationships
548(3)
Moderator Variables
551(2)
Multiple Regression with a Dichotomous Criterion
553(3)
Path Analysis
556(3)
Summary
559(1)
Exercises
560(1)
Key Formulas
561(2)
The Regression Approach to ANOVA
563(48)
Conceptual Foundation
563(14)
Dummy Coding
564(1)
The Regression Plane
564(1)
Effect Coding
565(1)
The General Linear Model
566(1)
Equivalence of Testing ANOVA and R2
566(1)
Two-Way ANOVA as Regression
567(2)
The GLM for Higher-Order ANOVA
569(1)
Analyzing Unbalanced Designs
570(3)
Methods for Controlling Variance
573(2)
Summary
575(1)
Exercises
576(1)
Basic Statistical Procedures
577(23)
Simple ANCOVA as Multiple Regression
578(2)
The Linear Regression Approach to ANCOVA
580(8)
Post Hoc Comparisons
588(1)
Performing ANCOVA by Multiple Regression
589(1)
Power and Effect Size
589(1)
The Assumptions of ANCOVA
590(1)
Additional Considerations
591(1)
Factorial ANCOVA
592(1)
Using Two or More Covariates
592(1)
Alternatives to ANCOVA
593(2)
Using ANCOVA with Intact Groups
595(1)
Summary
596(1)
Exercises
597(3)
Optional Material
600(11)
The Analysis of Trends
600(7)
Summary
607(1)
Exercises
608(1)
Key Formulas
609(2)
Part Seven Non Parametric Statistics 611(78)
The Binomial Distribution
611(23)
Conceptual Foundation
611(9)
The Origin of the Binomial Distribution
612(1)
The Binomial Distribution with N = 4
613(1)
The Binomial Distribution with N = 12
614(1)
When the Binomial Distribution Is Not Symmetrical
615(1)
The Normal Approximation to the Binomial Distribution
616(1)
The z Test for Proportions
617(1)
Summary
618(1)
Exercises
619(1)
Basic Statistical Procedures
620(6)
State the Hypotheses
620(1)
Select the Statistical Test and the Significance Level
620(1)
Select the Samples and Collect the Data
620(1)
Find the Region of Rejection
621(1)
Calculate the Test Statistic
621(1)
Make the Statistical Decision
621(1)
Interpreting the Results
622(1)
Assumptions of the Sign Test
622(1)
The Gambler's Fallacy
623(1)
When to Use the Binomial Distribution for Null Hypothesis Testing
623(2)
Summary
625(1)
Exercises
626(1)
Optional Material
626(8)
The Classical Approach to Probability
626(1)
The Rules of Probability Applied to Discrete Variables
627(1)
Permutations and Combinations
628(2)
Constructing the Binomial Distribution
630(1)
The Empirical Approach to Probability
631(1)
Summary
631(1)
Exercises
632(1)
Key Formulas
633(1)
Chi-Square Tests
634(28)
Conceptual Foundation
634(8)
The Multinomial Distribution
634(1)
The Chi-Square Distribution
635(1)
Expected and Observed Frequencies
635(1)
The Chi-Square Statistic
636(1)
Critical Values of Chi-Square
636(1)
Tails of the Chi-Square Distribution
637(1)
Expected Frequencies Based on No Preference
638(1)
The Varieties of One-Way Chi-Square Tests
639(2)
Summary
641(1)
Exercises
641(1)
Basic Statistical Procedures
642(10)
Two-Variable Contingency Tables
642(1)
Pearson's Chi-Square Test of Association
643(1)
An Example of Hypothesis Testing with Categorical Data
643(3)
The Simplest Case: 2 x 2 Tables
646(1)
Assumptions of the Chi-Square Test
647(1)
Some Uses for the Chi-Square Test for Independence
648(1)
Publishing the Results of a Chi-Square Test
649(1)
Summary
650(1)
Exercises
650(2)
Optional Material
652(10)
Measuring Strength of Association
652(3)
Measuring Interrater Agreement When Using Nominal Scales
655(2)
Fisher's Exact Test
657(1)
Contingency Tables Involving More Than Two Variables
658(1)
Summary
659(1)
Exercises
660(1)
Key Formulas
660(2)
Statistical Tests for Ordinal Data
662(27)
Conceptual Foundation
662(7)
Ranking Data
662(1)
Comparing the Ranks from Two Separate Groups
662(1)
The Sum of Ranks
663(1)
The U Statistic
663(1)
Dealing with Tied Scores
664(1)
When to Use the Mann-Whitney Test
665(2)
Repeated Measures or Matched Samples
667(1)
Summary
667(1)
Exercises
668(1)
Basic Statistical Procedures
669(12)
Testing for a Difference in Ranks between Two Independent Groups: The Mann-Whitney Test
669(3)
Ranking the Differences between Paired Scores: The Wilcoxon Signed-Ranks Test
672(4)
Correlation with Ordinal Data: The Spearman Correlation Coefficient
676(2)
Summary
678(1)
Exercises
679(2)
Optional Material
681(8)
Testing for Differences in Ranks among Several Groups: The Kruskal-Wallis Test
681(1)
Testing for Differences in Ranks among Matched Subjects: The Friedman Test
682(2)
Kendall's Coefficient of Concordance
684(2)
Summary
686(1)
Exercises
686(1)
Key Formulas
687(2)
Appendix A Statistical Tables 689(20)
A.1 Areas under the Standard Normal Distribution
689(3)
A.2 Critical Values of the t Distribution
692(1)
A.3 Power as a Function of δ and α
693(1)
A.4 δ As a Function of α and Power
694(1)
A.5 Critical Values of Pearson's r
695(1)
A.6 Table of Fisher's Transformation from r to Z
696(1)
A.7 Critical Values of the F Distribution for α = .05
697(1)
A.8 Critical Values of the F Distribution for α = .025
698(1)
A.9 Critical Values of the F Distribution for α = .01
699(1)
A.10 Power of ANOVA for α = .05
700(1)
A.11 Critical Values of the Studentized Range Statistic for α = .05
701(1)
A.12 Orthogonal Polynomial Trend Coefficients
702(1)
A.13 Probabilities of the Binomial Distribution for P = .5
703(1)
A.14 Critical Values of the X2 Distribution
704(1)
A.15 Critical Values for the Wilcoxon Rank-Sum Test
705(2)
A.16 Critical Values for the Wilcoxon Signed-Ranks Test
707(2)
Appendix B Answers to Selected Exercises 709(18)
References 727(6)
Index 733

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