Statistical Methods in Education and Psychology

by Glass, Gene V.; Hopkins, Kenneth D.

• ISBN13: 9780205142125
• ISBN10: 0205142125
• Edition: 3rd
• Format: Hardcover
• Copyright: 1996-01-01
• Publisher: Allyn & Bacon

Summary

The approach of SMEP-III is conceptual rather than mathematical. The authors stress the understanding, applications, and interpretation of concepts rather than derivation and proof or hand-computation.

Table of Contents

Preface	xii
Introduction	1	(5)
The ``Image'' of Statistics	1	(1)
Descriptive Statistics	2	(1)
Inferential Statistics	2	(1)
Statistics and Mathematics	3	(1)
Case Method	4	(1)
Our Targets	5	(1)
Variables, Measurement, Scales	6	(9)
Variables and Their Measurement	6	(1)
Measurement: The Observation of Variables	6	(1)
Measurement Scales: Nominal Measurement	7	(1)
Ordinal Measurement	7	(1)
Interval Measurement	8	(1)
Ratio Measurement	8	(1)
Interrelationships among Measurement Scales	9	(1)
Continuous and Discrete Variables	10	(1)
Chapter Summary	11	(1)
Case Study	11	(1)
Suggested Computer Activities	12	(3)
Mastery Test	12	(1)
Answers to Mastery Test	13	(2)
Frequency Distributions and Visual Displays of Data	15	(34)
Tabulating Data	15	(1)
Grouped Frequency Distributions	16	(3)
Grouping and Loss of Information	19	(1)
Graphing a Frequency Distribution: The Histogram	19	(1)
Frequency and Percentage Polygons	20	(3)
Types of Distributions	23	(1)
Cumulative Distributions and the Ogive Curve	24	(1)
Percentiles	25	(1)
Box-and-Whisker Plots	26	(3)
Stem-and-Leaf Displays	29	(2)
Time-Series Graphs	31	(1)
Misleading Graphs: How to Lie with Statistics	31	(6)
Chapter Summary	37	(1)
Case Study	37	(4)
Suggested Computer Activity	41	(8)
Mastery Test	41	(3)
Problems and Exercises	44	(3)
Answers to Mastery Test	47	(1)
Answers to Problems and Exercises	47	(2)
Measures of Central Tendency	49	(17)
Introduction	49	(1)
The Mode	49	(2)
The Median	51	(1)
Summation Notation	52	(1)
The Mean	53	(1)
More Summation Notation	53	(1)
Adding or Subtracting a Constant	54	(1)
Multiplying or Dividing by a Constant	54	(1)
Sum of Deviations	55	(1)
Sum of Squared Deviations	55	(1)
The Mean of the Sum of Two or More Scores	56	(1)
The Mean of a Difference	56	(1)
Mean, Median, and Mode of Two or More Groups Combined	56	(2)
Interpretation of Mode, Median, and Mean	58	(1)
Central Tendency and Skewness	58	(2)
Measures of Central Tendency as Inferential Statistics	60	(1)
Which Measure is Best?	61	(1)
Chapter Summary	61	(1)
Case Study	61	(2)
Suggested Computer Exercise	63	(3)
Mastery Test	63	(1)
Problems and Exercises	64	(1)
Answers to Mastery Test	65	(1)
Answers to Problems and Exercises	65	(1)
Measures of Variability	66	(14)
Introduction	66	(1)
The Range	66	(1)
H-Spread and the Interquartile Range	67	(1)
Deviation Scores	67	(1)
Sum of Squares	67	(1)
More about the Summation Operator, Σ	68	(1)
The Variance of a Population	69	(1)
The Variance Estimated from a Sample	69	(1)
The Standard Deviation	70	(1)
The Effect of Adding or Subtracting a Constant on Measures of Variability	71	(1)
The Effect of Multiplying or Dividing by a Constant on Measures of Variability	71	(1)
Variance of a Combined Distribution	72	(1)
Inferential Properties of the Range, s2, and s	73	(2)
Chapter Summary	75	(1)
Case Study	75	(1)
