Handbook of parametric and nonparametric statistical procedures:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2007
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| Edition: | 4. ed. |
| Subjects: | |
| Online Access: | Table of contents only Publisher description Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index Includes bibliographical references and index |
| Physical Description: | XXX, 1736 graph. Darst. |
| ISBN: | 9781584888147 1584888148 |
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MARC
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| 100 | 1 | |a Sheskin, David J. |d 1941- |e Verfasser |0 (DE-588)1013718429 |4 aut | |
| 245 | 1 | 0 | |a Handbook of parametric and nonparametric statistical procedures |c David J. Sheskin |
| 250 | |a 4. ed. | ||
| 264 | 1 | |a Boca Raton [u.a.] |b Chapman & Hall/CRC |c 2007 | |
| 300 | |a XXX, 1736 |b graph. Darst. | ||
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| 500 | |a Includes bibliographical references and index | ||
| 500 | |a Includes bibliographical references and index | ||
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| 650 | 4 | |a Statistik | |
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| 650 | 4 | |a Mathematical statistics |v Handbooks, manuals, etc | |
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| adam_text | FOURTH EDITION HANDBOOK OF PARAMETRIC AND NONPARAMETRIC STATISTICAL
PROCEDURES DAVID J.SHESLDN CHAPMAN & HALL/CRC TAYLOR & FRANCIS CROUP
BOCA RATON LONDON NEW YORK CHAPMAN & HALL/CRC IS AN IMPRINT OF THE
TAYLOR & FRANCIS CROUP, AN INFORMA BUSINESS TABLE OF CONTENTS WITH
SUMMARY OF TOPICS INTRODUCTION 1 DESCRIPTIVE VERSUS INFERENTIAL
STATISTICS 1 STATISTIC VERSUS PARAMETER .[.... 2 LEVELS OF MEASUREMENT 2
CONTINUOUS VERSUS DISCRETE VARIABLES ; 4 MEASURES OF CENTRAL TENDENCY
(MODE, MEDIAN, MEAN, WEIGHTED MEAN, GEOMETRIC MEAN, AND THE HARMONIC
MEAN) 4 MEASURES OF VARIABILITY (RANGE; QUANTILES, PERCENTILES, DECILES,
AND QUARTILES; VARIANCE AND STANDARD DEVIATION; THE COEFFICIENT OF
VARIATION) 10 MEASURES OF SKEWNESS AND KURTOSIS 16 VISUAL METHODS FOR
DISPLAYING DATA (TABLES AND GRAPHS, EXPLORATORY DATA ANALYSIS
(STEM-AND-LEAF DISPLAYS AND BOXPLOTS)) 29 THE NORMAL DISTRIBUTION .45
HYPOTHESIS TESTING 56 A HISTORY AND CRITIQUE OF THE CLASSICAL HYPOTHESIS
TESTING MODEL 68 ESTIMATION IN INFERENTIAL STATISTICS 74 RELEVANT
CONCEPTS, ISSUES, AND TERMINOLOGY IN CONDUCTING RESEARCH (THE CASE STUDY
METHOD; THE EXPERIMENTAL METHOD; THE CORRELATIONAL METHOD) 75
EXPERIMENTAL DESIGN (PRE-EXPERIMENTAL DESIGNS; QUASI-EXPERIMENTAL
DESIGNS . TRUE EXPERIMENTAL DESIGNS; SINGLE-SUBJECT DESIGNS) 82 SAMPLING
METHODOLOGIES 98 BASIC PRINCIPLES OF PROBABILITY 100 PARAMETRIC VERSUS
NONPARAMETRIC INFERENTIAL STATISTICAL TESTS ., 108 UNIVARIATE VERSUS
BIVARIATE VERSUS MULTIVARIATE STATISTICAL PROCEDURES 109 SELECTION OF
THE APPROPRIATE STATISTICAL PROCEDURE 110 OUTLINE OF INFERENTIAL
STATISTICAL TESTS AND MEASURES OF CORRELATION/ASSOCIATION 125 GUIDELINES
AND DECISION TABLES FOR SELECTING THE APPROPRIATE STATISTICAL PROCEDURE
133 INFERENTIAL STATISTICAL TESTS EMPLOYED WITH A SINGLE SAMPLE . 141
TEST 1: THE SINGLE-SAMPLE Z TEST 143 I. HYPOTHESIS EVALUATED WITH TEST
AND RELEVANT BACKGROUND INFORMATION 143 II. EXAMPLE . * = 143 III. NULL
VERSUS ALTERNATIVE HYPOTHESES ; 143 IV. TEST COMPUTATIONS 144 V.
INTERPRETATION OF THE TEST RESULTS 145 VI. ADDITIONAL ANALYTICAL
PROCEDURES FOR THE SINGLE-SAMPLE Z TEST AND/OR RELATED TESTS 146 VIII
HANDBOOK OF PARAMETRIC ANDNONPARAMETRIC STATISTICAL PROCEDURES VII.
ADDITIONAL DISCUSSION OF THE SINGLE-SAMPLE Z TEST 146 1. THE
INTERPRETATION OF A NEGATIVE Z VALUE 146 2. THE STANDARD ERROR OF THE
POPULATION MEAN AND GRAPHICAL REPRESENTATION OF THE RESULTS OF THE
SINGLE-SAMPLE Z TEST 147 3. ADDITIONAL EXAMPLES ILLUSTRATING THE
INTERPRETATION OF A COMPUTED Z VALUE 152 4. THE Z TEST FOR A POPULATION
PROPORTION 152 VIII. ADDITIONAL EXAMPLES ILLUSTRATING THE USE OF THE
SINGLE-SAMPLE Z TEST 153 TEST 2: THE SINGLE-SAMPLE / TEST 157 I.
HYPOTHESIS EVALUATED WITH TEST AND RELEVANT BACKGROUND INFORMATION 157
II. EXAMPLE 158 III. NULL VERSUS ALTERNATIVE HYPOTHESES 158 IV. TEST
COMPUTATIONS V : 158 V. INTERPRETATION OF THE TEST RESULTS . . .. 160
VI. ADDITIONAL ANALYTICAL PROCEDURES FOR THE SINGLE-SAMPLE T TEST AND/OR
RELATED TESTS . 162 1. DETERMINATION OF THE POWER OF THE SINGLE-SAMPLE
T TEST AND THE SINGLE- SAMPLE Z TEST, AND THE APPLICATION OF TEST 2A:
COHEN S D INDEX 162 2. COMPUTATION OF A CONFIDENCE INTERVAL FOR THE MEAN
OF THE POPULATION REPRESENTED BY A SAMPLE 173 VII. ADDITIONAL DISCUSSION
OF THE SINGLE-SAMPLE T TEST 183 1. DEGREES OF FREEDOM 183 VIII.
ADDITIONAL EXAMPLES ILLUSTRATING THE USE OF THE SINGLE-SAMPLE T TEST 184
TEST 3: THE SINGLE-SAMPLE CHI-SQUARE TEST FOR A POPULATION VARIANCE 191
I. HYPOTHESIS EVALUATED WITH TEST AND RELEVANT BACKGROUND INFORMATION
191 II. EXAMPLE 192 III. NULL VERSUS ALTERNATIVE HYPOTHESES 192 IV. TEST
COMPUTATIONS 193 V. INTERPRETATION OF THE TEST RESULTS 194 VI.
ADDITIONAL ANALYTICAL PROCEDURES FOR THE SINGLE-SAMPLE CHI-SQUARE TEST
FOR A POPULATION VARIANCE AND/OR RELATED TESTS . .^ 196 1. LARGE SAMPLE
NORMAL APPROXIMATION OF THE CHI-SQUARE DISTRIBUTION 196 2. COMPUTATION
OF A CONFIDENCE INTERVAL FOR THE VARIANCE OF A POPULATION REPRESENTED BY
A SAMPLE 197 3. SOURCES FOR COMPUTING THE POWER OF THE SINGLE-SAMPLE
CHI-SQUARE TEST FOR A POPULATION VARIANCE 200 VII. ADDITIONAL DISCUSSION
OF THE SINGLE-SAMPLE CHI-SQUARE TEST FOR A POPULATION VARIANCE , 200
VIII. ADDITIONAL EXAMPLES ILLUSTRATING THE USE OF THE SINGLE-SAMPLE CHI-
SQUARE TEST FOR A POPULATION VARIANCE , 200 TEST 4: THE SINGLE-SAMPLE
TEST FOR EVALUATING POPULATION SKEWNESS 205 I. HYPOTHESIS EVALUATED WITH
TEST AND RELEVANT BACKGROUND INFORMATION 205 II. EXAMPLE 206 III. NULL
VERSUS ALTERNATIVE HYPOTHESES ; 206 IV. TEST COMPUTATIONS 207 V.
INTERPRETATION OF THE TEST RESULTS 209 TABLE, OF CONTENTS IX VI.
ADDITIONAL ANALYTICAL PROCEDURES FOR THE SINGLE-SAMPLE TEST FOR .
EVALUATING POPULATION SKEWRIESS AND/OR RELATED TESTS :..:. .. 210 VII.
ADDITIONAL DISCUSSION OF THE SINGLE-SAMPLE TEST FOR EVALUATING
POPULATION SKEWNESS 210 1. EXACT TABLES FOR THE SINGLE-SAMPLE TEST FOR
EVALUATING POPULATION SKEWNESS : ., 210 2. NOTE ON A NONPARAMETRIC TEST
FOR EVALUATING SKEWNESS 210 VIII. ADDITIONAL EXAMPLES ILLUSTRATING THE
USE OF THE SINGLE-SAMPLE TEST FOR EVALUATING POPULATION SKEWNESS 211
TEST 5: THE SINGLE-SAMPLE TEST FOR EVALUATING POPULATION KURTOSIS 213 I.
HYPOTHESIS EVALUATED WITH TEST AND RELEVANT BACKGROUND INFORMATION 213
II. EXAMPLE ..... ; 214 . III. NULL VERSUS ALTERNATIVE HYPOTHESES 214
IV. TEST COMPUTATIONS ... 215 V. INTERPRETATION OFTHE TEST RESULTS 217
VI. ADDITIONAL ANALYTICAL PROCEDURES FOR THE SINGLE-SAMPLE TEST FOR
EVALUATING POPULATION KURTOSIS AND/OR RELATED TESTS ., 218 1. TEST 5A:
THE D AGOSTINO-PEARSON TEST OF NORMALITY 218 2. TEST 5B: THE JARQUE-BERA
TEST OF NORMALITY 219 VII. ADDITIONAL. DISCUSSION OFTHE SINGLE-SAMPLE
TEST FOR EVALUATING POPULATION KURTOSIS : 220 1. EXACT TABLES FOR THE
SINGLE-SAMPLE TEST FOR EVALUATING POPULATION KURTOSIS 220 2. ADDITIONAL
COMMENTS ON TESTS OF NORMALITY 220 VIII. ADDITIONAL EXAMPLES
ILLUSTRATING THE USE OFTHE SINGLE-SAMPLE TEST FOR EVALUATING POPULATION
KURTOSIS 221 TEST 6: THE WILCOXON SIGNED-RANKS TEST 225 I. HYPOTHESIS
EVALUATED WITH.TEST AND RELEVANT BACKGROUND INFORMATION 225 II. EXAMPLE
:* 225 III. NULL VERSUS ALTERNATIVE HYPOTHESES ;..... 226 IV. TEST
COMPUTATIONS . .-. . :* 226 V. INTERPRETATION OF THE TEST RESULTS ..:
228 VI. ADDITIONAL ANALYTICAL PROCEDURES FOR THE WILCOXON SIGNEDRRANKS
TEST AND/OR RELATED TESTS :....-. 230 1. THE NORMAL APPROXIMATION OF THE
WILCOXON R STATISTIC FOR LARGE SAMPLE SIZES , .* ; 230 2. THE CORRECTION
FOR CONTINUITY FOR THE NORMAL APPROXIMATION OF THE WILCOXON SIGNED-RANKS
TEST ......; 232 3. TIE CORRECTION FOR THE NORMAL APPROXIMATION OF THE
WILCOXON TEST STATISTIC - : *. : 233 A. COMPUTATION OF A CONFIDENCE
INTERVAL FOR A POPULATION MEDIAN 234 VII. ADDITIONAL DISCUSSION OFTHE
WILCOXON SIGNED-RANKS TEST 235 1. POWER-EFFICIENCY OFTHE WILCOXON
SIGNED-RANKS TEST AND THE CONCEPT OF ASYMPTOTIC RELATIVE EFFICIENCY 235
2. NOTE.ON SYMMETRIC POPULATION CONCERNING HYPOTHESES REGARDING MEDIAN
AND MEAN 236 VIII. ADDITIONAL EXAMPLES ILLUSTRATING THE USE OFTHE
WILCOXON SIGNED- RANKS TEST 237 XII HANDBOOK OF PARAMETRIC AND
NONPARAMETRIC STATISTICAL PROCEDURES SINGLE-SAMPLE RUNS TEST : : 393 3.
EXTENSION OFTHE RUNS TEST TO DATA WITH MORE THAN TWO CATEGORIES 394 4.
TEST 10A: THE RUNS TEST FOR SERIAL RANDOMNESS 395 VII. ADDITIONAL
DISCUSSION OF THE SINGLE-SAMPLE RUNS TEST 398 1. ADDITIONAL DISCUSSION
OFTHE CONCEPT OF RANDOMNESS 398 VII. ADDITIONAL EXAMPLES ILLUSTRATING
THE USE OFTHE SINGLE-SAMPLE RUNS TEST 399 IX. ADDENDUM * ;........: 402
1. THE GENERATION OF PSEUDORANDOM NUMBERS (THE MIDSQUARE METHOD; THE
MIDPRODUCT METHOD; THE LINEAR CONGRUENTIAL METHOD) 402 2. ALTERNATIVE
TESTS OF RANDOMNESS TEST 10B: THE FREQUENCY TEST , 407 TEST 10C: THE GAP
TEST .... 409 TEST LOD: THE POKER TEST : 413 TEST LOE: THE MAXIMUM TEST
/. 413 TEST LOF: THE COUPON COLLECTOR S TEST 414 TEST LOG: THE MEAN
SQUARE SUCCESSIVE DIFFERENCE TEST (FOR SERIAL RANDOMNESS 417 ADDITIONAL
TESTS OF RANDOMNESS (AUTOCORRELATION; THE SERIAL TEST; THE D 2 SQUARE
TEST OF RANDOM NUMBERS; TESTS OF TREND ANALYSIS/TIME SERIES ANALYSIS)
419 INFERENTIAL STATISTICAL TESTS EMPLOYED WITH TWO INDEPENDENT SAMPLES
(AND RELATED MEASURES OF ASSOCIATION/CORRELATION) 425 TEST 11: THE /
TEST FOR TWO INDEPENDENT SAMPLES 427 I. HYPOTHESIS EVALUATED WITH TEST
AND RELEVANT BACKGROUND INFORMATION 427 II. EXAMPLE 427 III. NULL VERSUS
ALTERNATIVE HYPOTHESES 428 IV. TEST COMPUTATIONS . 428 V.
INTERPRETATION OFTHE TEST RESULTS 431 VI. ADDITIONAL ANALYTICAL
PROCEDURES FOR THE T TEST FOR TWO INDEPENDENT SAMPLES AND/OR RELATED
TESTS . 43 2 1. THE EQUATION FOR THE T TEST FOR TWO INDEPENDENT
SAMPLES WHEN A VALUE FOR A DIFFERENCE OTHER THAN ZERO IS STATED IN THE
NULL HYPOTHESIS 432 2. TEST HA: HARTLEY S F MAI TEST FOR HOMOGENEITY OF
VARIANCE/ F TEST FOR TWO POPULATION VARIANCES: EVALUATION OF THE
HOMOGENEITY OF VARIANCE ASSUMPTION OFTHE T TEST FOR TWO INDEPENDENT
SAMPLES 434 3. COMPUTATION OFTHE POWER OFTHE / TEST FOR TWO INDEPENDENT
SAMPLES AND THE APPLICATION OF TEST LIB: COHEN S D INDEX 439 4. MEASURES
OF MAGNITUDE OF TREATMENT EFFECT FOR THE / TEST FOR TWO INDEPENDENT
SAMPLES: OMEGA SQUARED (TEST LIE) AND ETA SQUARED . (TEST LID) 446 5.
COMPUTATIONOFACONFIDENCEINTERVALFORTHEFTESTFORTWOINDEPENDENT SAMPLES 448
6. TEST LIE: THE Z TEST FOR TWO INDEPENDENT SAMPLES 450 VII. ADDITIONAL
DISCUSSION OFTHE T TEST FOR TWO INDEPENDENT SAMPLES . 452 1. UNEQUAL
SAMPLE SIZES 452 2. ROBUSTNESS OFTHE / TEST FOR TWO INDEPENDENT SAMPLES
453 TABLE OF CONTENTS XIII 3. OUTLIERS (BOX-AND-WHISKER PLOT CRITERIA;
STANDARD DEVIATION SCORE CRITERIA;TEST LLF: MEDIAN ABSOLUTE DEVIATION
TEST FOR IDEN- TIFYING OUTLIERS AND TEST LLG: EXTREME STUDENTIZED
DEVIATE TEST FOR IDENTIFYING OUTLIERS; TRIMMING DATA; WINSORIZATION) AND
DATA TRANSFORMATION 454 4. MISSING DATA . 468 5. CLINICAL TRIALS . 471
6. TESTS OF EQUIVALENCE (TEST LLH: THE WESTLAKE-SCHUIRMANN TEST OF
EQUIVALENCE OF TWO INDEPENDENT TREATMENTS (AND PROCEDURE FOR COMPUTING
SAMPLE SIZE IN REFERENCE TO THE POWER OFTHE TEST) AND TEST HI: TRYON S
TEST OF EQUIVALENCE OF TWO INDEPENDENT TREATMENTS) : 474 7. HOTELLING S
T 1 498 VIII. ADDITIONAL EXAMPLES ILLUSTRATING THE USE OFTHE T TEST FOR
TWO INDEPENDENT SAMPLES 499 TEST 12: THE MANN-WHITNEY U TEST 513 I.
HYPOTHESIS EVALUATED WITH TEST AND RELEVANT BACKGROUND INFORMATION 513
II. EXAMPLE ; 514 III. NULL VERSUS ALTERNATIVE HYPOTHESES ; 514 IV. TEST
COMPUTATIONS 515 V. INTERPRETATION OFTHE TESTRESULTS 518 VI. ADDITIONAL
ANALYTICAL PROCEDURES FOR THE MANN-WHITNEY [/TEST AND/OR RELATED TESTS
518 1. THE NORMAL APPROXIMATION OFTHE MANN-WHITNEY U STATISTIC FOR LARGE
SAMPLE SIZES 518 2. THE CORRECTION FOR CONTINUITY FOR THE NORMAL
APPROXIMATION OF THE MANN-WHITNEY [/TEST 520 3. TIE CORRECTION FOR THE
NORMAL APPROXIMATION OFTHE MANN*WHITNEY U , STATISTIC . 521 4.
COMPUTATION OF A CONFIDENCE INTERVAL FOR A DIFFERENCE BETWEEN THE
MEDIANS OF TWO INDEPENDENT POPULATIONS 521 VII. ADDITIONAL DISCUSSION
OFTHE MANN-WHITNEY [/TEST 524 1. POWER-EFFICIENCY OFTHE MANN-WHITNEY
[/TEST 524 2. EQUIVALENCY OFTHE NORMAL APPROXIMATION OF*HE MANN-WHITNEY
[/TEST AND THE T TEST FOR TWO INDEPENDENT SAMPLES WITH RANK-ORDERS 524
3. ALTERNATIVE NONPARAMETRIC RANK-ORDER PROCEDURES FOR EVALUATING A
DESIGN INVOLVING TWO INDEPENDENT SAMPLES 524 VIII. ADDITIONAL EXAMPLES
ILLUSTRATING THE USE OFTHE MANN-WHITNEY [/TEST 525 IX. ADDENDUM 526 1.
COMPUTER-INTENSIVE TESTS (RANDOMIZATION AND PERMUTATION TESTS: TEST *
12A: THE RANDOMIZATION TEST FOR TWO INDEPENDENT SAMPLES; TEST 12B: THE
BOOTSTRAP; TEST 12C: THE JACKKNIFE; FINAL COMMENTS ON COMPUTER-INTENSIVE
PROCEDURES) 526 2. SURVIVAL ANALYSIS (TEST 12D: KAPLAN-MEIER ESTIMATE)
540 3. PROCEDURES FOR EVALUATING CENSORED DATA IN A DESIGN INVOLVING TWO
INDEPENDENT SAMPLES (PERMUTATION TEST BASED ON THE MEDIAN FOR CENSORED
DATA, GEHAN S TEST FOR CENSORED DATA (TEST 12E), AND THE LOG-RANK TEST
(TEST 12F)) 550 XVI HANDBOOK OF PARAMETRIC AND NONPARAMETRIC STATISTICAL
PROCEDURES COHEN S KAPPA, AND TEST 16K-B: TEST OF SIGNIFICANCE FOR *
TWO INDEPENDENT VALUES OF COHEN S KAPPA) 669 12. COMBINING THE RESULTS
OF MULTIPLE 2X2 CONTINGENCY TABLES: 673 HETEROGENEITY CHI-SQUARE
ANALYSIS FOR A 2 * 2 CONTINGENCY TABLE ; 673 TEST 161: THE
MANTEL-HAENSZEL ANALYSIS (TEST 161-A: TEST OF HOMOGENEITY OF ODDS RATIOS
FOR MANTEL-HAENSZEL ANALYSIS, TEST 161-B: SUMMARY ODDS RATIO FOR MANTEL-
HAENSZEL ANALYSIS, AND TEST 161-C: MANTEL-HAENSZEL TEST OF ASSOCIATION)
676 VII. ADDITIONAL DISCUSSION OFTHE CHI-SQUARE TEST FOR R X C TABLES
688 1. EQUIVALENCY OFTHE CHI-SQUARE TEST FOR R X C TABLES WHEN C = 2
WITH THE T TEST FOR TWO INDEPENDENT SAMPLES (WHEN R = 2) AND THE
SINGLE-FACTOR BETWEEN-SUBJECTS ANALYSIS OF VARIANCE (WHEN R T. 2) 688 2.
TEST OF EQUIVALENCE FOR TWO INDEPENDENT PROPORTIONS: TES T 16M: THE
WESTLAKE-SCHUIRMANN TEST OF EQUIVALENCE OF TWO INDEPENDENT PROPORTIONS
(AND PROCEDURE FOR COMPUTING SAMPLE SIZE IN REFERENCE TO THE POWER OFTHE
TEST) 688 3. TEST 16N: THE LOG-LIKELIHOOD RATIO 698 4. SIMPSON S PARADOX
700 5. ANALYSIS OF MULTIDIMENSIONAL CONTINGENCY TABLES THROUGH USE OF A
CHI-SQUARE ANALYSIS 702 6. TEST 16O:ANALYSIS OF MULTIDIMENSIONAL
CONTINGENCY TABLES WITH LOG-LINEAR ANALYSIS 713 VIII. ADDITIONAL
EXAMPLES ILLUSTRATING THE USE OFTHE CHI-SQUARE TEST FOR R X C TABLES
. .... 727 INFERENTIAL STATISTICAL TESTS EMPLOYED WITH TWO DEPENDENT
SAMPLES (AND RELATED MEASURES OF ASSOCIATION/CORRELATION) 741 TEST 17:
THE T TEST FOR TWO DEPENDENT SAMPLES 743 I. HYPOTHESIS EVALUATED WITH
TEST AND RELEVANT BACKGROUND INFORMATION 743 II. EXAMPLE -.-. -- 744
III. NULL VERSUS ALTERNATIVE HYPOTHESES R 744 IV. TEST COMPUTATIONS 745
V. INTERPRETATION OFTHE TEST RESULTS 747 VI. ADDITIONAL ANALYTICAL
PROCEDURES FOR THE / TEST FOR TWO DEPENDENT SAMPLES AND/OR RELATED TESTS
748 1. ALTERNATIVE EQUATION FOR THE T TEST FOR TWO DEPENDENT SAMPLES 748
2. THE EQUATION FOR THE T TEST FOR TWO DEPENDENT SAMPLES WHEN A VALUE
FOR A DIFFERENCE OTHER THAN ZERO IS STATED IN THE NULL HYPOTHESIS 752 3.
TEST 17A: THE / TEST FOR HOMOGENEITY OF VARIANCE FOR TWO DEPEN- DENT
SAMPLES: EVALUATION OFTHE HOMOGENEITY OF VARIANCE ASSUMPTION OFTHE /
TEST FOR TWO DEPENDENT SAMPLES 752 4. COMPUTATION OF THE POWER OFTHE /
TEST FOR TWO DEPENDENT SAMPLES AND THE APPLICATION OF TEST 17B: COHEN S
D INDEX 755 5. MEASURE OF MAGNITUDE OF TREATMENT EFFECT FOR THE / TEST
FOR TWO DEPENDENT SAMPLES: OMEGA SQUARED (TEST 17C) 761 TABLE OF
CONTENTS XVII 6. COMPUTATION OF A CONFIDENCE INTERVAL FOR THE T TEST FOR
TWO DEPENDENT SAMPLES . 763 7. TEST 17D: SANDLER S A TEST 764 8. TEST
17E: THE Z TEST FOR TWO DEPENDENT SAMPLES 765 VII. ADDITIONAL DISCUSSION
OFTHE T TEST FOR TWO DEPENDENT SAMPLES 768 1; THE USE OF MATCHED
SUBJECTS IN A DEPENDENT SAMPLES DESIGN 768 2. RELATIVE POWER OFTHE T
TEST FOR TWO DEPENDENT SAMPLES AND THE T TEST FOR TWO INDEPENDENT
SAMPLES 771 3. COUNTERBALANCING AND ORDER EFFECTS .. . 772 4. ANALYSIS
OF A ONE-GROUP PRETEST-POSTTEST DESIGN WITH THE T TEST FOR TWO DEPENDENT
SAMPLES 774 5. TESTS OF EQUIVALENCE: TEST 17F: THE WESTLAKE-SCHUIRMANN
TEST OF EQUIVALENCE OF TWO DEPENDENT TREATMENTS (AND PROCEDURE FOR
COMPUTING SAMPLE SIZE IN REFERENCE TO THE POWER OFTHE TEST) AND TEST
17G: TRYON S TEST OF EQUIVALENCE OF TWO DEPENDENT TREATMENTS 776 VIII.
ADDITIONAL EXAMPLE ILLUSTRATING THE USE OFTHE T TEST FOR TWO DEPENDENT
SAMPLES 785 TEST 18: THE WILCOXON MATCHED-PAIRS SIGNED-RANKS TEST 791 I.
HYPOTHESIS EVALUATED WITH TEST AND RELEVANT BACKGROUND INFORMATION 791
II. EXAMPLE 792 III. NULL VERSUS ALTERNATIVE HYPOTHESES 792 IV. TEST
COMPUTATIONS . 793 V. INTERPRETATION OFTHE TEST RESULTS 794 VI.
ADDITIONAL ANALYTICAL PROCEDURES FOR THE WILCOXON MATCHED-PAIRS
SIGNED-RANKS TEST AND/OR RELATED TESTS 796 1. THE NORMAL APPROXIMATION
OFTHE WILCOXON T STATISTIC FOR LARGE SAMPLE SIZES 796 2. THE CORRECTION
FOR CONTINUITY FOR THE NORMAL APPROXIMATION OF THE WILCOXON
MATCHED-PAIRS SIGNED-RANKS TEST 797 3. TIE CORRECTION FOR THE NORMAL
APPROXIMATION OF THE WILCOXON TEST STATISTIC : 798 4. COMPUTATION OF
ATONFIDENCE INTERVAL FOR A MEDIAN DIFFERENCE BETWEEN TWO DEPENDENT
POPULATIONS .-... 799 VII. ADDITIONAL DISCUSSION OFTHE WILCOXON
MATCHED-EAIRS SIGNED-RANKS TEST *. .- 801 1. POWER-EFFICIENCY OFTHE
WILCOXON MATCHED-PAIRS SIGNED-RANKS TEST 801 2. PROBABILITY OF
SUPERIORITY AS A MEASURE OF EFFECT SIZE 801 3. ALTERNATIVE NONPARAMETRIC
PROCEDURES FOR EVALUATING A DESIGN INVOLVING TWO DEPENDENT SAMPLES _.
801 VIII. ADDITIONAL EXAMPLES ILLUSTRATING THE USE OFTHE WILCOXON
MATCHED- PAIRS SIGNED-RANKS TEST 802 TEST 19: THE BINOMIAL SIGN TEST FOR
TWO DEPENDENT SAMPLES 805 I. HYPOTHESIS EVALUATED WITH TEST AND RELEVANT
BACKGROUND INFORMATION 805 II. EXAMPLE 806 III. NULL VERSUS ALTERNATIVE
HYPOTHESES 806 IV. TEST COMPUTATIONS 807 V. INTERPRETATION OFTHE TEST
RESULTS 809 XVIII HANDBOOK OF PARAMETRIC AND NONPARAMETRIC STATISTICAL
PROCEDURES VI. ADDITIONAL ANALYTICAL PROCEDURES FOR THE BINOMIAL SIGN
TEST FOR TWO DEPENDENT SAMPLES AND/OR RELATED TESTS 810 1. THE NORMAL
APPROXIMATION OF THE BINOMIAL SIGN TEST FOR TWO DEPENDENT SAMPLES WITH
AND WITHOUT A CORRECTION FOR CONTINUITY 810 2. COMPUTATION OF A
CONFIDENCE INTERVAL FOR THE BINOMIAL SIGN TEST FOR TWO DEPENDENT SAMPLES
; 813 3. SOURCES FOR COMPUTING THE POWER OFTHE BINOMIAL SIGN TEST FOR
TWO DEPENDENT SAMPLES, AND COMMENTS ON ASYMPTOTIC RELATIVE EFFICIENCY
OFTHE TEST 814 VII. ADDITIONAL DISCUSSION OFTHE BINOMIAL SIGN TEST FOR
TWO DEPENDENT SAMPLES 815 *1. THE PROBLEM OF AN EXCESSIVE NUMBER OF ZERO
DIFFERENCE SCORES 815 2. EQUIVALENCY OFTHE BINOMIAL SIGN TEST FOR TWO
DEPENDENT SAMPLES AND THE FRIEDMAN TWO-WAY ANALYSIS VARIANCE BY RANKS
WHEN K = 2 815 VIII. ADDITIONAL EXAMPLES ILLUSTRATING THE USE OFTHE
BINOMIAL SIGN TEST FOR TWO DEPENDENT SAMPLES ... , 815 TEST 20: THE
MCNEMAR TEST 817 I. HYPOTHESIS EVALUATED WITH TEST AND RELEVANT
BACKGROUND INFORMATION 817 II. EXAMPLES 818 III. NULL VERSUS ALTERNATIVE
HYPOTHESES 820 IV. TEST COMPUTATIONS 822 V. INTERPRETATION OFTHE TEST
RESULTS 822 VI. ADDITIONAL ANALYTICAL PROCEDURES FOR THE MCNEMAR TEST
AND/OR RELATED , TESTS ; , 823 1. ALTERNATIVE EQUATION FOR THE MCNEMAR
TEST STATISTIC BASED ON THE NORMAL DISTRIBUTION 823 2. THE CORRECTION
FOR CONTINUITY FOR THE MCNEMAR TEST 824 3. COMPUTATION OFTHE EXACT
BINOMIAL PROBABILITY FOR THE MCNEMAR TEST MODEL WITH A SMALL SAMPLE SIZE
825 4. COMPUTATION OFTHE POWER OFTHE MCNEMAR TEST : 827 5. COMPUTATION
OF A CONFIDENCE INTERVAL FOR THE MCNEMAR TEST 828 6. COMPUTATION OF AN
ODDS RATIO FOR THE MCNEMAR TEST 829 7. ADDITIONAL ANALYTICAL PROCEDURES
FOR THE MCNEMAR TEST 830 8. TEST 20A: THE GART TEST FOR ORDER EFFECTS F
830 VII. ADDITIONAL DISCUSSION OFTHE MCNEMAR TEST 838 1. ALTERNATIVE
FORMAT FOR THE MCNEMAR TEST SUMMARY TABLE AND MODIFIED TEST EQUATION 838
2. THE EFFECT OF DISREGARDING MATCHING 839 3. ALTERNATIVE NONPARAMETRIC
PROCEDURES FOR EVALUATING A DESIGN WITH TWO DEPENDENT SAMPLES INVOLVING
CATEGORICAL DATA 840 4. TEST OF EQUIVALENCE FOR TWO INDEPENDENT
PROPORTIONS: TEST 20B: THE WESTLAKE-SCHUIRMANN TEST OF EQUIVALENCE OF
TWO DEPENDENT PROPORTIONS 840 VIII. ADDITIONAL EXAMPLES ILLUSTRATING THE
USE OFTHE MCNEMAR TEST 850 IX. ADDENDUM 852 EXTENSION OF THE MCNEMAR
TEST MODEL BEYOND 2X2 CONTINGENCY TABLES 852 1. TEST 20C:THE BOWKER TEST
OF INTERNAL SYMMETRY 852 2. TEST 20D:THE STUART-MAXWELL TEST OF MARGINAL
HOMOGENEITY 856 TABLE OF CONTENTS XIX INFERENTIAL STATISTICAL TESTS
EMPLOYED WITH TWO OR MORE INDEPENDENT SAMPLES (AND RELATED MEASURES OF
ASSOCIATION/CORRELATION) , 865 TEST 21: THE SINGLE-FACTOR
BETWEEN-SUBJECTS ANALYSIS OF VARIANCE 867 I. HYPOTHESIS EVALUATED WITH
TEST AND RELEVANT BACKGROUND INFORMATION 867 II. EXAMPLE 868 III. NULL
VERSUS ALTERNATIVE HYPOTHESES 868 IV. TEST COMPUTATIONS 869 V.
INTERPRETATION OF THE TEST RESULTS 873 VI. ADDITIONAL ANALYTICAL
PROCEDURES FOR THE SINGLE-FACTOR BETWEEN- SUBJECTS ANALYSIS OF VARIANCE
AND/OR RELATED TESTS 874 1. COMPARISONS FOLLOWING COMPUTATION OF THE
OMNIBUS F VALUE FOR THE SINGLE-FACTOR BETWEEN-SUBJECTS ANALYSIS OF
VARIANCE (PLANNED VERSUS UNPLANNED COMPARISONS (INCLUDING SIMPLE VERSUS
COMPLEX COM- PARISONS); LINEAR CONTRASTS; ORTHOGONAL COMPARISONS; TEST
21A: MULTIPLE T TESTS/FISHER S LSD TEST; TEST 21B: THE BONFERRONI- DUNN
TEST; TEST 21C: TUKEY SHSD TEST; TEST 21D: THENEWMAN- KEULS TEST; TEST
21 E: THE SCHEFFE TEST; TEST 21F: THE DUNNETT TEST; ADDITIONAL
DISCUSSION OF COMPARISON PROCEDURES AND FINAL RECOMMENDATIONS; THE
COMPUTATION OF A CONFIDENCE INTERVAL FOR A COMPARISON) 874 2. COMPARING
THE MEANS OF THREE OR NIORE GROUPS WHEN K SF 4 905 3. EVALUATION OF THE
HOMOGENEITY OF VARIANCE ASSUMPTION OF THE SINGLE- FACTOR
BETWEEN-SUBJECTS ANALYSIS OF VARIANCE (TEST LLA: HARTLEY S F MIU TEST
FOR HOMOGENEITY OF VARIANCE, TEST 21G: THE LEVENE TEST FOR HOMOGENEITY
OF VARIANCE, TEST 21H: THE BROWN*FORSYTHE TEST FOR HOMOGENEITY OF
VARIANCE). 906 4. COMPUTATION OF THE POWER OF THE SINGLE-FACTOR
BETWEEN-SUBJECTS ANALYSIS OF VARIANCE 913 5. MEASURES OF MAGNITUDE OF
TREATMENT EFFECT FOR THE SINGLE-FACTOR BETWEEN-SUBJECTS ANALYSIS OF
VARIANCE: OMEGA SQUARED (TEST 21 I), ETA SQUARED (TEST.21 J), AND
COHEN S/INDEX (TEST 21K) .. 916 6. COMPUTATION OF A CONFIDENCE INTERVAL
FOR THE^MEAN OF A TREATMENT POPULATION 920 7. TREND ANALYSIS 922 VII.
ADDITIONAL DISCUSSION OFTHE SINGLE-FACTOR BETWEEN-SUBJECTS ANALYSIS OF
VARIANCE 934 1. THEORETICAL RATIONALE UNDERLYING THE SINGLE-FACTOR
BETWEEN-SUBJECTS ANALYSIS OF VARIANCE 934 2. DEFINITIONAL EQUATIONS FOR
THE SINGLE-FACTOR BETWEEN-SUBJECTS ANALYSIS OF VARIANCE ......... 936 3.
EQUIVALENCYOFTHESINGLE-FACTORBETWEEN-SUBJECTSANALYSISOFVARIANCE AND THE
F TEST FOR TWO INDEPENDENT SAMPLES WHEN K = 1 938 4. ROBUSTNESS OF THE
SINGLE-FACTOR BETWEEN-SUBJECTS ANALYSIS OF VARIANCE 939 5. EQUIVALENCY
OFTHE SINGLE-FACTOR BETWEEN-SUBJECTS ANALYSIS OF VARIANCE AND THE / TEST
FOR TWO INDEPENDENT SAMPLES WITH THE CHI-SQUARE TEST FOR R X C TABLES
WHEN C = 2 . .* 939 XX HANDBOOK OF PARAMETRIC AND NONPARAMETRIC
STATISTICAL PROCEDURES 6. THE GENERAL LINEAR MODEL 943 7. FIXED-EFFECTS
VERSUS RANDOM-EFFECTS MODELS FOR THE SINGLE-FACTOR BETWEEN-SUBJECTS
ANALYSIS OF VARIANCE 944 8. MULTIVARIATE ANALYSIS OF VARIANCE (MANOVA)
944 VIII. ADDITIONAL EXAMPLES ILLUSTRATING THE USE OFTHE SINGLE-FACTOR
BETWEEN- SUBJECTS ANALYSIS OF VARIANCE 945 IX. ADDENDUM .946 1. TEST
211: THE SINGLE-FACTOR BETWEEN-SUBJECTS ANALYSIS OF COVARIANCE 946 TEST
22: THE KRUSKAL-WALLIS ONE-WAY ANALYSIS OF VARIANCE BY RANKS 981 I.
HYPOTHESIS EVALUATED WITH TEST AND RELEVANT BACKGROUND INFORMATION 981
II. EXAMPLE : . 982 III. NULL VERSUS ALTERNATIVE HYPOTHESES 983 IV.
TEST COMPUTATIONS 983 V. INTERPRETATION OFTHE TEST RESULTS 985 VI.
ADDITIONAL ANALYTICAL PROCEDURES FOR THE KRUSKAL-WALLIS ONE-WAY ANALYSIS
OF VARIANCE BY RANKS AND/OR RELATED TESTS 985 1. TIE CORRECTION FOR THE
KRUSKAL-WALLIS ONE-WAY ANALYSIS OF VARIANCE BY RANKS 985 2. PAIRWISE
COMPARISONS FOLLOWING COMPUTATION OFTHE TEST STATISTIC FOR THE
KRUSKAL-WALLIS ONE-WAY ANALYSIS OF VARIANCE BY RANKS .. . 986 VII.
ADDITIONAL DISCUSSION OF THE KRUSKAL-WALLIS ONE-WAY ANALYSIS OF VARIANCE
BY RANKS . ..... 990 1. EXACT TABLES OFTHE KRUSKAL-WALLIS DISTRIBUTION
990 2. EQUIVALENCY OFTHE KRUSKAL-WALLIS ONE-WAY ANALYSIS OF VARIANCE
BY RANKS AND THE MANN-WHITNEY [/TEST WHEN K-2 990 3. POWER-EFFICIENCY OF
THE KRUSKAL-WALLIS ONE-WAY ANALYSIS OF VARIANCE BY RANKS ., 991 4.
ALTERNATIVE NONPARAMETRIC RANK-ORDER PROCEDURES FOR EVALUATING A DESIGN
INVOLVING K INDEPENDENT SAMPLES 991 VIII. ADDITIONAL EXAMPLES
ILLUSTRATING THE USE OFTHE KRUSKAL-WALLIS ONE- WAY ANALYSIS OF VARIANCE
BY RANKS 992 IX. ADDENDUM 993 1. TEST 22A: THE JONCKHEERE-TERPSTRA TEST
FOR ORDERED ALTERNATIVES 993 TEST 23: THE VAN DER WAERDEN NORMAL-SCORES
TEST FOR K INDEPENDENT SAMPLES 1007 I. HYPOTHESIS EVALUATED WITH TEST
AND RELEVANT BACKGROUND INFORMATION 1007 II. EXAMPLE , 1008 III. NULL
VERSUS ALTERNATIVE HYPOTHESES 1008 IV. TEST COMPUTATIONS 1009 V.