Suggested Computer Exercise	76	(4)
Mastery Test	77	(1)
Problems and Exercises	78	(1)
Answers to Mastery Test	78	(1)
Answers to Problems and Exercises	79	(1)
The Normal Distribution and Standard Scores	80	(23)
The Importance of the Normal Distribution	80	(1)
God Loves the Normal Curve	80	(3)
The Standard Normal Distribution as a Standard Reference Distribution: z-Scores	83	(2)
Ordinates of the Normal Distribution	85	(1)
Areas under the Normal Curve	85	(1)
Other Standard Scores	86	(1)
T-Scores	87	(2)
Areas under the Normal Curve in Samples	89	(1)
Skewness	89	(3)
Kurtosis	92	(2)
Transformations	94	(1)
Normalized Scores	94	(1)
Chapter Summary	95	(1)
Case Study	95	(3)
Suggested Computer Exercise	98	(5)
Mastery Test	98	(2)
Problems and Exercises	100	(1)
Answers to Mastery Test	101	(1)
Answers to Problems and Exercises	102	(1)
Correlations: Measures of Relationship Between Two Variables	103	(49)
Introduction	103	(1)
The Concept of Correlation	103	(1)
Scatterplots	104	(2)
The Measurement of Correlation	106	(1)
The Use of Correlation Coefficients	107	(1)
Interpreting r as a Percent	107	(2)
Linear and Curvilinear Relationships	109	(2)
Calculating the Pearson Product-Moment Correlation Coefficient, r	111	(1)
A Computational Illustration of r	112	(1)
Scatterplots	113	(3)
Correlation Expressed in Terms of z-scores	116	(1)
Linear Transformations and Correlation	117	(1)
The Bivariate Normal Distribution	118	(3)
Effects of Variability on Correlation	121	(1)
Correcting for Restricted Variability	122	(1)
Effect of Measurement Error on r and the Correction for Attentuation	123	(4)
The Pearson r and Marginal Distributions	127	(1)
The Effect of the Unit of Analysis on Correlation: Ecological Correlations	127	(1)
The Variance of a Sum	128	(1)
The Variance of a Difference	129	(1)
Additional Measures of Relationship: The Spearman Rank Correlation rranks'	129	(1)
The Phi Coefficient: Both X and Y are Dichotomies	130	(3)
The Point-Biserial Coefficient	133	(1)
The Biserial Correlation	134	(2)
The Biserial versus Point-Biserial Correlation Coefficients	136	(1)
The Tetrachoric Coefficient	136	(1)
Causation and Correlation	137	(3)
Chapter Summary	140	(1)
Case Study	141	(3)
Suggested Computer Exercise	144	(8)
Mastery Test	144	(3)
Problems and Exercises	147	(3)
Answers to Mastery Test	150	(1)
Answers to Problems and Exercises	150	(2)
Regression and Prediction	152	(47)
Purposes of Regression Analysis	152	(1)
The Regression Effect	153	(1)
The Regression Equation Expressed in Standard z-scores	154	(1)
Use of Regression Equations	155	(1)
Cartesian Coordinates	156	(1)
Estimating Y from X: The Raw-Score Regression Equation	157	(2)
Error of Estimate	159	(1)
Proportion of Predictable Variance, r2	160	(1)
Least-Squares Criterion	161	(1)
Homoscedasticity and the Standard Error of Estimate	161	(3)
Regression and Pretest-Posttest Gains	164	(3)
Part Correlation	167	(1)
Partial Correlation	168	(1)
Second-Order Partial Correlation	169	(1)
Multiple Regression and Multiple Correlation	170	(1)
The Standardized Regression Equation	171	(1)
The Raw-Score Regression Equation	172	(1)
Multiple Correlation	173	(2)
Multiple Regression Equations with Three or More Independent Variables	175	(1)
Stepwise Multiple Regression	175	(1)