INTERPRETATION OFTHE TEST RESULTS 1011 VI. ADDITIONAL ANALYTICAL
PROCEDURES FOR THE VAN DER WAERDEN NORMAL- SCORES TEST FOR K INDEPENDENT
SAMPLES AND/OR RELATED TESTS 1012 1. PAIRWISE COMPARISONS FOLLOWING
COMPUTATION OFTHE TEST STATISTIC FOR THE VAN DER WAERDEN NORMAL-SCORES
TEST FOR K INDEPENDENT SAMPLES 1012 VII. ADDITIONAL DISCUSSION OFTHE VAN
DER WAERDEN NORMAL-SCORES TEST FOR K INDEPENDENT SAMPLES 1015 TABLE OF
CONTENTS ,V XXI 1. ALTERNATIVE NORMAL-SCORES TESTS 1015 VIII. ADDITIONAL
EXAMPLES ILLUSTRATING THE USE OFTHE VAN DER WAERDEN NORMAL-SCORES TEST
FOR K INDEPENDENT SAMPLES 1015 INFERENTIAL STATISTICAL TESTS EMPLOYED
WITH TWO OR MORE DEPENDENT SAMPLES (AND RELATED MEASURES OF
ASSOCIATION/CORRELATION) 1021 TEST 24: THE SINGLE-FACTOR WITHIN-SUBJECTS
ANALYSIS OF VARIANCE 1023 I. HYPOTHESIS EVALUATED WITH TEST AND RELEVANT
BACKGROUND INFORMATION 1023 II. EXAMPLE , 1025 III. NULL VERSUS
ALTERNATIVE HYPOTHESES 1025 IV. TEST COMPUTATIONS 1025 V. INTERPRETATION
OFTHE TEST RESULTS 1030 VI. ADDITIONAL ANALYTICAL PROCEDURES FOR THE
SINGLE-FACTOR WITHIN-SUBJECTS ANALYSIS OF VARIANCE AND/OR RELATED TESTS
1031 1. COMPARISONS FOLLOWING COMPUTATION OFTHE OMNIBUS F VALUE FOR THE
SINGLE-FACTOR WITHIN-SUBJECTS ANALYSIS OF VARIANCE (TEST 24A: MULTIPLE
/TESTS/FISHER S LSD TEST; TEST 24B: THE BONFERRONI- DUNN TEST; TEST 24C:
TUKEY S HSD TEST; TEST 24D: THE NEWMAN-KEULS TEST; TEST 24E: THE SCHEFFE
TEST; TEST 24F: THE DUNNETT TEST; THE COMPU- TATION OF A CONFIDENCE
INTERVAL FOR A COMPARISON; ALTERNATIVE METHOD- OLOGY FOR COMPUTING MS M
FOR A COMPARISON) 1031 2. COMPARING THE MEANS OF THREE OR MORE
CONDITIONS WHEN K Z 4 1039 3. EVALUATION OFTHE SPHERICITY ASSUMPTION
UNDERLYING THE SINGLE-FACTOR WITHIN-SUBJECTS ANALYSIS OF VARIANCE 1041
4. COMPUTATION OF THE POWER OF THE SINGLE-FACTOR WITHIN-SUBJECTS
ANALYSIS OF VARIANCE 1047 5. MEASURES OF MAGNITUDE OF TREATMENT EFFECT
FOR THE SINGLE-FACTOR WITHIN-SUBJECTS ANALYSIS OF VARIANCE: OMEGA
SQUARED (TEST 24G) AND COHEN S/ INDEX (TEST 24H) : 1049 6. COMPUTATION
OF A CONFIDENCE INTERVAL FOR THE MEAN OF A TREATMENT POPULATION 1051 7.
TEST 24I: THE INTRACLASS CORRELATION COEFFICIENT 1053 VII. ADDITIONAL
DISCUSSION OFTHE SINGLE-FACTOR WITHIN-SUBJECTS ANALYSIS OF VARIANCE 1055
1. THEORETICAL RATIONALE UNDERLYING THE SINGLE-FACTOR WITHIN-SUBJECTS
ANALYSIS OF VARIANCE 1055 2. DEFINITIONAL EQUATIONS FOR THE
SINGLE-FACTOR WITHIN-SUBJECTS ANALYSIS OF VARIANCE 1058 3. RELATIVE
POWER OFTHE SINGLE-FACTOR WITHIN-SUBJECTS ANALYSIS OF VAR- IANCE AND THE
SINGLE-FACTOR BETWEEN-SUBJECTS ANALYSIS OF VARIANCE 1061 4. EQUIVALENCY
OFTHE SINGLE-FACTOR WITHIN-SUBJECTS ANALYSIS OF VARIANCE AND THE T TEST
FOR TWO DEPENDENT SAMPLES WHEN K-2 1062 5. THE LATIN SQUARE DESIGN 1063
VIII. ADDITIONAL EXAMPLES ILLUSTRATING THE USE OFTHE SINGLE-FACTOR
WITHIN- SUBJECTS ANALYSIS OF VARIANCE 1065 XXII HANDBOOK OF PARAMETRIC
AND NONPARAMETRIC STATISTICAL PROCEDURES TEST 25: THE FRIEDMAN TWO-WAY
ANALYSIS OF VARIANCE BY RANKS 1075 I. HYPOTHESIS EVALUATED WITH TEST AND
RELEVANT BACKGROUND INFORMATION 1075 II. EXAMPLE 1076 III. NULL VERSUS
ALTERNATIVE HYPOTHESES 1076 IV. TEST COMPUTATIONS 1077 V. INTERPRETATION
OF THE TEST RESULTS 1 1078 VI. ADDITIONAL ANALYTICAL PROCEDURES FOR THE
FRIEDMAN TWO-WAY ANALYSIS VARIANCE BY RANKS AND/OR RELATED TESTS 1079 1.
TIE CORRECTION FOR THE FRIEDMAN TWO-WAY ANALYSIS VARIANCE BY RANKS ; *
1079 2. PAIRWISE COMPARISONS FOLLOWING COMPUTATION OFTHE TEST STATISTIC
FOR THE FRIEDMAN TWO-WAY ANALYSIS OF VARIANCE BY RANKS 1080 VII.
ADDITIONAL DISCUSSION OFTHE FRIEDMAN TWO-WAY ANALYSIS OF VARIANCE BY
RANKS 1085 1. EXACT TABLES OFTHE FRIEDMAN DISTRIBUTION 1085 2.
EQUIVALENCY OFTHE FRIEDMAN TWO-WAY ANALYSIS OF VARIANCE BY RANKS AND THE
BINOMIAL SIGN TEST FOR TWO DEPENDENT SAMPLES WHEN K = 2 1085 3.
POWER-EFFICIENCY OFTHE FRIEDMAN TWO-WAY ANALYSIS OF VARIANCE BY RANKS
1086 4. ALTERNATIVE NONPARAMETRIC RANK-ORDER PROCEDURES FOR EVALUATING A
DESIGN INVOLVING K DEPENDENT SAMPLES 1086 5. RELATIONSHIP BETWEEN THE
FRIEDMAN TWO-WAY ANALYSIS OF VARIANCE BY RANKS AND KENDALL S COEFFICIENT
OF CONCORDANCE 1087 VIII. ADDITIONAL EXAMPLES ILLUSTRATING THE USE OFTHE
FRIEDMAN TWO-WAY ANALYSIS OF VARIANCE BY RANKS ! 1087 IX. ADDENDUM *
1088 L.TEST 25A: THE PAGE TEST FOR ORDERED ALTERNATIVES 1088 TEST 26:
THE COCHRAN Q TEST 1099 I. HYPOTHESIS EVALUATED WITH TEST AND RELEVANT
BACKGROUND INFORMATION 1099 II. EXAMPLE 1100 III. NULL VERSUS
ALTERNATIVE HYPOTHESES 1100 IV. TEST COMPUTATIONS 1100 V. INTERPRETATION
OF THE TEST RESULTS *. 1102 VI. ADDITIONAL ANALYTICAL PROCEDURES FOR THE
COCHRAN Q TEST AND/OR RELATED TESTS 1102 1. PAIRWISE COMPARISONS
FOLLOWING COMPUTATION OFTHE TEST STATISTIC FOR THE COCHRAN GTEST 1102
VII. ADDITIONAL DISCUSSION OFTHE COCHRAN Q TEST 1106 1. ISSUES RELATING
TO SUBJECTS WHO OBTAIN THE SAME SCORE UNDER ALL OF THE EXPERIMENTAL
CONDITIONS 1106 2. EQUIVALENCY OF THE COCHRAN Q TEST AND THE MCNEMAR
TEST WHEN K = 2 1107 3. ALTERNATIVE NONPARAMETRIC PROCEDURES WITH
CATEGORICAL DATA FOR EVALUATING A DESIGN INVOLVING K DEPENDENT SAMPLES
1109 VIII. ADDITIONAL EXAMPLES ILLUSTRATING THE USE OFTHE COCHRAN Q TEST
1109 INFERENTIAL STATISTICAL TEST EMPLOYED WITH A FACTORIAL DESIGN (AND
RELATED MEASURES OF ASSOCIATION/CORRELATION) 1117 TABLE OF CONTENTS
XXIII TEST 27: THE BETWEEN-SUBJECTS FACTORIAL ANALYSIS OF VARIANCE 1119
I. HYPOTHESIS EVALUATED WITH TEST AND RELEVANT BACKGROUND INFORMATION
1119 II. EXAMPLE 1120 III. NULL VERSUS ALTERNATIVE HYPOTHESES 1120 IV.
TEST COMPUTATIONS : .... 1122 V. INTERPRETATION OF THE TEST RESULTS 1.
.1128 VI. ADDITIONAL ANALYTICAL PROCEDURES FOR THE BETWEEN-SUBJECTS
FACTORIAL ANALYSIS OF VARIANCE AND/OR RELATED TESTS 1132 1. COMPARISONS
FOLLOWING COMPUTATION OF THE F VALUES FOR THE BETWEEN- SUBJECTS
FACTORIAL ANALYSIS OF VARIANCE (TEST 27A: MULTIPLE T TESTS/ FISHER S LSD
TEST; TEST 27B: THE BONFERRONI-DUNN TEST; TEST 27C: TUKEY S HSD TEST;
TEST 27D: THE NEWMAN-KEULS TEST; TEST 27E: THE SCHEFFT TEST; TEST 27F:
THE DUNNETT TEST; COMPARISONS BETWEEN THE MARGINAL MEANS; EVALUATION OF
AN OMNIBUS HYPOTHESIS INVOLVING MORE THAN TWO MARGINAL MEANS;
COMPARISONS BETWEEN SPECIFIC GROUPS THAT ARE A COMBINATION OF BOTH
FACTORS; THE COMPUTATION OF A CONFIDENCE INTERVAL FOR A COMPARISON;
ANALYSIS OF SIMPLE EFFECTS) 1132 2. EVALUATION OFTHE HOMOGENEITY OF
VARIANCE ASSUMPTION OFTHE BETWEEN- SUBJECTS FACTORIAL ANALYSIS OF
VARIANCE 1143 3. COMPUTATION OFTHE POWER OFTHE BETWEEN-SUBJECTS
FACTORIAL ANALYSIS OF VARIANCE 1144 4. MEASURES OF MAGNITUDE OF
TREATMENT EFFECT FOR THE BETWEEN-SUBJECTS FACTORIAL ANALYSIS OF
VARIANCE: OMEGA SQUARED (TEST 27G) AND COHEN S /INDEX (TEST 27H) 1146 5.
COMPUTATION OF A CONFIDENCE INTERVAL FOR THE MEAN OF A POPULATION
REPRESENTED BY A GROUP 1150 VII. ADDITIONAL DISCUSSION OF THE
BETWEEN-SUBJECTS FACTORIAL ANALYSIS OF VARIANCE 1150 1. THEORETICAL
RATIONALE UNDERLYING THE BETWEEN-SUBJECTS FACTORIAL ANALYSIS OF VARIANCE
; . 1150 2. DEFINITIONAL EQUATIONS FOR THE BETWEEN-SUBJECTS FACTORIAL
ANALYSIS OF VARIANCE ... ..* 1151 3. UNEQUAL SAMPLE SIZES 1153 4. THE
RANDOMIZED-BLOCKS DESIGN -. 1154 5. ADDITIONAL COMMENTS ON THE
BETWEEN-SUBJECTS FACTORIAL ANALYSIS OF VARIANCE (FIXED-EFFECTS VERSUS
RANDOM-EFFECTS VERSUS MIXED-EFFECTS MODELS; NESTED
FACTORS/HIERARCHICAL DESIGNS AND DESIGNS INVOLVING MORE THAN TWO
FACTORS; SCREENING DESIGNS) 1158 VIII. ADDITIONAL EXAMPLES ILLUSTRATING
THE USE OFTHE BETWEEN-SUBJECTS FACTORIAL ANALYSIS OF VARIANCE 1161 DC.
ADDENDUM 1162 DISCUSSION OF AND COMPUTATIONAL PROCEDURES FOR
ADDITIONAL ANALYSIS OF VARIANCE PROCEDURES FOR FACTORIAL DESIGNS 1162 1.
TEST 27I: THE FACTORIAL ANALYSIS OF VARIANCE FOR A MIXED DESIGN : 1162
ANALYSIS OF A CROSSOVER DESIGN WITH A FACTORIAL ANALYSIS OF VARIANCE FOR
A MIXED DESIGN ;. . : . 1167 2. TEST 27J: ANALYSIS OF VARIANCE FOR A
LATIN SQUARE DESIGN 1 182 XX IV HANDBOOK OF PARAMETRIC AND NONPARAMETRIC
STATISTICAL PROCEDURES 3. TEST 27K: THE WITHIN-SUBJECTS FACTORIAL
ANALYSIS OF VARIANCE 1203 4. ANALYSIS OF HIGHER ORDER FACTORIAL DESIGNS
1208 MEASURES OF ASSOCIATION/CORRELATION 1219 TEST 28: THE PEARSON
PRODUCT-MOMENT CORRELATION COEFFICIENT 1221 I. HYPOTHESIS EVALUATED WITH
TEST AND RELEVANT BACKGROUND INFORMATION 1221 II. EXAMPLE 1225 III. NULL
VERSUS ALTERNATIVE HYPOTHESES 1225 IV. TEST COMPUTATIONS . 1226 V.
INTERPRETATION OFTHE TEST RESULTS (TEST 28A: TEST OF SIGNIFICANCE FOR A
PEARSON PRODUCT-MOMENT CORRELATION COEFFICIENT; THE COEFFICIENT OF
DETERMINATION) 1228 VI. ADDITIONAL ANALYTICAL PROCEDURES FOR THE PEARSON
PRODUCT-MOMENT CORRELATION COEFFICIENT AND/OR RELATED TESTS 1231 1.
DERIVATION OF A REGRESSION LINE 1231 2. THE STANDARD ERROR OF ESTIMATE
1240 3. COMPUTATION OF A CONFIDENCE INTERVAL FOR THE VALUE OF THE
CRITERION VARIABLE 1241 4. COMPUTATION OF A CONFIDENCE INTERVAL FOR A
PEARSON PRODUCT-MOMENT CORRELATION COEFFICIENT 1243 5. TEST 28B: TEST
FOR EVALUATING THE HYPOTHESIS THAT THE TRUE POPULATION CORRELATION IS A
SPECIFIC VALUE OTHER THAN ZERO .... 1244 6. COMPUTATION OF POWER FOR THE
PEARSON PRODUCT-MOMENT CORRELATION COEFFICIENT 1245 7. TEST 28C: TEST
FOR EVALUATING A HYPOTHESIS ON WHETHER THERE IS A SIGNIFICANT DIFFERENCE
BETWEEN TWO INDEPENDENT CORRELATIONS 1247 8. TEST 28D: TEST FOR
EVALUATING A HYPOTHESIS ON WHETHER K INDEPEN- DENT CORRELATIONS ARE
HOMOGENEOUS 1249 9. TEST 28E: TEST FOR EVALUATING THE NULL HYPOTHESIS H
0 :P X2 =P Y Z 1250 10. TESTS FOR EVALUATING A HYPOTHESIS REGARDING ONE
OR MORE REGRESSION COEFFICIENTS (TEST 28F: TEST FOR EVALUATING THE NULL
HYPOTHESIS H O : P = 0; TEST 28G: TEST FOR EVALUATING THE NULL
HYPOTHESIS H O : P , = P 2 ) ... 1252 11.
ADDITIONALCORRELATIONALPROCEDURES ; T 1254 VII. ADDITIONAL DISCUSSION
OF THE PEARSON PRODUCT-MOMENT CORRELATION COEFFICIENT . , 1255 1. THE
DEFINITIONAL EQUATION FOR THE PEARSON PRODUCT-MOMENT CORRELATION I
COEFFICIENT 1255 2. COVARIANCE 1256 3. THE HOMOSCEDASTICITY ASSUMPTION
OF THE PEARSON PRODUCT-MOMENT CORRELATION COEFFICIENT ,****. * * 1257 4.
RESIDUALS, ANALYSIS OF VARIANCE FOR REGRESSION ANALYSIS AND REGRESSION
DIAGNOSTICS 1258 5. AUTOCORRELATION (AND TEST 28H: DURBIN-WATSON TEST) .
1269 6. THE PHI COEFFICIENT AS A SPECIAL CASE OF THE PEARSON
PRODUCT-MOMENT CORRELATION COEFFICIENT 1284 7. ECOLOGICAL CORRELATION ;
1285 8. CROSS-LAGGED PANEL AND REGRESSION-DISCONTINUITY DESIGNS 1288
VIII. ADDITIONAL EXAMPLES ILLUSTRATING THE USE OFTHE PEARSON PRODUCT-
MOMENT CORRELATION COEFFICIENT 1295 TABLE OF CONTENTS XXV IX. ADDENDUM
1295 1. BIVARIATE MEASURES OF CORRELATION THAT ARE RELATED TO THE
PEARSON PRODUCT- MOMENT CORRELATION COEFFICIENT (TEST 28I: THE
POINT-BISERIAL CORRELATION COEFFICIENT (AND TEST 28I-A: TEST OF
SIGNIFICANCE FOR A POINT-BISERIAL CORRELATION COEFFICIENT); TEST 28J:
THE BISERIAL CORRELATION COEFFICIENT (AND TEST 28J-A: TEST OF
SIGNIFICANCE FOR A BISERIAL CORRELATION COEFFICIENT); TEST 28K: THE
TETRACHORIC CORRELATION COEFFICIENT (AND TEST 28K-A: TEST OF
SIGNIFICANCE FOR A TETRACHORIC CORRELATION COEFFICIENT)) 1296 2.
META-ANALYSIS AND RELATED TOPICS (MEASURES OF EFFECT SIZE; META-ANALYTIC
PROCEDURES (TEST 281: PROCEDURE FOR COMPARING K STUDIES WITH RESPECT TO
SIGNIFICANCE LEVEL; TEST 28M: THE STOUFFER PROCEDURE FOR OBTAINING A
COMBINED SIGNIFICANCE LEVEL (P VALUE) FOR K STUDIES; THE FILE DRAWER
PROBLEM; TEST 28N: PROCEDURE FOR COMPARING K STUDIES WITH RESPECT TO
EFFECT SIZE; TEST 28O: PROCEDURE FOR OBTAINING A COMBINED EFFECT SIZE
FOR K STUDIES); ALTERNATIVE META-ANALYTIC PROCEDURES; PRACTICAL
IMPLICATIONS OF MAGNITUDE OF EFFECT SIZE VALUE; TEST 28P: BINOMIAL
EFFECT SIZE DISPLAY; THE SIGNIFICANCE TEST CONTROVERSY; THE
MINIMUM-EFFECT HYPOTHESIS TESTING MODEL) 1306 TEST 29: SPEARMAN S
RANK-ORDER CORRELATION COEFFICIENT 1353 I. HYPOTHESIS EVALUATED WITH
TEST AND RELEVANT BACKGROUND INFORMATION 1353 II. EXAMPLE 1355 III. NULL
VERSUS ALTERNATIVE HYPOTHESES 1355 IV. TEST COMPUTATIONS 1356 V.
INTERPRETATION OFTHE TEST RESULTS (TEST 29A: TEST OF SIGNIFICANCE FOR
SPEARMAN S RANK-ORDER CORRELATION COEFFICIENT) 1357 VI. ADDITIONAL
ANALYTICAL PROCEDURES FOR SPEARMAN S RANK-ORDER CORRELATION COEFFICIENT
AND/OR RELATED TESTS ****** 1359 1. TIE CORRECTION FOR SPEARMAN S
RANK-ORDER CORRELATION COEFFICIENT 1359 2. SPEARMAN S RANK-ORDER
CORRELATION COEFFICIENT AS A SPECIAL CASE OFTHE PEARSON PRODUCT-MOMENT
CORRELATION COEFFICIENT 1361 3. REGRESSION ANALYSIS AND SPEARMAN S
RANK-ORDER CORRELATION COEFFICIENT 1362 4. PARTIAL RANK CORRELATION ^
1363 5. USE OF FISHER S Z R TRANSFORMATION WITH SPEARMAN S RANK- ORDER
CORRELATION COEFFICIENT 1364 VII. ADDITIONAL DISCUSSION OF SPEARMAN S
RANK-ORDER CORRELATION COEFFICIENT 1364 1. THE RELATIONSHIP BETWEEN
SPEARMAN S RANK-ORDER CORRELATION COEFFICIENT, KENDALL S COEFFICIENT OF
CONCORDANCE, AND THE FRIEDMAN TWO-WAY ANALYSIS OF VARIANCE BY RANKS :
1364 2. POWER EFFICIENCY OF SPEARMAN S RANK-ORDER CORRELATION
COEFFICIENT 1367 3. BRIEF DISCUSSION OF KENDALL S TAU: AN ALTERNATIVE
MEASURE OF ASSOCIATION FOR TWO SETS OF RANKS 1367 4. WEIGHTED
RANK/TOP-DOWN CORRELATION 1367 VIII. ADDITIONAL EXAMPLES ILLUSTRATING
THE USE OFTHE SPEARMAN S RANK-ORDER CORRELATION COEFFICIENT 1368 XXVI
HANDBOOK OF PARAMETRIC AND NONPARAMETRIC STATISTICAL PROCEDURES TEST 30:
KENDALL S TAU 1371 I. HYPOTHESIS EVALUATED WITH TEST AND RELEVANT
BACKGROUND INFORMATION 1371 II. EXAMPLE 1373 III. NULL VERSUS
ALTERNATIVE HYPOTHESES 1373 IV. TEST COMPUTATIONS 1374 V. INTERPRETATION
OF THE TEST RESULTS (TEST 30A: TEST OF SIGNIFICANCE FOR KENDALL S TAU)
1376 VI. ADDITIONAL ANALYTICAL PROCEDURES FOR KENDALL S TAU AND/OR
RELATED TESTS 1379 1. TIE CORRECTION FOR KENDALL S TAU 1379 2.
REGRESSION ANALYSIS AND KENDALL S TAU 1382 3. PARTIAL RANK CORRELATION
1382 4. SOURCES FOR COMPUTING A CONFIDENCE INTERVAL FOR KENDALL S TAU
1382 VII. ADDITIONAL DISCUSSION OF KENDALL S TAU 1382 1. POWER
EFFICIENCY OF KENDALL S TAU 1382 2. KENDALL S COEFFICIENT OF AGREEMENT
1382 VIII. ADDITIONAL EXAMPLES ILLUSTRATING THE USE OF KENDALL S TAU
1382 TEST 31: KENDALL S COEFFICIENT OF CONCORDANCE 1387 I. HYPOTHESIS
EVALUATED WITH TEST AND RELEVANT BACKGROUND INFORMATION 1387 II. EXAMPLE
1388 III. NULL VERSUS ALTERNATIVE HYPOTHESES 1388 IV. TEST COMPUTATIONS
1389 V. INTERPRETATION OFTHE TEST RESULTS (TEST 31A: TEST OF
SIGNIFICANCE FOR KENDALL S COEFFICIENT OF CONCORDANCE) 1390 VI.
ADDITIONAL ANALYTICAL PROCEDURES FOR KENDALL S COEFFICIENT OF
CONCORDANCE AND/OR RELATED TESTS , 1391 1. TIE CORRECTION FOR KENDALL S
COEFFICIENT OF CONCORDANCE . 1391 VII. ADDITIONAL DISCUSSION OF
KENDALL S COEFFICIENT OF CONCORDANCE 1393 1. RELATIONSHIP BETWEEN
KENDALL S COEFFICIENT OF CONCORDANCE AND SPEARMAN S RANK-ORDER
CORRELATION COEFFICIENT 1393 2. RELATIONSHIP BETWEEN KENDALL S
COEFFICIENT OF CONCORDANCE AND THE FRIEDMAN TWO-WAY ANALYSIS OF VARIANCE
BY RANKS 1394 3. WEIGHTED RANK/TOP-DOWN CONCORDANCE . . ^ 1396 4.
KENDALL S COEFFICIENT OF CONCORDANCE VERSUS THE INTRACLASS CORRELATION
COEFFICIENT 1396 VIII. ADDITIONAL EXAMPLES ILLUSTRATING THE USE OF
KENDALL S COEFFICIENT OF CONCORDANCE 1398 TEST 32: GOODMAN AND KRUSKAL S
GAMMA 1403 I. HYPOTHESIS EVALUATED WITH TEST AND RELEVANT BACKGROUND
INFORMATION 1403 II. -EXAMPLE 1404 III. NULL VERSUS ALTERNATIVE
HYPOTHESES 1405 IV. TEST COMPUTATIONS 1406 V. INTERPRETATION OF THE TEST
RESULTS (TEST 32A: TEST OF SIGNIFICANCE FOR GOODMAN AND KRUSKAL S GAMMA)
1409 VI. ADDITIONAL ANALYTICAL PROCEDURES FOR GOODMAN AND KRUSKAL S
GAMMA AND/OR RELATED TESTS 1410 TABLE OF CONTENTS XXVII 1. THE
COMPUTATION OF A CONFIDENCE INTERVAL FOR THE VALUE OF GOODMAN AND
KRUSKAL S GAMMA , 1410 2. TEST 32B: TEST FOR EVALUATING THE NULL
HYPOTHESIS //*: YI = Y, 1411 3. SOURCES FOR COMPUTING A PARTIAL
CORRELATION COEFFICIENT FOR GOODMAN AND KRUSKAL S GAMMA 1412 VII.
ADDITIONAL DISCUSSION OF GOODMAN AND KRUSKAL S GAMMA .. .. 1412 1.
RELATIONSHIP BETWEEN GOODMAN AND KRUSKAL S GAMMA AND YULE S Q ... 1412
2. SOMERS DELTA AS AN ALTERNATIVE MEASURE OF ASSOCIATION FOR AN ORDERED
CONTINGENCY TABLE : 1412 VIII. ADDITIONAL EXAMPLES ILLUSTRATING THE USE
OF GOODMAN AND KRUSKAL S GAMMA 1413 MULTIVARIATE STATISTICAL ANALYSIS
1417 MATRIX ALGEBRA AND MULTIVARIATE ANALYSIS , 1419 I. INTRODUCTORY
COMMENTS ON MULTIVARIATE STATISTICAL ANALYSIS .1419 II. INTRODUCTION TO
MATRIX ALGEBRA 1420 TEST 33: MULTIVARIATE REGRESSION , 1433 I.
HYPOTHESIS EVALUATED WITH TEST AND RELEVANT BACKGROUND INFORMATION 1433
II. EXAMPLES : 1439 III. NULL VERSUS ALTERNATIVE HYPOTHESES .-.* 1441
RWV. TEST COMPUTATIONS AND INTERPRETATION OFTHE TEST RESULTS TEST
COMPUTATIONS AND INTERPRETATION OF RESULTS FOR EXAMPLE 33.1 (COMPUTATION
OFTHE MULTIPLE CORRELATION COEFFICIENT; THE COEFFICIENT OF MULTIPLE
DETERMINATION; TEST OF SIGNIFICANCE FOR A MULTIPLE CORRELATION
COEFFICIENT; THE MULTIPLE REGRESSION EQUATION; THE STANDARD ERROR OF
MULTIPLE ESTIMATE; COMPUTATION OF A CONFIDENCE INTERVAL FOR Y ; EVALUA-
TION OFTHE RELATIVE IMPORTANCE OFTHE PREDICTOR VARIABLES; EVALUATING THE
SIGNIFICANCE OF A REGRESSION COEFFICIENT; COMPUTATION OF A CONFIDENCE
INTERVAL FOR A REGRESSION COEFFICIENT; ANALYSIS OF VARIANCE FOR MULTIPLE
REGRESSION; SEMIPARTIAL AND PARTIAL CORRELATION (TES T 33A: COMPUTATION
OF A SEMIPARTIAL CORRELATION COEFFICIENT; TEST OF SIGNIFICANCE FOR A
SEMIPARTIAL CORRELATION COEFFICIENT; TEST 33B: COMPUTATION OF A PARTIAL
CORRELATION COEFFICIENT; TEST OF SIGNIFICANCE FOR A PARTIAL CORRELATION
COEFFICIENT) 1442 TEST COMPUTATIONS AND INTERPRETATION OF RESULTS FOR
EXAMPLE 33.2 WITH SPSS 1459 VI. ADDITIONAL ANALYTICAL PROCEDURES FOR
MULTIPLE REGRESSION .-/.,. AND/OR RELATED TESTS V. . Y . 1470 1.
CROSS-VALIDATION OF SAMPLE DATA 1470 VII. ADDITIONAL DISCUSSION OF
MULTIVARIATE REGRESSION , 1471 1. FINAL COMMENTS ON MULTIPLE REGRESSION
ANALYSIS ;. 1471 2. CAUSAL MODELING: PATH ANALYSIS AND STRUCTURAL *
EQUATION MODELING R 1472 3. BRIEF NOTE ON LOGISTIC REGRESSION 1473 VIII.
ADDITIONAL EXAMPLES ILLUSTRATING THE USE OF MULTIVARIATE REGRESSION 1474
XXVIII HANDBOOK OF PARAMETRIC AND NONPARAMETRIC STATISTICAL PROCEDURES
TEST 34: HOTELLING S T 1 1483 L HYPOTHESIS EVALUATED WITH TEST AND
RELEVANT BACKGROUND INFORMATION 1483 II. EXAMPLE 1483 III. NULL VERSUS
ALTERNATIVE HYPOTHESES 1484 IV. TEST COMPUTATIONS . ,. 1485 V.
INTERPRETATION OFTHE TEST RESULTS . ...* 1486 VI. ADDITIONAL ANALYTICAL
PROCEDURES FOR HOTELLING S T 2 AND/OR RELATED TESTS 1488 1. ADDITIONAL
ANALYSES FOLLOWING THE TEST OF THE OMNIBUS NULL HYPOTHESIS : 1488 2.
TEST 34A: THE SINGLE-SAMPLE HOTELLING S T 1 1489 3. TEST 34B: THE USE OF
THE SINGLE-SAMPLE HOTELLING S T 1 TO EVALUATE A DEPENDENT SAMPLES DESIGN
1491 VII. ADDITIONAL DISCUSSION OF HOTELLING S T 2 1495 1. HOTELLING S T
2 AND MAHALANOBIS D 2 STATISTIC 1495 VIII. ADDITIONAL EXAMPLES
ILLUSTRATING THE USE OF HOTELLING S T 2 1495 TEST 35: MULTIVARIATE
ANALYSIS OF VARIANCE 1499 I. HYPOTHESIS EVALUATED WITH TEST AND RELEVANT
BACKGROUND INFORMATION 1499 II. EXAMPLE , 1500 III. NULL VERSUS
ALTERNATIVE HYPOTHESES 1501 IV. TEST COMPUTATIONS 1502 V. INTERPRETATION
OFTHE TEST RESULTS 1503 VI. ADDITIONAL ANALYTICAL PROCEDURES FOR THE
MULTIVARIATE ANALYSIS OF VARIANCE AND/OR RELATED TESTS 1510 VII.
ADDITIONAL DISCUSSION OFTHE MULTIVARIATE ANALYSIS OF VARIANCE 1510 1.
CONCEPTUALIZING THE HYPOTHESIS FOR THE MULTIVARIATE ANALYSIS OF VARIANCE
WITHIN THE CONTEXT OF A LINEAR COMBINATION 1510 2. MULTICOLLINEARITY AND
THE MULTIVARIATE ANALYSIS OF VARIANCE .1510 VIII. ADDITIONAL EXAMPLES
ILLUSTRATING THE USE OFTHE MULTIVARIATE ANALYSIS OF VARIANCE - 1511 TEST
36: MULTIVARIATE ANALYSIS OF COVARIANCE 1515 I. HYPOTHESIS EVALUATED
WITH TEST AND RELEVANT BACKGROUND INFORMATION 1515 II. EXAMPLE : 1516
III. NULL VERSUS ALTERNATIVE HYPOTHESES 1517 IV. TEST COMPUTATIONS : :
1517 V. INTERPRETATION OFTHE TEST RESULTS 1518 VI. ADDITIONAL ANALYTICAL
PROCEDURES FOR THE MULTIVARIATE ANALYSIS OF COVARIANCE AND/OR RELATED
TESTS 1521 VII. ADDITIONAL DISCUSSION OFTHE MULTIVARIATE ANALYSIS OF
COVARIANCE 1521 1. MULTIPLE COVARIATES 1521 VIII. ADDITIONAL EXAMPLES
ILLUSTRATING THE USE OFTHE MULTIVARIATE ANALYSIS OF COVARIANCE 1522 TEST
37: DISCRIMINANT FUNCTION ANALYSIS 1525 I. HYPOTHESIS EVALUATED WITH
TEST AND RELEVANT BACKGROUND INFORMATION 1525 II. EXAMPLES 1527 III.
NULL VERSUS ALTERNATIVE HYPOTHESES 1528 TABLE OF CONTENTS XXIX IV. TEST
COMPUTATIONS : 1529 V. INTERPRETATION OFTHE TEST RESULTS 1531 ANALYSIS
OF EXAMPLE 37.1 1531 ANALYSIS OF EXAMPLE 37.2 1543 VI. ADDITIONAL
ANALYTICAL PROCEDURES FOR DISCRIMINANT FUNCTION ANALYSIS AND/OR RELATED
TESTS 1552 VII. ADDITIONAL DISCUSSION OF DISCRIMINANT FUNCTION ANALYSIS
1552 VIII. ADDITIONAL EXAMPLES ILLUSTRATING THE USE OF DISCRIMINANT
FUNCTION ANALYSIS 1552 TEST 38: CANONICAL CORRELATIONAL 1557 I.
HYPOTHESIS EVALUATED WITH TEST AND RELEVANT BACKGROUND INFORMATION 1557
II. EXAMPLE 1560 III. NULL VERSUS ALTERNATIVE HYPOTHESES 1560 IV. TEST
COMPUTATIONS 1560 V. INTERPRETATION OFTHE TEST RESULTS 1561 VI.
ADDITIONAL ANALYTICAL PROCEDURES FOR CANONICAL CORRELATION AND/OR
RELATED TESTS 1574 VII. ADDITIONAL DISCUSSION OF CANONICAL CORRELATION
1574 VIII. ADDITIONAL EXAMPLES ILLUSTRATING THE USE OF CANONICAL
CORRELATION 1575 TEST39: LOGISTIC REGRESSION 1581 I. HYPOTHESIS
EVALUATED WITH TEST AND RELEVANT BACKGROUND INFORMATION 1581 II. EXAMPLE
1584 III. NULL VERSUS ALTERNATIVE HYPOTHESES 1584 IV. TEST COMPUTATIONS
1587 V. INTERPRETATION OFTHE TEST RESULTS 1590 RESULTS FOR A BINARY
LOGISTIC REGRESSION WITH ONE PREDICTOR VARIABLE 1590 RESULTS FOR A
BINARY LOGISTIC REGRESSION WITH MULTIPLE PREDICTOR VARIABLES . 1598 VI.
ADDITIONAL ANALYTICAL PROCEDURES FOR LOGISTIC REGRESSION AND/OR RELATED
TESTS 1605 VII. ADDITIONAL DISCUSSION OF LOGISTIC REGRESSION 1606 VIII.
ADDITIONAL EXAMPLES ILLUSTRATING THE USE OF LOGISTIC REGRESSION 1606
TEST 40: PRINCIPAL COMPONENTS ANALYSIS AND FACTOR ANALYSIS 1615 I.
HYPOTHESIS EVALUATED WITH TEST AND RELEVANT BACKGROUND INFORMATION 1615
II. EXAMPLE 1618 III. NULL VERSUS ALTERNATIVE HYPOTHESES 1618 IV. TEST
COMPUTATIONS 1618 V. INTERPRETATION OFTHE TEST RESULTS 1622 VI.