Illustration of Stepwise Multiple Regression	176	(1)
Dichotomous and Categorical Variables as Predictors	177	(1)
The Standard Error of Estimate in Multiple Regression	178	(1)
The Multiple Correlation as an Inferential Statistic: Correction for Bias	178	(2)
Assumptions	180	(1)
Curvilinear Regression and Correlation	180	(1)
Measuring Nonlinear Relationships between Two Variables: η	180	(2)
Transforming Nonlinear Relationships into Linear Relationships	182	(1)
Dichotomous Dependent Variables: Logistic Regression	182	(2)
Categorical Dependent Variables with More than Two Categories: Discriminant Analysis	184	(1)
Chapter Summary	184	(1)
Case Study	185	(3)
Suggested Computer Activity	188	(11)
Mastery Test	189	(3)
Problems and Exercises	192	(3)
Answers to Mastery Test	195	(1)
Answers to Problems and Exercises	196	(3)
Probability	199	(24)
Introduction	199	(1)
Probability as a Mathematical System	199	(2)
First Addition Rule of Probabilities	201	(2)
Second Addition Rule of Probabilities	203	(2)
Multiplication Rule of Probabilities	205	(1)
Conditional Probability	206	(1)
Bayes's Theorem	207	(1)
Permutations	208	(1)
Combinations	209	(1)
Binomial Probabilities	210	(2)
The Binomial and Sign Test	212	(1)
Intuition and Probability	213	(2)
Probability as an Area	215	(1)
Combining Probabilities	216	(1)
Expectations and Moments	217	(1)
Chapter Summary	218	(1)
Suggested Computer Activity	219	(4)
Mastery Test	219	(1)
Problems and Exercises	220	(1)
Answers to Mastery Test	221	(1)
Answers to Problems and Exercises	221	(2)
Statistical Inference: Sampling and Interval Estimation	223	(32)
Overview	223	(1)
Populations and Samples: Parameters and Statistics	223	(1)
Infinite versus Finite Populations	224	(1)
Randomness and Random Sampling	225	(1)
Accidental or Convenience Samples	226	(1)
Random Samples	226	(2)
Independence	228	(1)
Systematic Sampling	229	(1)
Point and Interval Estimates	230	(1)
Sampling Distributions	230	(1)
The Standard Error of the Mean	231	(1)
Relationship of σx to n	232	(1)
Confidence Intervals	232	(2)
Confidence Intervals when σ Is Known: An Example	234	(1)
Central Limit Theorem: A Demonstration	235	(4)
The Use of Sampling Distributions	239	(1)
Proof that σ2=σ2/n	239	(3)
Properties of Estimators	242	(1)
Unbiasedness	242	(2)
Consistency	244	(1)
Relative Efficiency	245	(2)
Chapter Summary	247	(1)
Case Study	248	(1)
Suggested Computer Activity	248	(7)
Mastery Test	250	(2)
Problems and Exercises	252	(1)
Answers to Mastery Test	253	(1)
Answers to Problems and Exercises	254	(1)
Introduction to Hypothesis Testing	255	(28)
Introduction	255	(1)
Statistical Hypotheses and Explanations	255	(1)
Statistical versus Scientific Hypotheses	256	(1)
Testing Hypotheses about μ	257	(1)
Testing Ho:μ=K, a One-Sample z-Test	258	(1)
Two Types of Errors in Hypothesis Testing	259	(2)
Hypothesis Testing and Confidence Intervals	261	(1)
Type-II Error, β, and Power	262	(1)
Power	263	(1)
Effect of α on Power	263	(1)
Power and the Value Hypothesized in the Alternative Hypothesis	264	(2)
Methods of Increasing Power	266	(1)
Nondirectional and Directional Alternatives: Two-Tailed versus One-Tailed Tests	267	(2)
Statistical Significance versus Practical Significance	269	(1)
Confidence Limits for the Population Median	269	(1)
Inferences Regarding μ When σ Is Not Known: t versus z	270	(1)
The t-Distribution	271	(3)
Confidence Intervals Using the t-Distribution	274	(1)
Accuracy of Confidence Intervals when Sampling Non-Normal Distributions	274	(1)
Chapter Summary	275	(1)
Case Study	276	(7)
Mastery Test	277	(2)
Problems and Exercises	279	(2)
Answers to Mastery Test	281	(1)
Answers to Problems and Exercises	281	(2)
Inferences About the Difference between Two Means	283	(36)
Introduction	283	(1)
Testing Statistical Hypotheses Involving Two Means	283	(1)
The Null Hypothesis, Ho: μ1-μ2=0	284	(1)
The t-Test for Comparing Two Independent Means	284	(1)
Computing sx1-x2	285	(2)
An Illustration	287	(2)
Confidence Intervals about Mean Differences	289	(1)
Effect Size	289	(1)
t-Test Assumptions and Robustness	290	(3)
Homogeneity of Variance	293	(2)
What if Sample Sizes Are Unequal and Variances Are Heterogeneous: The Welch t'Test	295	(1)
Independence of Observations	295	(1)
Testing Ho: μ1 = μ2 with Paired Observations	296	(3)
Direct-Difference for the t-Test with Paired Observations	299	(2)
Cautions Regarding the Matched-Pair Designs in Research	301	(1)
Power when Comparing Means	302	(1)
Non-Parametric Alternatives: The Mann-Whitney Test and the Wilcoxon Signed Rank Test	303	(1)
Chapter Summary	304	(1)
Case Study	305	(5)
Suggested Computer Activity	310	(9)
Mastery Test	310	(3)
Problems and Exercises	313	(3)
Answers to Mastery Test	316	(1)
Answers to Problems and Exercises	317	(2)
Statistics for Categorical Dependent Variables: Inferences about Proportions	319	(30)
Overview	319	(1)
The Proportion as a Mean	319	(1)
The Variance of a Proportion	320	(1)
The Sampling Distribution of a Proportion: The Standard Error of p	321	(1)
The Influence of n on σp	322	(1)
Influence of the Sampling Fraction on σp	323	(1)
The Influence of &pie; on σp	324	(1)
Confidence Intervals for &pie;	325	(2)
Quick Confidence Intervals for &pie;	327	(1)
Testing Ho: &pie;=K	328	(2)
Testing Empirical versus Theoretical Distributions: The Chi-Square Goodness-of-Fit Test	330	(3)
Testing Differences among Proportions: The Chi-Square Test of Association	333	(2)
Other Formulas for the Chi-Square Test of Association	335	(2)
The χ2 Median Test	337	(1)
Chi-Square and the Phi Coefficient	337	(1)
Independence of Observations	338	(1)
Inferences about Ho: μ1 =μ2 when Observations are Paired: McNemar's Test for Correlated Proportions	339	(1)
Chapter Summary	340	(1)
Case Study	341	(1)
Suggested Computer Activity	342	(7)
Mastery Test	342	(2)
Problems and Exercises	344	(3)
Answers to Mastery Test	347	(1)
Answers to Problems and Exercises	347	(2)
Inferences About Correlation Coefficients	349	(28)
Testing Statistical Hypotheses Regarding ρ	349	(1)
Testing Ho: ρ = O Using the t-Test	350	(3)
Directional Alternatives: ``Two-Tailed'' vs. ``One-Tailed'' Tests	353	(1)
Sampling Distribution of r	354	(1)
The Fisher Z-Transformation	355	(2)
Setting Confidence Intervals for ρ	357	(1)
Determining Confidence Intervals Graphically	358	(1)
Testing the Difference between Independent Correlation Coefficients: Ho: ρ1 = ρ2	359	(2)
Testing Differences among Several Independent Correlation Coefficients:	361	(1)
Averaging r's	362	(1)
Testing Differences between Two Dependent Correlation Coefficients: Ho: p31=p32	362	(1)