ADDITIONAL ANALYTICAL PROCEDURES FOR PRINCIPAL COMPONENTS ANALYSIS AND
FACTOR ANALYSIS AND/OR RELATED TESTS 1634 1. PRINCIPAL AXIS FACTOR
ANALYSIS OF EXAMPLE 40.1 1634 VII. ADDITIONAL DISCUSSION OF PRINCIPAL
COMPONENTS ANALYSIS AND FACTOR ANALYSIS 1635 1. CRITICISMS OF FACTOR
ANALYTIC PROCEDURES 1635 2. CLUSTER ANALYSIS 1635 3. MULTIDIMENSIONAL
SCALING 1636 XXX HANDBOOK OF PARAMETRIC AND NONPARAMETRIC STATISTICAL
PROCEDURES VIII. ADDITIONAL EXAMPLES ILLUSTRATING THE USE OF PRINCIPAL
COMPONENTS ANALYSIS AND FACTOR ANALYSIS 1637 APPENDIX: TABLES 1647 TABLE
AL. TABLE OFTHE NORMAL DISTRIBUTION ..; 1651 TABLE A2. TABLE OF
STUDENT S /DISTRIBUTION 1656 TABLE A3. POWER CURVES FOR STUDENT S /
DISTRIBUTION 1657 TABLE A4. TABLE OFTHE CHI-SQUARE DISTRIBUTION 1661
TABLE A5. TABLE OF CRITICAL T VALUES FOR WILCOXON S SIGNED-RANKS AND
MATCHED-PAIRS SIGNED-RANKS TESTS 1662 TABLE A6. TABLE OFTHE BINOMIAL
DISTRIBUTION, INDIVIDUAL PROBABILITIES 1663 TABLE A7. TABLE OFTHE
BINOMIAL DISTRIBUTION, CUMULATIVE PROBABILITIES 1666 TABLE A8. TABLE OF
CRITICAL VALUES FOR THE SINGLE-SAMPLE RUNS TEST 1669 TABLE A9. TABLE
OFTHE F MM DISTRIBUTION 1670 TABLE A10. TABLE OFTHE F DISTRIBUTION 1671
TABLE ALL. TABLE OF CRITICAL VALUES FOR MANN-WHITNEY {/STATISTIC 1679
TABLE A12. TABLE OF SANDLER S/4 STATISTIC 1681 TABLE A13. TABLE OFTHE
STUDENTIZED RANGE STATISTIC 1682 TABLE A14. TABLE OF DUNNETT S MODIFIED
T STATISTIC FOR A CONTROL GROUP COMPARISON 1684 TABLE A15. GRAPHS OFTHE
POWER FUNCTION FOR THE ANALYSIS OF VARIANCE 1686 TABLE A16. TABLE OF
CRITICAL VALUES FOR PEARSON R 1690 TABLE A17. TABLE OF FISHER S Z R
TRANSFORMATION 1691 TABLE A18. TABLE OF CRITICAL VALUES FOR SPEARMAN S
RHO 1692 TABLE A19. TABLE OF CRITICAL VALUES FOR KENDALL S TAU 1693
TABLE A20. TABLE OF CRITICAL VALUES FOR KENDALL S COEFFICIENT OF
CONCORDANCE . 1694 TABLE A21. TABLE OF CRITICAL VALUES FOR THE
KOLMOGOROV-SMIRNOV GOODNESS-OF-FIT TEST FOR A SINGLE SAMPLE 1695 TABLE
A22. TABLE OF CRITICAL VALUES FOR THE LILLIEFORS TEST FOR NORMALITY 1696
TABLE A23. TABLE OF CRITICAL VALUES FOR THE KOLMOGOROV-SMIRNOV TEST FOR
TWO INDEPENDENT SAMPLES 1697 TABLE A24. TABLE OF CRITICAL VALUES FOR THE
JONCKHEERE-TERPSTRA TEST STATISTIC . 1699 TABLE A25. TABLE OF CRITICAL
VALUES FOR THE PAGE TEST STATISTIC 1701 TABLE A26. TABLE OF EXTREME
STUDENTIZED DEVIATE OUTLIER STATISTIC 1703 TABLE A27. TABLE OF
DURBIN-WATSON TEST STATISTIC 1704 INDEX 1707
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| adam_txt |
FOURTH EDITION HANDBOOK OF PARAMETRIC AND NONPARAMETRIC STATISTICAL
PROCEDURES DAVID J.SHESLDN CHAPMAN & HALL/CRC TAYLOR & FRANCIS CROUP
BOCA RATON LONDON NEW YORK CHAPMAN & HALL/CRC IS AN IMPRINT OF THE
TAYLOR & FRANCIS CROUP, AN INFORMA BUSINESS TABLE OF CONTENTS WITH
SUMMARY OF TOPICS INTRODUCTION 1 DESCRIPTIVE VERSUS INFERENTIAL
STATISTICS 1 STATISTIC VERSUS PARAMETER .[. 2 LEVELS OF MEASUREMENT 2
CONTINUOUS VERSUS DISCRETE VARIABLES ;' 4 MEASURES OF CENTRAL TENDENCY
(MODE, MEDIAN, MEAN, WEIGHTED MEAN, GEOMETRIC MEAN, AND THE HARMONIC
MEAN) 4 MEASURES OF VARIABILITY (RANGE; QUANTILES, PERCENTILES, DECILES,
AND QUARTILES; VARIANCE AND STANDARD DEVIATION; THE COEFFICIENT OF
VARIATION) 10 MEASURES OF SKEWNESS AND KURTOSIS 16 VISUAL METHODS FOR
DISPLAYING DATA (TABLES AND GRAPHS, EXPLORATORY DATA ANALYSIS
(STEM-AND-LEAF DISPLAYS AND BOXPLOTS)) 29 THE NORMAL DISTRIBUTION .45
HYPOTHESIS TESTING 56 A HISTORY AND CRITIQUE OF THE CLASSICAL HYPOTHESIS
TESTING MODEL 68 ESTIMATION IN INFERENTIAL STATISTICS 74 RELEVANT
CONCEPTS, ISSUES, AND TERMINOLOGY IN CONDUCTING RESEARCH (THE CASE STUDY
METHOD; THE EXPERIMENTAL METHOD; THE CORRELATIONAL METHOD) 75
EXPERIMENTAL DESIGN (PRE-EXPERIMENTAL DESIGNS; QUASI-EXPERIMENTAL
DESIGNS . TRUE EXPERIMENTAL DESIGNS; SINGLE-SUBJECT DESIGNS) 82 SAMPLING
METHODOLOGIES 98 BASIC PRINCIPLES OF PROBABILITY 100 PARAMETRIC VERSUS
NONPARAMETRIC INFERENTIAL STATISTICAL TESTS ., 108 UNIVARIATE VERSUS
BIVARIATE VERSUS MULTIVARIATE STATISTICAL PROCEDURES 109 SELECTION OF
THE APPROPRIATE STATISTICAL PROCEDURE 110 OUTLINE OF INFERENTIAL
STATISTICAL TESTS AND MEASURES OF CORRELATION/ASSOCIATION 125 GUIDELINES
AND DECISION TABLES FOR SELECTING THE APPROPRIATE STATISTICAL PROCEDURE
133 INFERENTIAL STATISTICAL TESTS EMPLOYED WITH A SINGLE SAMPLE ". 141
TEST 1: THE SINGLE-SAMPLE Z TEST 143 I. HYPOTHESIS EVALUATED WITH TEST
AND RELEVANT BACKGROUND INFORMATION 143 II. EXAMPLE . * = 143 III. NULL
VERSUS ALTERNATIVE HYPOTHESES ; 143 IV. TEST COMPUTATIONS 144 V.
INTERPRETATION OF THE TEST RESULTS 145 VI. ADDITIONAL ANALYTICAL
PROCEDURES FOR THE SINGLE-SAMPLE Z TEST AND/OR RELATED TESTS 146 VIII
HANDBOOK OF PARAMETRIC ANDNONPARAMETRIC STATISTICAL PROCEDURES VII.
ADDITIONAL DISCUSSION OF THE SINGLE-SAMPLE Z TEST 146 1. THE
INTERPRETATION OF A NEGATIVE Z VALUE 146 2. THE STANDARD ERROR OF THE
POPULATION MEAN AND GRAPHICAL REPRESENTATION OF THE RESULTS OF THE
SINGLE-SAMPLE Z TEST 147 3. ADDITIONAL EXAMPLES ILLUSTRATING THE
INTERPRETATION OF A COMPUTED Z VALUE 152 4. THE Z TEST FOR A POPULATION
PROPORTION 152 VIII. ADDITIONAL EXAMPLES ILLUSTRATING THE USE OF THE
SINGLE-SAMPLE Z TEST 153 TEST 2: THE SINGLE-SAMPLE / TEST 157 I.
HYPOTHESIS EVALUATED WITH TEST AND RELEVANT BACKGROUND INFORMATION 157
II. EXAMPLE 158 III. NULL VERSUS ALTERNATIVE HYPOTHESES 158 IV. TEST
COMPUTATIONS V : 158 V. INTERPRETATION OF THE TEST RESULTS .'. . 160
VI. ADDITIONAL ANALYTICAL PROCEDURES FOR THE SINGLE-SAMPLE T TEST AND/OR
RELATED TESTS '. 162 1. DETERMINATION OF THE POWER OF THE SINGLE-SAMPLE
T TEST AND THE SINGLE- SAMPLE Z TEST, AND THE APPLICATION OF TEST 2A:
COHEN'S D INDEX 162 2. COMPUTATION OF A CONFIDENCE INTERVAL FOR THE MEAN
OF THE POPULATION REPRESENTED BY A SAMPLE 173 VII. ADDITIONAL DISCUSSION
OF THE SINGLE-SAMPLE T TEST 183 1. DEGREES OF FREEDOM 183 VIII.
ADDITIONAL EXAMPLES ILLUSTRATING THE USE OF THE SINGLE-SAMPLE T TEST 184
TEST 3: THE SINGLE-SAMPLE CHI-SQUARE TEST FOR A POPULATION VARIANCE 191
I. HYPOTHESIS EVALUATED WITH TEST AND RELEVANT BACKGROUND INFORMATION
191 II. EXAMPLE 192 III. NULL VERSUS ALTERNATIVE HYPOTHESES 192 IV. TEST
COMPUTATIONS 193 V. INTERPRETATION OF THE TEST RESULTS 194 VI.
ADDITIONAL ANALYTICAL PROCEDURES FOR THE SINGLE-SAMPLE CHI-SQUARE TEST
FOR A POPULATION VARIANCE AND/OR RELATED TESTS . .^ 196 1. LARGE SAMPLE
NORMAL APPROXIMATION OF THE CHI-SQUARE DISTRIBUTION 196 2. COMPUTATION
OF A CONFIDENCE INTERVAL FOR THE VARIANCE OF A POPULATION REPRESENTED BY
A SAMPLE 197 3. SOURCES FOR COMPUTING THE POWER OF THE SINGLE-SAMPLE
CHI-SQUARE TEST FOR A POPULATION VARIANCE 200 VII. ADDITIONAL DISCUSSION
OF THE SINGLE-SAMPLE CHI-SQUARE TEST FOR A POPULATION VARIANCE , 200
VIII. ADDITIONAL EXAMPLES ILLUSTRATING THE USE OF THE SINGLE-SAMPLE CHI-
SQUARE TEST FOR A POPULATION VARIANCE , 200 TEST 4: THE SINGLE-SAMPLE
TEST FOR EVALUATING POPULATION SKEWNESS 205 I. HYPOTHESIS EVALUATED WITH
TEST AND RELEVANT BACKGROUND INFORMATION 205 II. EXAMPLE 206 III. NULL
VERSUS ALTERNATIVE HYPOTHESES ; 206 IV. TEST COMPUTATIONS 207 V.
INTERPRETATION OF THE TEST RESULTS 209 TABLE, OF CONTENTS IX VI.
ADDITIONAL ANALYTICAL PROCEDURES FOR THE SINGLE-SAMPLE TEST FOR .
EVALUATING POPULATION SKEWRIESS AND/OR RELATED TESTS :.:. . 210 VII.
ADDITIONAL DISCUSSION OF THE SINGLE-SAMPLE TEST FOR EVALUATING
POPULATION SKEWNESS 210 1. EXACT TABLES FOR THE SINGLE-SAMPLE TEST FOR
EVALUATING POPULATION SKEWNESS : ., 210 2. NOTE ON A NONPARAMETRIC TEST
FOR EVALUATING SKEWNESS 210 VIII. ADDITIONAL EXAMPLES ILLUSTRATING THE
USE OF THE SINGLE-SAMPLE TEST FOR EVALUATING POPULATION SKEWNESS 211
TEST 5: THE SINGLE-SAMPLE TEST FOR EVALUATING POPULATION KURTOSIS 213 I.
HYPOTHESIS EVALUATED WITH TEST AND RELEVANT BACKGROUND INFORMATION 213
II. EXAMPLE . ; 214 . III. NULL VERSUS ALTERNATIVE HYPOTHESES 214
IV. TEST COMPUTATIONS . 215 V. INTERPRETATION OFTHE TEST RESULTS 217
VI. ADDITIONAL ANALYTICAL PROCEDURES FOR THE SINGLE-SAMPLE TEST FOR
EVALUATING POPULATION KURTOSIS AND/OR RELATED TESTS ., 218 1. TEST 5A:
THE D'AGOSTINO-PEARSON TEST OF NORMALITY 218 2. TEST 5B: THE JARQUE-BERA
TEST OF NORMALITY 219 VII. ADDITIONAL. DISCUSSION OFTHE SINGLE-SAMPLE
TEST FOR EVALUATING POPULATION KURTOSIS : 220 1. EXACT TABLES FOR THE
SINGLE-SAMPLE TEST FOR EVALUATING POPULATION KURTOSIS 220 2. ADDITIONAL
COMMENTS ON TESTS OF NORMALITY 220 VIII. ADDITIONAL EXAMPLES
ILLUSTRATING THE USE OFTHE SINGLE-SAMPLE TEST FOR EVALUATING POPULATION
KURTOSIS 221 TEST 6: THE WILCOXON SIGNED-RANKS TEST 225 I. HYPOTHESIS
EVALUATED WITH.TEST AND RELEVANT BACKGROUND INFORMATION 225 II. EXAMPLE
:* 225 III. NULL VERSUS ALTERNATIVE HYPOTHESES ;. 226 IV. TEST
COMPUTATIONS . .-. .':* 226 V. INTERPRETATION OF THE TEST RESULTS .:
228 VI. ADDITIONAL ANALYTICAL PROCEDURES FOR THE WILCOXON SIGNEDRRANKS
TEST AND/OR RELATED TESTS :.-. 230 1. THE NORMAL APPROXIMATION OF THE
WILCOXON R STATISTIC FOR LARGE SAMPLE SIZES , .* ; 230 2. THE CORRECTION
FOR CONTINUITY FOR THE NORMAL APPROXIMATION OF THE WILCOXON SIGNED-RANKS
TEST .; 232 3. TIE CORRECTION FOR THE NORMAL APPROXIMATION OF THE
WILCOXON TEST STATISTIC -' : '*. : 233 A. COMPUTATION OF A CONFIDENCE
INTERVAL FOR A POPULATION MEDIAN 234 VII. ADDITIONAL DISCUSSION OFTHE
WILCOXON SIGNED-RANKS TEST 235 1. POWER-EFFICIENCY OFTHE WILCOXON
SIGNED-RANKS TEST AND THE CONCEPT OF ASYMPTOTIC RELATIVE EFFICIENCY 235
2. NOTE.ON SYMMETRIC POPULATION CONCERNING HYPOTHESES REGARDING MEDIAN
AND MEAN 236 VIII. ADDITIONAL EXAMPLES ILLUSTRATING THE USE OFTHE
WILCOXON SIGNED- RANKS TEST 237 XII HANDBOOK OF PARAMETRIC AND
NONPARAMETRIC STATISTICAL PROCEDURES SINGLE-SAMPLE RUNS TEST : : 393 3.
EXTENSION OFTHE RUNS TEST TO DATA WITH MORE THAN TWO CATEGORIES 394 4.
TEST 10A: THE RUNS TEST FOR SERIAL RANDOMNESS 395 VII. ADDITIONAL
DISCUSSION OF THE SINGLE-SAMPLE RUNS TEST 398 1. ADDITIONAL DISCUSSION
OFTHE CONCEPT OF RANDOMNESS 398 VII. ADDITIONAL EXAMPLES ILLUSTRATING
THE USE OFTHE SINGLE-SAMPLE RUNS TEST 399 IX. ADDENDUM *";.: 402
1. THE GENERATION OF PSEUDORANDOM NUMBERS (THE MIDSQUARE METHOD; THE
MIDPRODUCT METHOD; THE LINEAR CONGRUENTIAL METHOD) 402 2. ALTERNATIVE
TESTS OF RANDOMNESS TEST 10B: THE FREQUENCY TEST , 407 TEST 10C: THE GAP
TEST . 409 TEST LOD: THE POKER TEST ': 413 TEST LOE: THE MAXIMUM TEST
/. 413 TEST LOF: THE COUPON COLLECTOR'S TEST' 414 TEST LOG: THE MEAN
SQUARE SUCCESSIVE DIFFERENCE TEST (FOR SERIAL RANDOMNESS 417 ADDITIONAL
TESTS OF RANDOMNESS (AUTOCORRELATION; THE SERIAL TEST; THE D 2 SQUARE
TEST OF RANDOM NUMBERS; TESTS OF TREND ANALYSIS/TIME SERIES ANALYSIS)
419 INFERENTIAL STATISTICAL TESTS EMPLOYED WITH TWO INDEPENDENT SAMPLES
(AND RELATED MEASURES OF ASSOCIATION/CORRELATION) 425 TEST 11: THE /
TEST FOR TWO INDEPENDENT SAMPLES 427 I. HYPOTHESIS EVALUATED WITH TEST
AND RELEVANT BACKGROUND INFORMATION 427 II. EXAMPLE 427 III. NULL VERSUS
ALTERNATIVE HYPOTHESES 428 IV. TEST COMPUTATIONS .' 428 V.
INTERPRETATION OFTHE TEST RESULTS 431 VI. ADDITIONAL ANALYTICAL
PROCEDURES FOR THE T TEST FOR TWO INDEPENDENT SAMPLES AND/OR RELATED
TESTS' '. 43 2 1. THE EQUATION FOR THE T TEST FOR TWO INDEPENDENT
SAMPLES WHEN A VALUE FOR A DIFFERENCE OTHER THAN ZERO IS STATED IN THE
NULL HYPOTHESIS 432 2. TEST HA: HARTLEY'S F MAI TEST FOR HOMOGENEITY OF
VARIANCE/ F TEST FOR TWO POPULATION VARIANCES: EVALUATION OF THE
HOMOGENEITY OF VARIANCE ASSUMPTION OFTHE T TEST FOR TWO INDEPENDENT
SAMPLES 434 3. COMPUTATION OFTHE POWER OFTHE / TEST FOR TWO INDEPENDENT
SAMPLES AND THE APPLICATION OF TEST LIB: COHEN'S D INDEX 439 4. MEASURES
OF MAGNITUDE OF TREATMENT EFFECT FOR THE / TEST FOR TWO INDEPENDENT
SAMPLES: OMEGA SQUARED (TEST LIE) AND ETA SQUARED . (TEST LID) 446 5.
COMPUTATIONOFACONFIDENCEINTERVALFORTHEFTESTFORTWOINDEPENDENT SAMPLES 448
6. TEST LIE: THE Z TEST FOR TWO INDEPENDENT SAMPLES 450 VII. ADDITIONAL
DISCUSSION OFTHE T TEST FOR TWO INDEPENDENT SAMPLES '. 452 1. UNEQUAL
SAMPLE SIZES 452 2. ROBUSTNESS OFTHE / TEST FOR TWO INDEPENDENT SAMPLES
453 TABLE OF CONTENTS XIII 3. OUTLIERS (BOX-AND-WHISKER PLOT CRITERIA;
STANDARD DEVIATION SCORE CRITERIA;TEST LLF: MEDIAN ABSOLUTE DEVIATION
TEST FOR IDEN- TIFYING OUTLIERS AND TEST LLG: EXTREME STUDENTIZED
DEVIATE TEST FOR IDENTIFYING OUTLIERS; TRIMMING DATA; WINSORIZATION) AND
DATA TRANSFORMATION 454 4. MISSING DATA '. 468 5. CLINICAL TRIALS '. 471
6. TESTS OF EQUIVALENCE (TEST LLH: THE WESTLAKE-SCHUIRMANN TEST OF
EQUIVALENCE OF TWO INDEPENDENT TREATMENTS (AND PROCEDURE FOR COMPUTING
SAMPLE SIZE IN REFERENCE TO THE POWER OFTHE TEST) AND TEST HI: TRYON'S
TEST OF EQUIVALENCE OF TWO INDEPENDENT TREATMENTS) : 474 7. HOTELLING'S
T 1 498 VIII. ADDITIONAL EXAMPLES ILLUSTRATING THE USE OFTHE T TEST FOR
TWO INDEPENDENT SAMPLES 499 TEST 12: THE MANN-WHITNEY U TEST 513 I.
HYPOTHESIS EVALUATED WITH TEST AND RELEVANT BACKGROUND INFORMATION 513
II. EXAMPLE ; 514 III. NULL VERSUS ALTERNATIVE HYPOTHESES ; 514 IV. TEST
COMPUTATIONS 515 V. INTERPRETATION OFTHE TESTRESULTS 518 VI. ADDITIONAL
ANALYTICAL PROCEDURES FOR THE MANN-WHITNEY [/TEST AND/OR RELATED TESTS
518 1. THE NORMAL APPROXIMATION OFTHE MANN-WHITNEY U STATISTIC FOR LARGE
SAMPLE SIZES 518 2. THE CORRECTION FOR CONTINUITY FOR THE NORMAL
APPROXIMATION OF THE MANN-WHITNEY [/TEST 520 3. TIE CORRECTION FOR THE
NORMAL APPROXIMATION OFTHE MANN*WHITNEY U , STATISTIC '. 521 4.
COMPUTATION OF A CONFIDENCE INTERVAL FOR A DIFFERENCE BETWEEN THE
MEDIANS OF TWO INDEPENDENT POPULATIONS 521 VII. ADDITIONAL DISCUSSION
OFTHE MANN-WHITNEY [/TEST 524 1. POWER-EFFICIENCY OFTHE MANN-WHITNEY
[/TEST 524 2. EQUIVALENCY OFTHE NORMAL APPROXIMATION OF*HE MANN-WHITNEY
[/TEST AND THE T TEST FOR TWO INDEPENDENT SAMPLES WITH RANK-ORDERS 524
3. ALTERNATIVE NONPARAMETRIC RANK-ORDER PROCEDURES FOR EVALUATING A
DESIGN INVOLVING TWO INDEPENDENT SAMPLES 524 VIII. ADDITIONAL EXAMPLES
ILLUSTRATING THE USE OFTHE MANN-WHITNEY [/TEST 525 IX. ADDENDUM 526 1.