Inferences about Other Correlation Coefficients	363	(1)
The Point-Biserial Correlation Coefficient rpb	364	(1)
Spearman's Rank Correlation: Ho: Pranks =0	365	(1)
Partial Correlation, Hp: p123 = 0	365	(1)
Significance of a Multiple Correlation Coefficient	366	(1)
Statistical Significance in Stepwise Multiple Regression	367	(1)
Significance of the Biserial Correlation Coefficient Rbis	368	(1)
Significance of the Tetrachoric Correlation Coefficient rtet	369	(1)
Significance of the Correlation Ratio, η2	369	(1)
Testing for Nonlinearity of Regression	370	(1)
Chapter Summary	371	(1)
Case Study	371	(1)
Suggested Computer Activity	372	(5)
Mastery Test	372	(1)
Problems and Exercises	373	(2)
Answers to Mastery Test	375	(1)
Answers to Problems and Exercises	375	(2)
One-Factor Analysis of Variance	377	(45)
Introduction	377	(1)
Why Not Several t-Tests?	377	(1)
ANOVA Nomenclature	378	(1)
ANOVA Computation	379	(1)
Sum of Squares Between, SSB	380	(1)
Sum of Square Within, SSW	381	(1)
ANOVA Computational Illustration	382	(1)
ANOVA Theory	382	(3)
Mean Square Between Groups, MSW	385	(1)
Mean Square Within Groups, MSW	385	(1)
The F-Test	386	(1)
ANOVA with Equal n's	386	(2)
A Statistical Model for the Data	388	(1)
Estimates of the Terms in the Model	389	(1)
Sums of Squares	389	(2)
Restatement of the Null Hypothesis in Terms of Population Means	391	(1)
Degrees of Freedom	391	(2)
Mean Squares: The Expected Value of MSW	393	(1)
The Expected Value of MSB	394	(1)
Some Distribution Theory	395	(3)
The F-Test of the Null Hypothesis: Rationale and Procedure	398	(2)
Type-I versus Type-II Errors: α and β	400	(2)
A Summary of Procedures for One-Factor ANOVA	402	(1)
Consequences of Failure to Meet the ANOVA Assumptions: The ``Robustness'' of ANOVA,	402	(3)
The Welch and Brown-Forsythe Modifications of ANOVA: What Does One Do When σ2's and n's Differ?	405	(1)
The Power of the F-Test	406	(1)
An Illustration	407	(1)
Power When σ is Unknown	408	(1)
A Table for Estimating Power When J = 2	409	(2)
The Non-Parametric Alternative: The Krukal-Wallis Test	411	(1)
Chapter Summary	411	(1)
Case Study	412	(2)
Suggested Computer Activity	414	(8)
Mastery Test	414	(2)
Problems and Exercises	416	(3)
Answers to Mastery Test	419	(1)
Answers to Problems and Exercises	420	(2)
Inferences About Variances	422	(22)
Introduction	422	(1)
Chi-Square Distributions	422	(2)
Chi-Square Distributions with v > 1: X22 and X23	424	(1)
The Chi-Square Distribution with v Degrees of Freedom, X2v	425	(1)
Inferences about the Population Variance: Ho: σ=K	426	(2)
F-Distributions	428	(2)
Inferences about Two Independent Variances: Ho: σ21 = σ22	430	(2)
Testing Homogeneity of Variance: Hartley's Fmax Test	432	(2)
Testing Homogeneity of Variance from J Independence Samples: The Bartlett Test	434	(2)
Other Tests of Homogeneity of Variance: The Levene and Brown-Forsythe Tests	436	(1)
Inferences about Ho: σ12 = σ22 with Paired Observations	437	(1)
Relationships among the Normal, t, χ, and F-Distributions	438	(1)
Chapter Summary	439	(1)
Case Study and Computer Activity	440	(4)
Mastery Test	440	(1)
Problems and Exercises	441	(2)
Answers to Mastery Test	443	(1)
Answers to Problems and Exercises	443	(1)
Multiple Comparisons and Trend Analysis	444	(38)
Introduction	444	(2)
Testing All Pairs of Means: The Studentized Range Statistic, q	446	(1)
The Tukey Method of Multiple Comparisons	447	(2)
The Effect Size of Mean Differences	449	(1)
The Basis for Type-I Error Rate: Contrast versus Family	449	(1)
The Newman-Keuls Method	450	(1)
The Tukey and Newman-Keuls Methods Compared	451	(1)
The Definition of a Contrast	452	(1)
Simple versus Complex Contrasts	453	(1)
The Standard Error of a Contrast	454	(1)
The t-ratio for a Contrast	455	(1)
Planned versus Post Hoc Comparisons	456	(1)
Dunn (Bonferroni) Method of Multiple Comparisons	456	(1)
Dunnett Method of Multiple Comparisons	457	(1)
Scheffe Method of Multiple Comparisons	458	(1)
Planned Orthogonal Contrasts	459	(1)
Confidence Intervals for Contrasts	460	(1)
Relative Power of Multiple Comparison Techniques	461	(1)
Trend Analysis	462	(2)
Significance of Trend Components	464	(2)
Relation of Trends to Correlation Coefficients	466	(1)
Assumptions of MC Methods	467	(1)
Multiple Comparisons among Other Statistics	467	(2)
Chapter Summary and Criteria for Selecting a Multiple Comparison Method	469	(2)
Case Study	471	(3)
Suggested Computer Activity	474	(8)
Mastery Test	474	(2)
Problems	476	(1)
Exercises	477	(2)
Answers to Mastery Test	479	(1)
Answers to Problems	480	(1)
Answers to Exercises	480	(2)
Two-and Three-Factor ANOVA: an Introduction to Factorial Designs	482	(54)
Introduction	482	(1)
The Meaning of Interaction	483	(2)
Interaction and Generalizability: Factors Do Not Interact	485	(1)
Interaction and Generalizability: Factors Interact	486	(1)
Interpreting Main Effects when Interaction Is Present	487	(2)
Statistical Significance and Interaction	489	(1)
Data Layout and Notation	489	(2)
A Model for the Data	491	(1)
Least-Squares Estimation of the Model	492	(2)
Statement of Null Hypotheses	494	(3)
Sums of Squares in the Two-Factor ANOVA	497	(2)
Degrees of Freedom	499	(1)
Mean Squares	500	(1)
Illustration of the Computation for the Two-Factor ANOVA	501	(2)
Expected Values of Mean Squares	503	(3)
The Distribution of the Mean Squares	506	(3)
Hypothesis Tests of the Null Hypotheses	509	(4)
Determining Power in Factorial Designs	513	(1)
Multiple Comparisons in Factorial ANOVA Designs	514	(2)
Confidence Intervals for Means in Two-Factor ANOVA	516	(1)
Three-Factor ANOVA	517	(1)
Three-Factor ANOVA: An Illustration	517	(3)
Three-Factor ANOVA Computation	520	(1)
The Interpretation of Three-Factor Interactions	521	(1)
Confidence Intervals in Three-Factor ANOVA	522	(1)
How Factorial Designs Increase Power	522	(1)
Factorial ANOVA with Unbalanced Designs	523	(1)
Chapter Summary	524	(1)
Case Study and Computer Activity	524	(12)
Mastery Test	525	(2)
Problems and Exercises	527	(4)
Answers to Mastery Test	531	(1)
Answers to Problems and Exercises	532	(4)
Multi-Factor ANOVA Designs: Random, Mixed, and Fixed Effects	536	(36)
Introduction	535	(1)
The Random-Effects ANOVA Model	535	(2)
Assumptions of the Random ANOVA Model	537	(1)
An Example	538	(1)
Mean Square Within, MSw	539	(1)
Mean Square Between, MSBetween	539	(1)
The Variance Component, σa2	540	(2)
Confidence Interval for σa2/σe2	542	(1)
Summary of Random ANOVA Model	543	(1)
The Mixed-Effects ANOVA Model	544	(3)
Mixed-Model ANOVA Assumptions	547	(1)
Mixed-Model ANOVA Computation	547	(3)