COMPUTER-INTENSIVE TESTS (RANDOMIZATION AND PERMUTATION TESTS: TEST *
12A: THE RANDOMIZATION TEST FOR TWO INDEPENDENT SAMPLES; TEST 12B: THE
BOOTSTRAP; TEST 12C: THE JACKKNIFE; FINAL COMMENTS ON COMPUTER-INTENSIVE
PROCEDURES) 526 2. SURVIVAL ANALYSIS (TEST 12D: KAPLAN-MEIER ESTIMATE)
540 3. PROCEDURES FOR EVALUATING CENSORED DATA IN A DESIGN INVOLVING TWO
INDEPENDENT SAMPLES (PERMUTATION TEST BASED ON THE MEDIAN FOR CENSORED
DATA, GEHAN'S TEST FOR CENSORED DATA (TEST 12E), AND THE LOG-RANK TEST
(TEST 12F)) 550 XVI HANDBOOK OF PARAMETRIC AND NONPARAMETRIC STATISTICAL
PROCEDURES COHEN'S KAPPA, AND TEST 16K-B: TEST OF SIGNIFICANCE FOR *
TWO INDEPENDENT VALUES OF COHEN'S KAPPA) 669 12. COMBINING THE RESULTS
OF MULTIPLE 2X2 CONTINGENCY TABLES: 673 HETEROGENEITY CHI-SQUARE
ANALYSIS FOR A 2 * 2 CONTINGENCY TABLE ; 673 TEST 161: THE
MANTEL-HAENSZEL ANALYSIS (TEST 161-A: TEST OF HOMOGENEITY OF ODDS RATIOS
FOR MANTEL-HAENSZEL ANALYSIS, TEST 161-B: SUMMARY ODDS RATIO FOR MANTEL-
HAENSZEL ANALYSIS, AND TEST 161-C: MANTEL-HAENSZEL TEST OF ASSOCIATION)
676 VII. ADDITIONAL DISCUSSION OFTHE CHI-SQUARE TEST FOR R X C TABLES
688 1. EQUIVALENCY OFTHE CHI-SQUARE TEST FOR R X C TABLES WHEN C = 2
WITH THE T TEST FOR TWO INDEPENDENT SAMPLES (WHEN R = 2) AND THE
SINGLE-FACTOR BETWEEN-SUBJECTS ANALYSIS OF VARIANCE (WHEN R T. 2) 688 2.
TEST OF EQUIVALENCE FOR TWO INDEPENDENT PROPORTIONS: TES T 16M: THE
WESTLAKE-SCHUIRMANN TEST OF EQUIVALENCE OF TWO INDEPENDENT PROPORTIONS
(AND PROCEDURE FOR COMPUTING SAMPLE SIZE IN REFERENCE TO THE POWER OFTHE
TEST) 688 3. TEST 16N: THE LOG-LIKELIHOOD RATIO 698 4. SIMPSON'S PARADOX
700 5. ANALYSIS OF MULTIDIMENSIONAL CONTINGENCY TABLES THROUGH USE OF A
CHI-SQUARE ANALYSIS 702 6. TEST 16O:ANALYSIS OF MULTIDIMENSIONAL
CONTINGENCY TABLES WITH LOG-LINEAR ANALYSIS 713 VIII. ADDITIONAL
EXAMPLES ILLUSTRATING THE USE OFTHE CHI-SQUARE TEST FOR R X C TABLES
.'"'. 727 INFERENTIAL STATISTICAL TESTS EMPLOYED WITH TWO DEPENDENT
SAMPLES (AND RELATED MEASURES OF ASSOCIATION/CORRELATION) 741 TEST 17:
THE T TEST FOR TWO DEPENDENT SAMPLES 743 I. HYPOTHESIS EVALUATED WITH
TEST AND RELEVANT BACKGROUND INFORMATION 743 II. EXAMPLE -.-. -- 744
III. NULL VERSUS ALTERNATIVE HYPOTHESES R 744 IV. TEST COMPUTATIONS 745
V. INTERPRETATION OFTHE TEST RESULTS 747 VI. ADDITIONAL ANALYTICAL
PROCEDURES FOR THE / TEST FOR TWO DEPENDENT SAMPLES AND/OR RELATED TESTS
748 1. ALTERNATIVE EQUATION FOR THE T TEST FOR TWO DEPENDENT SAMPLES 748
2. THE EQUATION FOR THE T TEST FOR TWO DEPENDENT SAMPLES WHEN A VALUE
FOR A DIFFERENCE OTHER THAN ZERO IS STATED IN THE NULL HYPOTHESIS 752 3.
TEST 17A: THE / TEST FOR HOMOGENEITY OF VARIANCE FOR TWO DEPEN- DENT
SAMPLES: EVALUATION OFTHE HOMOGENEITY OF VARIANCE ASSUMPTION OFTHE /
TEST FOR TWO DEPENDENT SAMPLES 752 4. COMPUTATION OF THE POWER OFTHE /
TEST FOR TWO DEPENDENT SAMPLES AND THE APPLICATION OF TEST 17B: COHEN'S
D INDEX 755 5. MEASURE OF MAGNITUDE OF TREATMENT EFFECT FOR THE / TEST
FOR TWO DEPENDENT SAMPLES: OMEGA SQUARED (TEST 17C) 761 TABLE OF
CONTENTS XVII 6. COMPUTATION OF A CONFIDENCE INTERVAL FOR THE T TEST FOR
TWO DEPENDENT SAMPLES ." 763 7. TEST 17D: SANDLER'S A TEST 764 8. TEST
17E: THE Z TEST FOR TWO DEPENDENT SAMPLES 765 VII. ADDITIONAL DISCUSSION
OFTHE T TEST FOR TWO DEPENDENT SAMPLES 768 1; THE USE OF MATCHED
SUBJECTS IN A DEPENDENT SAMPLES DESIGN 768 2. RELATIVE POWER OFTHE T
TEST FOR TWO DEPENDENT SAMPLES AND THE T TEST FOR TWO INDEPENDENT
SAMPLES 771 3. COUNTERBALANCING AND ORDER EFFECTS ". '. 772 4. ANALYSIS
OF A ONE-GROUP PRETEST-POSTTEST DESIGN WITH THE T TEST FOR TWO DEPENDENT
SAMPLES 774 5. TESTS OF EQUIVALENCE: TEST 17F: THE WESTLAKE-SCHUIRMANN
TEST OF EQUIVALENCE OF TWO DEPENDENT TREATMENTS (AND PROCEDURE FOR
COMPUTING SAMPLE SIZE IN REFERENCE TO THE POWER OFTHE TEST) AND TEST
17G: TRYON'S TEST OF EQUIVALENCE OF TWO DEPENDENT TREATMENTS 776 VIII.
ADDITIONAL EXAMPLE ILLUSTRATING THE USE OFTHE T TEST FOR TWO DEPENDENT
SAMPLES 785 TEST 18: THE WILCOXON MATCHED-PAIRS SIGNED-RANKS TEST 791 I.
HYPOTHESIS EVALUATED WITH TEST AND RELEVANT BACKGROUND INFORMATION 791
II. EXAMPLE 792 III. NULL VERSUS ALTERNATIVE HYPOTHESES 792 IV. TEST
COMPUTATIONS '. 793 V. INTERPRETATION OFTHE TEST RESULTS 794 VI.
ADDITIONAL ANALYTICAL PROCEDURES FOR THE WILCOXON MATCHED-PAIRS
SIGNED-RANKS TEST AND/OR RELATED TESTS 796 1. THE NORMAL APPROXIMATION
OFTHE WILCOXON T STATISTIC FOR LARGE SAMPLE SIZES 796 2. THE CORRECTION
FOR CONTINUITY FOR THE NORMAL APPROXIMATION OF THE WILCOXON
MATCHED-PAIRS SIGNED-RANKS TEST 797 3. TIE CORRECTION FOR THE NORMAL
APPROXIMATION OF THE WILCOXON TEST STATISTIC : 798 4. COMPUTATION OF
ATONFIDENCE INTERVAL FOR A MEDIAN DIFFERENCE BETWEEN TWO DEPENDENT
POPULATIONS .-.' 799 VII. ADDITIONAL DISCUSSION OFTHE WILCOXON
MATCHED-EAIRS SIGNED-RANKS TEST *. .- 801 1. POWER-EFFICIENCY OFTHE
WILCOXON MATCHED-PAIRS SIGNED-RANKS TEST 801 2. PROBABILITY OF
SUPERIORITY AS A MEASURE OF EFFECT SIZE 801 3. ALTERNATIVE NONPARAMETRIC
PROCEDURES FOR EVALUATING A DESIGN INVOLVING TWO DEPENDENT SAMPLES _.
801 VIII. ADDITIONAL EXAMPLES ILLUSTRATING THE USE OFTHE WILCOXON
MATCHED- PAIRS SIGNED-RANKS TEST 802 TEST 19: THE BINOMIAL SIGN TEST FOR
TWO DEPENDENT SAMPLES 805 I. HYPOTHESIS EVALUATED WITH TEST AND RELEVANT
BACKGROUND INFORMATION 805 II. EXAMPLE 806 III. NULL VERSUS ALTERNATIVE
HYPOTHESES 806 IV. TEST COMPUTATIONS 807 V. INTERPRETATION OFTHE TEST
RESULTS 809 XVIII HANDBOOK OF PARAMETRIC AND NONPARAMETRIC STATISTICAL
PROCEDURES VI. ADDITIONAL ANALYTICAL PROCEDURES FOR THE BINOMIAL SIGN
TEST FOR TWO DEPENDENT SAMPLES AND/OR RELATED TESTS 810 1. THE NORMAL
APPROXIMATION OF THE BINOMIAL SIGN TEST FOR TWO DEPENDENT SAMPLES WITH
AND WITHOUT A CORRECTION FOR CONTINUITY 810 2. COMPUTATION OF A
CONFIDENCE INTERVAL FOR THE BINOMIAL SIGN TEST FOR TWO DEPENDENT SAMPLES
; 813 3. SOURCES FOR COMPUTING THE POWER OFTHE BINOMIAL SIGN TEST FOR
TWO DEPENDENT SAMPLES, AND COMMENTS ON ASYMPTOTIC RELATIVE EFFICIENCY
OFTHE TEST 814 VII. ADDITIONAL DISCUSSION OFTHE BINOMIAL SIGN TEST FOR
TWO DEPENDENT SAMPLES 815 *1. THE PROBLEM OF AN EXCESSIVE NUMBER OF ZERO
DIFFERENCE SCORES 815 2. EQUIVALENCY OFTHE BINOMIAL SIGN TEST FOR TWO
DEPENDENT SAMPLES AND THE FRIEDMAN TWO-WAY ANALYSIS VARIANCE BY RANKS
WHEN K = 2 815 VIII. ADDITIONAL EXAMPLES ILLUSTRATING THE USE OFTHE
BINOMIAL SIGN TEST FOR TWO DEPENDENT SAMPLES . , 815 TEST 20: THE
MCNEMAR TEST 817 I. HYPOTHESIS EVALUATED WITH TEST AND RELEVANT
BACKGROUND INFORMATION 817 II. EXAMPLES 818 III. NULL VERSUS ALTERNATIVE
HYPOTHESES 820 IV. TEST COMPUTATIONS 822 V. INTERPRETATION OFTHE TEST
RESULTS 822 VI. ADDITIONAL ANALYTICAL PROCEDURES FOR THE MCNEMAR TEST
AND/OR RELATED , TESTS ; , 823 1. ALTERNATIVE EQUATION FOR THE MCNEMAR
TEST STATISTIC BASED ON THE NORMAL DISTRIBUTION 823 2. THE CORRECTION
FOR CONTINUITY FOR THE MCNEMAR TEST 824 3. COMPUTATION OFTHE EXACT
BINOMIAL PROBABILITY FOR THE MCNEMAR TEST MODEL WITH A SMALL SAMPLE SIZE
825 4. COMPUTATION OFTHE POWER OFTHE MCNEMAR TEST : 827 5. COMPUTATION
OF A CONFIDENCE INTERVAL FOR THE MCNEMAR TEST 828 6. COMPUTATION OF AN
ODDS RATIO FOR THE MCNEMAR TEST 829 7. ADDITIONAL ANALYTICAL PROCEDURES
FOR THE MCNEMAR TEST 830 8. TEST 20A: THE GART TEST FOR ORDER EFFECTS "F
830 VII. ADDITIONAL DISCUSSION OFTHE MCNEMAR TEST 838 1. ALTERNATIVE
FORMAT FOR THE MCNEMAR TEST SUMMARY TABLE AND MODIFIED TEST EQUATION 838
2. THE EFFECT OF DISREGARDING MATCHING 839 3. ALTERNATIVE NONPARAMETRIC
PROCEDURES FOR EVALUATING A DESIGN WITH TWO DEPENDENT SAMPLES INVOLVING
CATEGORICAL DATA 840 4. TEST OF EQUIVALENCE FOR TWO INDEPENDENT
PROPORTIONS: TEST 20B: THE WESTLAKE-SCHUIRMANN TEST OF EQUIVALENCE OF
TWO DEPENDENT PROPORTIONS 840 VIII. ADDITIONAL EXAMPLES ILLUSTRATING THE
USE OFTHE MCNEMAR TEST 850 IX. ADDENDUM 852 EXTENSION OF THE MCNEMAR
TEST MODEL BEYOND 2X2 CONTINGENCY TABLES 852 1. TEST 20C:THE BOWKER TEST
OF INTERNAL SYMMETRY 852 2. TEST 20D:THE STUART-MAXWELL TEST OF MARGINAL
HOMOGENEITY 856 TABLE OF CONTENTS XIX INFERENTIAL STATISTICAL TESTS
EMPLOYED WITH TWO OR MORE INDEPENDENT SAMPLES (AND RELATED MEASURES OF
ASSOCIATION/CORRELATION) , 865 TEST 21: THE SINGLE-FACTOR
BETWEEN-SUBJECTS ANALYSIS OF VARIANCE 867 I. HYPOTHESIS EVALUATED WITH
TEST AND RELEVANT BACKGROUND INFORMATION 867 II. EXAMPLE 868 III. NULL
VERSUS ALTERNATIVE HYPOTHESES 868 IV. TEST COMPUTATIONS 869 V.
INTERPRETATION OF THE TEST RESULTS 873 VI. ADDITIONAL ANALYTICAL
PROCEDURES FOR THE SINGLE-FACTOR BETWEEN- SUBJECTS ANALYSIS OF VARIANCE
AND/OR RELATED TESTS 874 1. COMPARISONS FOLLOWING COMPUTATION OF THE
OMNIBUS F VALUE FOR THE SINGLE-FACTOR BETWEEN-SUBJECTS ANALYSIS OF
VARIANCE (PLANNED VERSUS UNPLANNED COMPARISONS (INCLUDING SIMPLE VERSUS
COMPLEX COM- PARISONS); LINEAR CONTRASTS; ORTHOGONAL COMPARISONS; TEST
21A: MULTIPLE T TESTS/FISHER'S LSD TEST; TEST 21B: THE BONFERRONI- DUNN
TEST; TEST 21C: TUKEY'SHSD TEST; TEST 21D: THENEWMAN- KEULS TEST; TEST
21 E: THE SCHEFFE TEST; TEST 21F: THE DUNNETT TEST; ADDITIONAL
DISCUSSION OF COMPARISON PROCEDURES AND FINAL RECOMMENDATIONS; THE
COMPUTATION OF A CONFIDENCE INTERVAL FOR A COMPARISON) 874 2. COMPARING
THE MEANS OF THREE OR NIORE GROUPS WHEN K SF 4 905 3. EVALUATION OF THE
HOMOGENEITY OF VARIANCE ASSUMPTION OF THE SINGLE- FACTOR
BETWEEN-SUBJECTS ANALYSIS OF VARIANCE (TEST LLA: HARTLEY'S F MIU TEST
FOR HOMOGENEITY OF VARIANCE, TEST 21G: THE LEVENE TEST FOR HOMOGENEITY
OF VARIANCE, TEST 21H: THE BROWN*FORSYTHE TEST FOR HOMOGENEITY OF
VARIANCE). 906 4. COMPUTATION OF THE POWER OF THE SINGLE-FACTOR
BETWEEN-SUBJECTS ANALYSIS OF VARIANCE 913 5. MEASURES OF MAGNITUDE OF
TREATMENT EFFECT FOR THE SINGLE-FACTOR BETWEEN-SUBJECTS ANALYSIS OF
VARIANCE: OMEGA SQUARED (TEST 21 I), ETA SQUARED (TEST.21 J), AND
COHEN'S/INDEX (TEST 21K) . 916 6. COMPUTATION OF A 'CONFIDENCE INTERVAL
FOR THE^MEAN OF A TREATMENT POPULATION 920 7. TREND ANALYSIS 922 VII.
ADDITIONAL DISCUSSION OFTHE SINGLE-FACTOR BETWEEN-SUBJECTS ANALYSIS OF
VARIANCE 934 1. THEORETICAL RATIONALE UNDERLYING THE SINGLE-FACTOR
BETWEEN-SUBJECTS ANALYSIS OF VARIANCE 934 2. DEFINITIONAL EQUATIONS FOR
THE SINGLE-FACTOR BETWEEN-SUBJECTS ANALYSIS OF VARIANCE . 936 3.
EQUIVALENCYOFTHESINGLE-FACTORBETWEEN-SUBJECTSANALYSISOFVARIANCE AND THE
F TEST FOR TWO INDEPENDENT SAMPLES WHEN K = 1 938 4. ROBUSTNESS OF THE
SINGLE-FACTOR BETWEEN-SUBJECTS ANALYSIS OF VARIANCE 939 5. EQUIVALENCY
OFTHE SINGLE-FACTOR BETWEEN-SUBJECTS ANALYSIS OF VARIANCE AND THE / TEST
FOR TWO INDEPENDENT SAMPLES WITH THE CHI-SQUARE TEST FOR R X C TABLES
WHEN C = 2 . .* 939 XX HANDBOOK OF PARAMETRIC AND NONPARAMETRIC
STATISTICAL PROCEDURES 6. THE GENERAL LINEAR MODEL 943 7. FIXED-EFFECTS
VERSUS RANDOM-EFFECTS MODELS FOR THE SINGLE-FACTOR BETWEEN-SUBJECTS
ANALYSIS OF VARIANCE 944 8. MULTIVARIATE ANALYSIS OF VARIANCE (MANOVA)
944 VIII. ADDITIONAL EXAMPLES ILLUSTRATING THE USE OFTHE SINGLE-FACTOR
BETWEEN- SUBJECTS ANALYSIS OF VARIANCE 945 IX. ADDENDUM .946 1. TEST
211: THE SINGLE-FACTOR BETWEEN-SUBJECTS ANALYSIS OF COVARIANCE 946 TEST
22: THE KRUSKAL-WALLIS ONE-WAY ANALYSIS OF VARIANCE BY RANKS 981 I.
HYPOTHESIS EVALUATED WITH TEST AND RELEVANT BACKGROUND INFORMATION 981
II. EXAMPLE : '. 982 III. NULL VERSUS ALTERNATIVE HYPOTHESES 983 IV.
TEST COMPUTATIONS 983 V. INTERPRETATION OFTHE TEST RESULTS 985 VI.
ADDITIONAL ANALYTICAL PROCEDURES FOR THE KRUSKAL-WALLIS ONE-WAY ANALYSIS
OF VARIANCE BY RANKS AND/OR RELATED TESTS 985 1. TIE CORRECTION FOR THE
KRUSKAL-WALLIS ONE-WAY ANALYSIS OF VARIANCE BY RANKS 985 2. PAIRWISE
COMPARISONS FOLLOWING COMPUTATION OFTHE TEST STATISTIC FOR THE
KRUSKAL-WALLIS ONE-WAY ANALYSIS OF VARIANCE BY RANKS .''.' 986 VII.
ADDITIONAL DISCUSSION OF THE KRUSKAL-WALLIS ONE-WAY ANALYSIS OF VARIANCE
BY RANKS . .' 990 1. EXACT TABLES OFTHE KRUSKAL-WALLIS DISTRIBUTION
990 2. EQUIVALENCY OFTHE KRUSKAL-WALLIS ONE-WAY ANALYSIS OF ' VARIANCE
BY RANKS AND THE MANN-WHITNEY [/TEST WHEN K-2 990 3. POWER-EFFICIENCY OF
THE KRUSKAL-WALLIS ONE-WAY ANALYSIS OF VARIANCE BY RANKS ., 991 4.
ALTERNATIVE NONPARAMETRIC RANK-ORDER PROCEDURES FOR EVALUATING A DESIGN
INVOLVING K INDEPENDENT SAMPLES 991 VIII. ADDITIONAL EXAMPLES
ILLUSTRATING THE USE OFTHE KRUSKAL-WALLIS ONE- WAY ANALYSIS OF VARIANCE
BY RANKS 992 IX. ADDENDUM 993 1. TEST 22A: THE JONCKHEERE-TERPSTRA TEST
FOR ORDERED ALTERNATIVES 993 TEST 23: THE VAN DER WAERDEN NORMAL-SCORES
TEST FOR K INDEPENDENT SAMPLES 1007 I. HYPOTHESIS EVALUATED WITH TEST
AND RELEVANT BACKGROUND INFORMATION 1007 II. EXAMPLE , 1008 III. NULL
VERSUS ALTERNATIVE HYPOTHESES 1008 IV. TEST COMPUTATIONS 1009 V.