Multiple Comparisons in the Two-Factor Mixed Model	550	(1)
Crossed and Nested Factors	551	(2)
Computation of Sums of Squares for Nested Factors	553	(1)
Determining the Sources of Variation in the ANOVA Table	554	(1)
Degrees of Freedom for Nested Factors	554	(1)
Determining Expected Mean Squares	555	(1)
Error Mean Squares in Complex ANOVA Designs	556	(1)
The Incremental Generalization Strategy: Inferential ``Concentric Circles,''	556	(4)
Model Simplification and Pooling	560	(1)
The Experimental Unit and the Observational Unit	561	(2)
Chapter Summary	563	(1)
Case Study/Application	563	(9)
Mastery Test	566	(3)
Problems and Exercises	569	(1)
Answers to Mastery Test	570	(1)
Answers to Problems and Exercises	571	(1)
Repeated-Measures ANOVA	572	(21)
Introduction	572	(1)
A Simple Repeated-Measures ANOVA	572	(1)
Repeated-Measures Assumptions	573	(3)
Trend Analysis on Repeated-Measures Factors	576	(1)
Estimating Reliability via Repeated-Measures ANOVA	576	(2)
Repeated-Measures Designs with a Between-Subjects Factor	578	(2)
Repeated-Measures ANOVA with Two Between-Subjects Factors	580	(2)
Trend Analysis on Between-Subjects Factors	582	(1)
Repeated-Measures ANOVA with Two Within-Subjects Factors and Two Between-Subjects Factors	582	(1)
Repeated-Measures ANOVA versus MANOVA	583	(2)
Chapter Summary	585	(1)
Case Study	585	(2)
Suggested Computer Activity	587	(6)
Mastery Test	587	(2)
Problems and Exercises	589	(2)
Answers to Mastery Test	591	(1)
Answers to Problems and Exercises	592	(1)
An Introduction to the Analysis of Covariance	593	(21)
The Functions of ANCOVA	593	(1)
ANOVA Results	594	(1)
ANCOVA Model	594	(3)
ANCOVA Computations, SStotal	597	(1)
The Adjusted Within Sum of Squares, SS'W	597	(1)
The Adjusted Sum of Squares Between Groups, SS'B	598	(1)
Degrees of Freedom in ANCOVA and the ANCOVA Table	598	(2)
Adjusted Means, Y'j	600	(1)
Confidence Intervals and Multiple Comparisons for Adjusted Means	601	(1)
ANCOVA Illustrated Graphically	602	(2)
ANCOVA Assumptions	604	(1)
ANCOVA Precautions	605	(1)
Covarying versus Stratifying	606	(1)
Chapter Summary	607	(1)
Case Study	608	(1)
Suggested Computer Activity	609	(5)
Mastery Test	609	(1)
Problems and Exercises	610	(2)
Answers to Mastery Test	612	(1)
Answers to Problems and Exercises	612	(2)
APPENDIX: TABLES	614	(37)
Table A: Area of the Unit-Normal (z) Distribution	615	(5)
Table B: Random Digits	620	(1)
Table C: Percentile Points of the t-Distribution	621	(2)
Table D: Percentile Points of Chi-Square Distributions	623	(2)
Table E: Fisher's Z-Transformation of r	625	(1)
Table F: Critical Values of F	626	(8)
Table G: Power Curves for the F-Test	634	(3)
Table H: Hartley's Fmax-Distribution	637	(1)
Table I: Critical Values of the Studentized Range Statistic: q-Distribution	638	(3)
Table J: Critical Values of r	641	(1)
Table K: Critical Values of rranks' Spearman's Rank Correlation	642	(1)
Table L: Critical t-Ratios for the Dunn (Bonferroni) Method of Multiple Comparison	643	(3)
Table M: Critical t-Values for the Dunnett Statistic for Comparing Treatment Means with a Control	646	(2)
Table N: Coefficients of Orthogonal Polynomials for Trend Analysis	648	(1)
Table O: Binomial Probabilities when &pie; = .5	649	(2)
Bibliography	651	(14)
Index	665	(1)
Author Index	665	(2)
Subject Index	667