INTERPRETATION OFTHE TEST RESULTS 1011 VI. ADDITIONAL ANALYTICAL
PROCEDURES FOR THE VAN DER WAERDEN NORMAL- SCORES TEST FOR K INDEPENDENT
SAMPLES AND/OR RELATED TESTS 1012 1. PAIRWISE COMPARISONS FOLLOWING
COMPUTATION OFTHE TEST STATISTIC FOR THE VAN DER WAERDEN NORMAL-SCORES
TEST FOR K INDEPENDENT SAMPLES 1012 VII. ADDITIONAL DISCUSSION OFTHE VAN
DER WAERDEN NORMAL-SCORES TEST FOR K INDEPENDENT SAMPLES 1015 TABLE OF
CONTENTS ,V XXI 1. ALTERNATIVE NORMAL-SCORES TESTS 1015 VIII. ADDITIONAL
EXAMPLES ILLUSTRATING THE USE OFTHE VAN DER WAERDEN NORMAL-SCORES TEST
FOR K INDEPENDENT SAMPLES 1015 INFERENTIAL STATISTICAL TESTS EMPLOYED
WITH TWO OR MORE DEPENDENT SAMPLES (AND RELATED MEASURES OF
ASSOCIATION/CORRELATION) 1021 TEST 24: THE SINGLE-FACTOR WITHIN-SUBJECTS
ANALYSIS OF VARIANCE 1023 I. HYPOTHESIS EVALUATED WITH TEST AND RELEVANT
BACKGROUND INFORMATION 1023 II. EXAMPLE , 1025 III. NULL VERSUS
ALTERNATIVE HYPOTHESES 1025 IV. TEST COMPUTATIONS 1025 V. INTERPRETATION
OFTHE TEST RESULTS 1030 VI. ADDITIONAL ANALYTICAL PROCEDURES FOR THE
SINGLE-FACTOR WITHIN-SUBJECTS ANALYSIS OF VARIANCE AND/OR RELATED TESTS
1031 1. COMPARISONS FOLLOWING COMPUTATION OFTHE OMNIBUS F VALUE FOR THE
SINGLE-FACTOR WITHIN-SUBJECTS ANALYSIS OF VARIANCE (TEST 24A: MULTIPLE
/TESTS/FISHER'S LSD TEST; TEST 24B: THE BONFERRONI- DUNN TEST; TEST 24C:
TUKEY'S HSD TEST; TEST 24D: THE NEWMAN-KEULS TEST; TEST 24E: THE SCHEFFE
TEST; TEST 24F: THE DUNNETT TEST; THE COMPU- TATION OF A CONFIDENCE
INTERVAL FOR A COMPARISON; ALTERNATIVE METHOD- OLOGY FOR COMPUTING MS M
FOR A COMPARISON) 1031 2. COMPARING THE MEANS OF THREE OR MORE
CONDITIONS WHEN K Z 4 1039 3. EVALUATION OFTHE SPHERICITY ASSUMPTION
UNDERLYING THE SINGLE-FACTOR WITHIN-SUBJECTS ANALYSIS OF VARIANCE 1041
4. COMPUTATION OF THE POWER OF THE SINGLE-FACTOR WITHIN-SUBJECTS
ANALYSIS OF VARIANCE 1047 5. MEASURES OF MAGNITUDE OF TREATMENT EFFECT
FOR THE SINGLE-FACTOR WITHIN-SUBJECTS ANALYSIS OF VARIANCE: OMEGA
SQUARED (TEST 24G) AND COHEN'S/ INDEX (TEST 24H) : 1049 6. COMPUTATION
OF A CONFIDENCE INTERVAL FOR THE MEAN OF A TREATMENT POPULATION 1051 7.
TEST 24I: THE INTRACLASS CORRELATION COEFFICIENT 1053 VII. ADDITIONAL
DISCUSSION OFTHE SINGLE-FACTOR WITHIN-SUBJECTS ANALYSIS OF VARIANCE 1055
1. THEORETICAL RATIONALE UNDERLYING THE SINGLE-FACTOR WITHIN-SUBJECTS
ANALYSIS OF VARIANCE 1055 2. DEFINITIONAL EQUATIONS FOR THE
SINGLE-FACTOR WITHIN-SUBJECTS ANALYSIS OF VARIANCE 1058 3. RELATIVE
POWER OFTHE SINGLE-FACTOR WITHIN-SUBJECTS ANALYSIS OF VAR- IANCE AND THE
SINGLE-FACTOR BETWEEN-SUBJECTS ANALYSIS OF VARIANCE 1061 4. EQUIVALENCY
OFTHE SINGLE-FACTOR WITHIN-SUBJECTS ANALYSIS OF VARIANCE AND THE T TEST
FOR TWO DEPENDENT SAMPLES WHEN K-2 1062 5. THE LATIN SQUARE DESIGN 1063
VIII. ADDITIONAL EXAMPLES ILLUSTRATING THE USE OFTHE SINGLE-FACTOR
WITHIN- SUBJECTS ANALYSIS OF VARIANCE 1065 XXII HANDBOOK OF PARAMETRIC
AND NONPARAMETRIC STATISTICAL PROCEDURES TEST 25: THE FRIEDMAN TWO-WAY
ANALYSIS OF VARIANCE BY RANKS 1075 I. HYPOTHESIS EVALUATED WITH TEST AND
RELEVANT BACKGROUND INFORMATION 1075 II. EXAMPLE 1076 III. NULL VERSUS
ALTERNATIVE HYPOTHESES 1076 IV. TEST COMPUTATIONS 1077 V. INTERPRETATION
OF THE TEST RESULTS 1 1078 VI. ADDITIONAL ANALYTICAL PROCEDURES FOR THE
FRIEDMAN TWO-WAY ANALYSIS VARIANCE BY RANKS AND/OR RELATED TESTS 1079 1.
TIE CORRECTION FOR THE FRIEDMAN TWO-WAY ANALYSIS VARIANCE BY RANKS ; '*
1079 2. PAIRWISE COMPARISONS FOLLOWING COMPUTATION OFTHE TEST STATISTIC
FOR THE FRIEDMAN TWO-WAY ANALYSIS OF VARIANCE BY RANKS 1080 VII.
ADDITIONAL DISCUSSION OFTHE FRIEDMAN TWO-WAY ANALYSIS OF VARIANCE BY
RANKS 1085 1. EXACT TABLES OFTHE FRIEDMAN DISTRIBUTION 1085 2.
EQUIVALENCY OFTHE FRIEDMAN TWO-WAY ANALYSIS OF VARIANCE BY RANKS AND THE
BINOMIAL SIGN TEST FOR TWO DEPENDENT SAMPLES WHEN K = 2 1085 3.
POWER-EFFICIENCY OFTHE FRIEDMAN TWO-WAY ANALYSIS OF VARIANCE BY RANKS
1086 4. ALTERNATIVE NONPARAMETRIC RANK-ORDER PROCEDURES FOR EVALUATING A
DESIGN INVOLVING K DEPENDENT SAMPLES 1086 5. RELATIONSHIP BETWEEN THE
FRIEDMAN TWO-WAY ANALYSIS OF VARIANCE BY RANKS AND KENDALL'S COEFFICIENT
OF CONCORDANCE 1087 VIII. ADDITIONAL EXAMPLES ILLUSTRATING THE USE OFTHE
FRIEDMAN TWO-WAY ANALYSIS OF VARIANCE BY RANKS ! 1087 IX. ADDENDUM *
1088 L.TEST 25A: THE PAGE TEST FOR ORDERED ALTERNATIVES 1088 TEST 26:
THE COCHRAN Q TEST 1099 I. HYPOTHESIS EVALUATED WITH TEST AND RELEVANT
BACKGROUND INFORMATION 1099 II. EXAMPLE 1100 III. NULL VERSUS
ALTERNATIVE HYPOTHESES 1100 IV. TEST COMPUTATIONS 1100 V. INTERPRETATION
OF THE TEST RESULTS *. 1102 VI. ADDITIONAL ANALYTICAL PROCEDURES FOR THE
COCHRAN Q TEST AND/OR RELATED TESTS 1102 1. PAIRWISE COMPARISONS
FOLLOWING COMPUTATION OFTHE TEST STATISTIC FOR THE COCHRAN GTEST 1102
VII. ADDITIONAL DISCUSSION OFTHE COCHRAN Q TEST 1106 1. ISSUES RELATING
TO SUBJECTS WHO OBTAIN THE SAME SCORE UNDER ALL OF THE EXPERIMENTAL
CONDITIONS 1106 2. EQUIVALENCY OF THE COCHRAN Q TEST AND THE MCNEMAR
TEST WHEN K = 2 1107 3. ALTERNATIVE NONPARAMETRIC PROCEDURES WITH
CATEGORICAL DATA FOR EVALUATING A DESIGN INVOLVING K DEPENDENT SAMPLES
1109 VIII. ADDITIONAL EXAMPLES ILLUSTRATING THE USE OFTHE COCHRAN Q TEST
1109 INFERENTIAL STATISTICAL TEST EMPLOYED WITH A FACTORIAL DESIGN (AND
RELATED MEASURES OF ASSOCIATION/CORRELATION) 1117 TABLE OF CONTENTS
XXIII TEST 27: THE BETWEEN-SUBJECTS FACTORIAL ANALYSIS OF VARIANCE 1119
I. HYPOTHESIS EVALUATED WITH TEST AND RELEVANT BACKGROUND INFORMATION
1119 II. EXAMPLE 1120 III. NULL VERSUS ALTERNATIVE HYPOTHESES 1120 IV.
TEST COMPUTATIONS : . 1122 V. INTERPRETATION OF THE TEST RESULTS 1.
.1128 VI. ADDITIONAL ANALYTICAL PROCEDURES FOR THE BETWEEN-SUBJECTS
FACTORIAL ANALYSIS OF VARIANCE AND/OR RELATED TESTS 1132 1. COMPARISONS
FOLLOWING COMPUTATION OF THE F VALUES FOR THE BETWEEN- SUBJECTS
FACTORIAL ANALYSIS OF VARIANCE (TEST 27A: MULTIPLE T TESTS/ FISHER'S LSD
TEST; TEST 27B: THE BONFERRONI-DUNN TEST; TEST 27C: TUKEY'S HSD TEST;
TEST 27D: THE NEWMAN-KEULS TEST; TEST 27E: THE SCHEFFT TEST; TEST 27F:
THE DUNNETT TEST; COMPARISONS BETWEEN THE MARGINAL MEANS; EVALUATION OF
AN OMNIBUS HYPOTHESIS INVOLVING MORE THAN TWO MARGINAL MEANS;
COMPARISONS BETWEEN SPECIFIC GROUPS THAT ARE A COMBINATION OF BOTH
FACTORS; THE COMPUTATION OF A CONFIDENCE INTERVAL FOR A COMPARISON;
ANALYSIS OF SIMPLE EFFECTS) 1132 2. EVALUATION OFTHE HOMOGENEITY OF
VARIANCE ASSUMPTION OFTHE BETWEEN- SUBJECTS FACTORIAL ANALYSIS OF
VARIANCE 1143 3. COMPUTATION OFTHE POWER OFTHE BETWEEN-SUBJECTS
FACTORIAL ANALYSIS OF VARIANCE 1144 4. MEASURES OF MAGNITUDE OF
TREATMENT EFFECT FOR THE BETWEEN-SUBJECTS FACTORIAL ANALYSIS OF
VARIANCE: OMEGA SQUARED (TEST 27G) AND COHEN'S /INDEX (TEST 27H) 1146 5.
COMPUTATION "OF A CONFIDENCE INTERVAL FOR THE MEAN OF A POPULATION
REPRESENTED BY A GROUP 1150 VII. ADDITIONAL DISCUSSION OF THE
BETWEEN-SUBJECTS FACTORIAL ANALYSIS OF VARIANCE 1150 1. THEORETICAL
RATIONALE UNDERLYING THE BETWEEN-SUBJECTS FACTORIAL ANALYSIS OF VARIANCE
";'. 1150 2. DEFINITIONAL EQUATIONS FOR THE BETWEEN-SUBJECTS FACTORIAL
ANALYSIS OF VARIANCE '.'.* 1151 3. UNEQUAL SAMPLE SIZES 1153 4. THE
RANDOMIZED-BLOCKS DESIGN -. 1154 5. ADDITIONAL COMMENTS ON THE
BETWEEN-SUBJECTS FACTORIAL ANALYSIS OF VARIANCE (FIXED-EFFECTS VERSUS
RANDOM-EFFECTS VERSUS MIXED-EFFECTS ' MODELS; NESTED
FACTORS/HIERARCHICAL DESIGNS AND DESIGNS INVOLVING MORE THAN TWO
FACTORS; SCREENING DESIGNS) 1158 VIII. ADDITIONAL EXAMPLES ILLUSTRATING
THE USE OFTHE BETWEEN-SUBJECTS FACTORIAL ANALYSIS OF VARIANCE 1161 DC.
ADDENDUM ' 1162 DISCUSSION OF AND COMPUTATIONAL PROCEDURES FOR
ADDITIONAL ANALYSIS OF VARIANCE PROCEDURES FOR FACTORIAL DESIGNS 1162 1.
TEST 27I: THE FACTORIAL ANALYSIS OF VARIANCE FOR A MIXED DESIGN : 1162
ANALYSIS OF A CROSSOVER DESIGN WITH A FACTORIAL ANALYSIS OF VARIANCE FOR
A MIXED DESIGN ;. '.':'. 1167 2. TEST 27J: ANALYSIS OF VARIANCE FOR A
LATIN SQUARE DESIGN 1 182 XX IV HANDBOOK OF PARAMETRIC AND NONPARAMETRIC
STATISTICAL PROCEDURES 3. TEST 27K: THE WITHIN-SUBJECTS FACTORIAL
ANALYSIS OF VARIANCE 1203 4. ANALYSIS OF HIGHER ORDER FACTORIAL DESIGNS
1208 MEASURES OF ASSOCIATION/CORRELATION 1219 TEST 28: THE PEARSON
PRODUCT-MOMENT CORRELATION COEFFICIENT 1221 I. HYPOTHESIS EVALUATED WITH
TEST AND RELEVANT BACKGROUND INFORMATION 1221 II. EXAMPLE 1225 III. NULL
VERSUS ALTERNATIVE HYPOTHESES 1225 IV. TEST COMPUTATIONS . 1226 V.
INTERPRETATION OFTHE TEST RESULTS (TEST 28A: TEST OF SIGNIFICANCE FOR A
PEARSON PRODUCT-MOMENT CORRELATION COEFFICIENT; THE COEFFICIENT OF
DETERMINATION) 1228 VI. ADDITIONAL ANALYTICAL PROCEDURES FOR THE PEARSON
PRODUCT-MOMENT CORRELATION COEFFICIENT AND/OR RELATED TESTS 1231 1.
DERIVATION OF A REGRESSION LINE 1231 2. THE STANDARD ERROR OF ESTIMATE
1240 3. COMPUTATION OF A CONFIDENCE INTERVAL FOR THE VALUE OF THE
CRITERION VARIABLE 1241 4. COMPUTATION OF A CONFIDENCE INTERVAL FOR A
PEARSON PRODUCT-MOMENT CORRELATION COEFFICIENT 1243 5. TEST 28B: TEST
FOR EVALUATING THE HYPOTHESIS THAT THE TRUE POPULATION CORRELATION IS A
SPECIFIC VALUE OTHER THAN ZERO . 1244 6. COMPUTATION OF POWER FOR THE
PEARSON PRODUCT-MOMENT CORRELATION COEFFICIENT 1245 7. TEST 28C: TEST
FOR EVALUATING A HYPOTHESIS ON WHETHER THERE IS A SIGNIFICANT DIFFERENCE
BETWEEN TWO INDEPENDENT CORRELATIONS 1247 8. TEST 28D: TEST FOR
EVALUATING A HYPOTHESIS ON WHETHER K INDEPEN- DENT CORRELATIONS ARE
HOMOGENEOUS 1249 9. TEST 28E: TEST FOR EVALUATING THE NULL HYPOTHESIS H
0 :P X2 =P Y Z 1250 10. TESTS FOR EVALUATING A HYPOTHESIS REGARDING ONE
OR MORE REGRESSION COEFFICIENTS (TEST 28F:' TEST FOR EVALUATING THE NULL
HYPOTHESIS H O : P = 0; TEST 28G: TEST FOR EVALUATING THE NULL
HYPOTHESIS H O : P" , = P" 2 ) . 1252 11.
ADDITIONALCORRELATIONALPROCEDURES ; "T 1254 VII. ADDITIONAL DISCUSSION
OF THE PEARSON PRODUCT-MOMENT CORRELATION COEFFICIENT '. , 1255 1. THE
DEFINITIONAL EQUATION FOR THE PEARSON PRODUCT-MOMENT CORRELATION I
COEFFICIENT 1255 2. COVARIANCE 1256 3. THE HOMOSCEDASTICITY ASSUMPTION
OF THE PEARSON PRODUCT-MOMENT CORRELATION COEFFICIENT ,****. * * 1257 4.
RESIDUALS, ANALYSIS OF VARIANCE FOR REGRESSION ANALYSIS AND REGRESSION
DIAGNOSTICS 1258 5. AUTOCORRELATION (AND TEST 28H: DURBIN-WATSON TEST) .
1269 6. THE PHI COEFFICIENT AS A SPECIAL CASE OF THE PEARSON
PRODUCT-MOMENT CORRELATION COEFFICIENT 1284 7. ECOLOGICAL CORRELATION ;
1285 8. CROSS-LAGGED PANEL AND REGRESSION-DISCONTINUITY DESIGNS 1288
VIII. ADDITIONAL EXAMPLES ILLUSTRATING THE USE OFTHE PEARSON PRODUCT-
MOMENT CORRELATION COEFFICIENT 1295 TABLE OF CONTENTS XXV IX. ADDENDUM
1295 1. BIVARIATE MEASURES OF CORRELATION THAT ARE RELATED TO THE
PEARSON PRODUCT- MOMENT CORRELATION COEFFICIENT (TEST 28I: THE
POINT-BISERIAL CORRELATION COEFFICIENT (AND TEST 28I-A: TEST OF
SIGNIFICANCE FOR A POINT-BISERIAL CORRELATION COEFFICIENT); TEST 28J:
THE BISERIAL CORRELATION COEFFICIENT (AND TEST 28J-A: TEST OF
SIGNIFICANCE FOR A BISERIAL CORRELATION COEFFICIENT); TEST 28K: THE
TETRACHORIC CORRELATION COEFFICIENT (AND TEST 28K-A: TEST OF
SIGNIFICANCE FOR A TETRACHORIC CORRELATION COEFFICIENT)) 1296 2.
META-ANALYSIS AND RELATED TOPICS (MEASURES OF EFFECT SIZE; META-ANALYTIC
PROCEDURES (TEST 281: PROCEDURE FOR COMPARING K STUDIES WITH RESPECT TO
SIGNIFICANCE LEVEL; TEST 28M: THE STOUFFER PROCEDURE FOR OBTAINING A
COMBINED SIGNIFICANCE LEVEL (P VALUE) FOR K STUDIES; THE FILE DRAWER
PROBLEM; TEST 28N: PROCEDURE FOR COMPARING K STUDIES WITH RESPECT TO
EFFECT SIZE; TEST 28O: PROCEDURE FOR OBTAINING A COMBINED EFFECT SIZE
FOR K STUDIES); ALTERNATIVE META-ANALYTIC PROCEDURES; PRACTICAL
IMPLICATIONS OF MAGNITUDE OF EFFECT SIZE VALUE; TEST 28P: BINOMIAL
EFFECT SIZE DISPLAY; THE SIGNIFICANCE TEST CONTROVERSY; THE
MINIMUM-EFFECT HYPOTHESIS TESTING MODEL) 1306 TEST 29: SPEARMAN'S
RANK-ORDER CORRELATION COEFFICIENT 1353 I. HYPOTHESIS EVALUATED WITH
TEST AND RELEVANT BACKGROUND INFORMATION 1353 II. EXAMPLE 1355 III. NULL
VERSUS ALTERNATIVE HYPOTHESES 1355 IV. TEST COMPUTATIONS 1356 V.
INTERPRETATION OFTHE TEST RESULTS (TEST 29A: TEST OF SIGNIFICANCE FOR
SPEARMAN'S RANK-ORDER CORRELATION COEFFICIENT) 1357 VI. ADDITIONAL
ANALYTICAL PROCEDURES FOR SPEARMAN'S RANK-ORDER CORRELATION COEFFICIENT
AND/OR RELATED TESTS ****** 1359 1. TIE CORRECTION FOR SPEARMAN'S
RANK-ORDER CORRELATION COEFFICIENT 1359 2. SPEARMAN'S RANK-ORDER
CORRELATION COEFFICIENT AS A SPECIAL CASE OFTHE PEARSON PRODUCT-MOMENT
CORRELATION COEFFICIENT 1361 3. REGRESSION ANALYSIS AND SPEARMAN'S
RANK-ORDER CORRELATION COEFFICIENT 1362 4. PARTIAL RANK CORRELATION ^
1363 5. USE OF FISHER'S Z R TRANSFORMATION WITH SPEARMAN'S RANK- ORDER
CORRELATION COEFFICIENT 1364 VII. ADDITIONAL DISCUSSION OF SPEARMAN'S
RANK-ORDER CORRELATION COEFFICIENT 1364 1. THE RELATIONSHIP BETWEEN
SPEARMAN'S RANK-ORDER CORRELATION COEFFICIENT, KENDALL'S COEFFICIENT OF
CONCORDANCE, AND THE FRIEDMAN TWO-WAY ANALYSIS OF VARIANCE BY RANKS :
1364 2. POWER EFFICIENCY OF SPEARMAN'S RANK-ORDER CORRELATION
COEFFICIENT 1367 3. BRIEF DISCUSSION OF KENDALL'S TAU: AN ALTERNATIVE
MEASURE OF ASSOCIATION FOR TWO SETS OF RANKS 1367 4. WEIGHTED
RANK/TOP-DOWN CORRELATION 1367 VIII. ADDITIONAL EXAMPLES ILLUSTRATING
THE USE OFTHE SPEARMAN'S RANK-ORDER CORRELATION COEFFICIENT 1368 XXVI
HANDBOOK OF PARAMETRIC AND NONPARAMETRIC STATISTICAL PROCEDURES TEST 30:
KENDALL'S TAU 1371 I. HYPOTHESIS EVALUATED WITH TEST AND RELEVANT
BACKGROUND INFORMATION 1371 II. EXAMPLE 1373 III. NULL VERSUS
ALTERNATIVE HYPOTHESES 1373 IV. TEST COMPUTATIONS 1374 V. INTERPRETATION
OF THE TEST RESULTS (TEST 30A: TEST OF SIGNIFICANCE FOR KENDALL'S TAU)
1376 VI. ADDITIONAL ANALYTICAL PROCEDURES FOR KENDALL'S TAU AND/OR
RELATED TESTS 1379 1. TIE CORRECTION FOR KENDALL'S TAU 1379 2.
REGRESSION ANALYSIS AND KENDALL'S TAU 1382 3. PARTIAL RANK CORRELATION
1382 4. SOURCES FOR COMPUTING A CONFIDENCE INTERVAL FOR KENDALL'S TAU
1382 VII. ADDITIONAL DISCUSSION OF KENDALL'S TAU 1382 1. POWER
EFFICIENCY OF KENDALL'S TAU 1382 2. KENDALL'S COEFFICIENT OF AGREEMENT
1382 VIII. ADDITIONAL EXAMPLES ILLUSTRATING THE USE OF KENDALL'S TAU
1382 TEST 31: KENDALL'S COEFFICIENT OF CONCORDANCE 1387 I. HYPOTHESIS
EVALUATED WITH TEST AND RELEVANT BACKGROUND INFORMATION 1387 II. EXAMPLE
1388 III. NULL VERSUS ALTERNATIVE HYPOTHESES 1388 IV. TEST COMPUTATIONS
1389 V. INTERPRETATION OFTHE TEST RESULTS (TEST 31A: TEST OF
SIGNIFICANCE FOR KENDALL'S COEFFICIENT OF CONCORDANCE) 1390 VI.
ADDITIONAL ANALYTICAL PROCEDURES FOR KENDALL'S COEFFICIENT OF
CONCORDANCE AND/OR RELATED TESTS , 1391 1. TIE CORRECTION FOR KENDALL'S
COEFFICIENT OF CONCORDANCE .' 1391 VII. ADDITIONAL DISCUSSION OF
KENDALL'S COEFFICIENT OF CONCORDANCE 1393 1. RELATIONSHIP BETWEEN
KENDALL'S COEFFICIENT OF CONCORDANCE AND SPEARMAN'S RANK-ORDER
CORRELATION COEFFICIENT 1393 2. RELATIONSHIP BETWEEN KENDALL'S
COEFFICIENT OF CONCORDANCE AND THE FRIEDMAN TWO-WAY ANALYSIS OF VARIANCE
BY RANKS 1394 3. WEIGHTED RANK/TOP-DOWN CONCORDANCE . . ^ 1396 4.
KENDALL'S COEFFICIENT OF CONCORDANCE VERSUS THE INTRACLASS CORRELATION
COEFFICIENT 1396 VIII. ADDITIONAL EXAMPLES ILLUSTRATING THE USE OF
KENDALL'S COEFFICIENT OF CONCORDANCE 1398 TEST 32: GOODMAN AND KRUSKAL'S
GAMMA 1403 I. HYPOTHESIS EVALUATED WITH TEST AND RELEVANT BACKGROUND
INFORMATION 1403 II. -EXAMPLE 1404 III. NULL VERSUS ALTERNATIVE
HYPOTHESES 1405 IV. TEST COMPUTATIONS 1406 V. INTERPRETATION OF THE TEST
RESULTS (TEST 32A: TEST OF SIGNIFICANCE FOR GOODMAN AND KRUSKAL'S GAMMA)
1409 VI. ADDITIONAL ANALYTICAL PROCEDURES FOR GOODMAN AND KRUSKAL'S
GAMMA AND/OR RELATED TESTS 1410 TABLE OF CONTENTS XXVII 1. THE
COMPUTATION OF A CONFIDENCE INTERVAL FOR THE VALUE OF GOODMAN AND
KRUSKAL'S GAMMA , 1410 2. TEST 32B: TEST FOR EVALUATING THE NULL
HYPOTHESIS //*: YI = Y, ' 1411 3. SOURCES FOR COMPUTING A PARTIAL
CORRELATION COEFFICIENT FOR GOODMAN AND KRUSKAL'S GAMMA 1412 VII.
ADDITIONAL DISCUSSION OF GOODMAN AND KRUSKAL'S GAMMA . .' 1412 1.
RELATIONSHIP BETWEEN GOODMAN AND KRUSKAL'S GAMMA AND YULE'S Q . 1412
2. SOMERS' DELTA AS AN ALTERNATIVE MEASURE OF ASSOCIATION FOR AN ORDERED
CONTINGENCY TABLE : 1412 VIII. ADDITIONAL EXAMPLES ILLUSTRATING THE USE
OF GOODMAN AND KRUSKAL'S GAMMA 1413 MULTIVARIATE STATISTICAL ANALYSIS
1417 MATRIX ALGEBRA AND MULTIVARIATE ANALYSIS , 1419 I. INTRODUCTORY
COMMENTS ON MULTIVARIATE STATISTICAL ANALYSIS .1419 II. INTRODUCTION TO
MATRIX ALGEBRA 1420 TEST 33: MULTIVARIATE REGRESSION , 1433 I.
HYPOTHESIS EVALUATED WITH TEST AND RELEVANT BACKGROUND INFORMATION 1433
II. EXAMPLES : 1439 III. NULL VERSUS ALTERNATIVE HYPOTHESES .-.*' 1441
RWV. TEST COMPUTATIONS AND INTERPRETATION OFTHE TEST RESULTS TEST
COMPUTATIONS AND INTERPRETATION OF RESULTS FOR EXAMPLE 33.1 (COMPUTATION
OFTHE MULTIPLE CORRELATION COEFFICIENT; THE COEFFICIENT OF MULTIPLE
DETERMINATION; TEST OF SIGNIFICANCE FOR A MULTIPLE CORRELATION
COEFFICIENT; THE MULTIPLE REGRESSION EQUATION; THE STANDARD ERROR OF
MULTIPLE ESTIMATE; COMPUTATION OF A CONFIDENCE INTERVAL FOR Y'; EVALUA-
TION OFTHE RELATIVE IMPORTANCE OFTHE PREDICTOR VARIABLES; EVALUATING THE
SIGNIFICANCE OF A REGRESSION COEFFICIENT; COMPUTATION OF A CONFIDENCE
INTERVAL FOR A REGRESSION COEFFICIENT; ANALYSIS OF VARIANCE FOR MULTIPLE
REGRESSION; SEMIPARTIAL AND PARTIAL CORRELATION (TES T 33A: COMPUTATION
OF A SEMIPARTIAL CORRELATION COEFFICIENT; TEST OF SIGNIFICANCE FOR A
SEMIPARTIAL CORRELATION COEFFICIENT; TEST 33B: COMPUTATION OF A PARTIAL
CORRELATION COEFFICIENT; TEST OF SIGNIFICANCE FOR A PARTIAL CORRELATION
COEFFICIENT) 1442 TEST COMPUTATIONS AND INTERPRETATION OF RESULTS FOR
EXAMPLE 33.2 WITH SPSS 1459 VI. ADDITIONAL ANALYTICAL PROCEDURES FOR
MULTIPLE REGRESSION .-/.,. AND/OR RELATED TESTS V. . Y . 1470 1.
CROSS-VALIDATION OF SAMPLE DATA 1470 VII. ADDITIONAL DISCUSSION OF
MULTIVARIATE REGRESSION , 1471 1. FINAL COMMENTS ON MULTIPLE REGRESSION
ANALYSIS ;. 1471 2. CAUSAL MODELING: PATH ANALYSIS AND STRUCTURAL *
EQUATION MODELING R 1472 3. BRIEF NOTE ON LOGISTIC REGRESSION 1473 VIII.
ADDITIONAL EXAMPLES ILLUSTRATING THE USE OF MULTIVARIATE REGRESSION 1474
XXVIII HANDBOOK OF PARAMETRIC AND NONPARAMETRIC STATISTICAL PROCEDURES
TEST 34: HOTELLING'S T 1 1483 L HYPOTHESIS EVALUATED WITH TEST AND
RELEVANT BACKGROUND INFORMATION 1483 II. EXAMPLE 1483 III. NULL VERSUS
ALTERNATIVE HYPOTHESES 1484 IV. TEST COMPUTATIONS '. ,. 1485 V.
INTERPRETATION OFTHE TEST RESULTS .'.* 1486 VI. ADDITIONAL ANALYTICAL
PROCEDURES FOR HOTELLING'S T 2 AND/OR RELATED TESTS 1488 1. ADDITIONAL
ANALYSES FOLLOWING THE TEST OF THE OMNIBUS NULL HYPOTHESIS : 1488 2.
TEST 34A: THE SINGLE-SAMPLE HOTELLING'S T 1 1489 3. TEST 34B: THE USE OF
THE SINGLE-SAMPLE HOTELLING'S T 1 TO EVALUATE A DEPENDENT SAMPLES DESIGN
1491 VII. ADDITIONAL DISCUSSION OF HOTELLING'S T 2 1495 1. HOTELLING'S T
2 AND MAHALANOBIS' D 2 STATISTIC 1495 VIII. ADDITIONAL EXAMPLES
ILLUSTRATING THE USE OF HOTELLING'S T 2 1495 TEST 35: MULTIVARIATE
ANALYSIS OF VARIANCE 1499 I. HYPOTHESIS EVALUATED WITH TEST AND RELEVANT
BACKGROUND INFORMATION 1499 II. EXAMPLE , 1500 III. NULL VERSUS
ALTERNATIVE HYPOTHESES 1501 IV. TEST COMPUTATIONS 1502 V. INTERPRETATION
OFTHE TEST RESULTS 1503 VI. ADDITIONAL ANALYTICAL PROCEDURES FOR THE
MULTIVARIATE ANALYSIS OF VARIANCE AND/OR RELATED TESTS 1510 VII.
ADDITIONAL DISCUSSION OFTHE MULTIVARIATE ANALYSIS OF VARIANCE 1510 1.
CONCEPTUALIZING THE HYPOTHESIS FOR THE MULTIVARIATE ANALYSIS OF VARIANCE
WITHIN THE CONTEXT OF A LINEAR COMBINATION 1510 2. MULTICOLLINEARITY AND
THE MULTIVARIATE ANALYSIS OF VARIANCE .1510 VIII. ADDITIONAL EXAMPLES
ILLUSTRATING THE USE OFTHE MULTIVARIATE ANALYSIS OF VARIANCE - 1511 TEST
36: MULTIVARIATE ANALYSIS OF COVARIANCE 1515 I. HYPOTHESIS EVALUATED
WITH TEST AND RELEVANT BACKGROUND INFORMATION 1515 II. EXAMPLE : 1516
III. NULL VERSUS ALTERNATIVE HYPOTHESES 1517 IV. TEST COMPUTATIONS : ':
1517 V. INTERPRETATION OFTHE TEST RESULTS 1518 VI. ADDITIONAL ANALYTICAL
PROCEDURES FOR THE MULTIVARIATE ANALYSIS OF COVARIANCE AND/OR RELATED
TESTS 1521 VII. ADDITIONAL DISCUSSION OFTHE MULTIVARIATE ANALYSIS OF
COVARIANCE 1521 1. MULTIPLE COVARIATES 1521 VIII. ADDITIONAL EXAMPLES
ILLUSTRATING THE USE OFTHE MULTIVARIATE ANALYSIS OF COVARIANCE 1522 TEST
37: DISCRIMINANT FUNCTION ANALYSIS 1525 I. HYPOTHESIS EVALUATED WITH
TEST AND RELEVANT BACKGROUND INFORMATION 1525 II. EXAMPLES 1527 III.
NULL VERSUS ALTERNATIVE HYPOTHESES 1528 TABLE OF CONTENTS XXIX IV. TEST
COMPUTATIONS : 1529 V. INTERPRETATION OFTHE TEST RESULTS 1531 ANALYSIS
OF EXAMPLE 37.1 1531 ANALYSIS OF EXAMPLE 37.2 1543 VI. ADDITIONAL
ANALYTICAL PROCEDURES FOR DISCRIMINANT FUNCTION ANALYSIS AND/OR RELATED
TESTS 1552 VII. ADDITIONAL DISCUSSION OF DISCRIMINANT FUNCTION ANALYSIS
1552 VIII. ADDITIONAL EXAMPLES ILLUSTRATING THE USE OF DISCRIMINANT
FUNCTION ANALYSIS 1552 TEST 38: CANONICAL CORRELATIONAL 1557 I.
HYPOTHESIS EVALUATED WITH TEST AND RELEVANT BACKGROUND INFORMATION 1557
II. EXAMPLE 1560 III. NULL VERSUS ALTERNATIVE HYPOTHESES 1560 IV. TEST
COMPUTATIONS 1560 V. INTERPRETATION OFTHE TEST RESULTS 1561 VI.
ADDITIONAL ANALYTICAL PROCEDURES FOR CANONICAL CORRELATION AND/OR
RELATED TESTS 1574 VII. ADDITIONAL DISCUSSION OF CANONICAL CORRELATION
1574 VIII. ADDITIONAL EXAMPLES ILLUSTRATING THE USE OF CANONICAL
CORRELATION 1575 TEST39: LOGISTIC REGRESSION 1581 I. HYPOTHESIS
EVALUATED WITH TEST AND RELEVANT BACKGROUND INFORMATION 1581 II. EXAMPLE
1584 III. NULL VERSUS ALTERNATIVE HYPOTHESES 1584 IV. TEST COMPUTATIONS
1587 V. INTERPRETATION OFTHE TEST RESULTS 1590 RESULTS FOR A BINARY
LOGISTIC REGRESSION WITH ONE PREDICTOR VARIABLE 1590 RESULTS FOR A
BINARY LOGISTIC REGRESSION WITH MULTIPLE PREDICTOR VARIABLES . 1598 VI.
ADDITIONAL ANALYTICAL PROCEDURES FOR LOGISTIC REGRESSION AND/OR RELATED
TESTS 1605 VII. ADDITIONAL DISCUSSION OF LOGISTIC REGRESSION 1606 VIII.
ADDITIONAL EXAMPLES ILLUSTRATING THE USE OF LOGISTIC REGRESSION 1606
TEST 40: PRINCIPAL COMPONENTS ANALYSIS AND FACTOR ANALYSIS 1615 I.
HYPOTHESIS EVALUATED WITH TEST AND RELEVANT BACKGROUND INFORMATION 1615
II. EXAMPLE 1618 III. NULL VERSUS ALTERNATIVE HYPOTHESES 1618 IV. TEST
COMPUTATIONS 1618 V. INTERPRETATION OFTHE TEST RESULTS 1622 VI.
ADDITIONAL ANALYTICAL PROCEDURES FOR PRINCIPAL COMPONENTS ANALYSIS AND
FACTOR ANALYSIS AND/OR RELATED TESTS 1634 1. PRINCIPAL AXIS FACTOR
ANALYSIS OF EXAMPLE 40.1 1634 VII. ADDITIONAL DISCUSSION OF PRINCIPAL
COMPONENTS ANALYSIS AND FACTOR ANALYSIS 1635 1. CRITICISMS OF FACTOR
ANALYTIC PROCEDURES 1635 2. CLUSTER ANALYSIS 1635 3. MULTIDIMENSIONAL
SCALING 1636 XXX HANDBOOK OF PARAMETRIC AND NONPARAMETRIC STATISTICAL
PROCEDURES VIII. ADDITIONAL EXAMPLES ILLUSTRATING THE USE OF PRINCIPAL
COMPONENTS ANALYSIS AND FACTOR ANALYSIS 1637 APPENDIX: TABLES 1647 TABLE
AL. TABLE OFTHE NORMAL DISTRIBUTION .; 1651 TABLE A2. TABLE OF
STUDENT'S /DISTRIBUTION 1656 TABLE A3. POWER CURVES FOR STUDENT'S /
DISTRIBUTION 1657 TABLE A4. TABLE OFTHE CHI-SQUARE DISTRIBUTION 1661
TABLE A5. TABLE OF CRITICAL T VALUES FOR WILCOXON'S SIGNED-RANKS AND
MATCHED-PAIRS SIGNED-RANKS TESTS 1662 TABLE A6. TABLE OFTHE BINOMIAL
DISTRIBUTION, INDIVIDUAL PROBABILITIES 1663 TABLE A7. TABLE OFTHE
BINOMIAL DISTRIBUTION, CUMULATIVE PROBABILITIES 1666 TABLE A8. TABLE OF
CRITICAL VALUES FOR THE SINGLE-SAMPLE RUNS TEST 1669 TABLE A9. TABLE
OFTHE F MM DISTRIBUTION 1670 TABLE A10. TABLE OFTHE F DISTRIBUTION 1671
TABLE ALL. TABLE OF CRITICAL VALUES FOR MANN-WHITNEY {/STATISTIC 1679
TABLE A12. TABLE OF SANDLER'S/4 STATISTIC 1681 TABLE A13. TABLE OFTHE
STUDENTIZED RANGE STATISTIC 1682 TABLE A14. TABLE OF DUNNETT'S MODIFIED
T STATISTIC FOR A CONTROL GROUP COMPARISON 1684 TABLE A15. GRAPHS OFTHE
POWER FUNCTION FOR THE ANALYSIS OF VARIANCE 1686 TABLE A16. TABLE OF
CRITICAL VALUES FOR PEARSON R 1690 TABLE A17. TABLE OF FISHER'S Z R
TRANSFORMATION 1691 TABLE A18. TABLE OF CRITICAL VALUES FOR SPEARMAN'S
RHO 1692 TABLE A19. TABLE OF CRITICAL VALUES FOR KENDALL'S TAU 1693
TABLE A20. TABLE OF CRITICAL VALUES FOR KENDALL'S COEFFICIENT OF
CONCORDANCE '. 1694 TABLE A21. TABLE OF CRITICAL VALUES FOR THE
KOLMOGOROV-SMIRNOV GOODNESS-OF-FIT TEST FOR A SINGLE SAMPLE 1695 TABLE
A22. TABLE OF CRITICAL VALUES FOR THE LILLIEFORS TEST FOR NORMALITY 1696
TABLE A23. TABLE OF CRITICAL VALUES FOR THE KOLMOGOROV-SMIRNOV TEST FOR
TWO INDEPENDENT SAMPLES 1697 TABLE A24. TABLE OF CRITICAL VALUES FOR THE
JONCKHEERE-TERPSTRA TEST STATISTIC . 1699 TABLE A25. TABLE OF CRITICAL
VALUES FOR THE PAGE TEST STATISTIC 1701 TABLE A26. TABLE OF EXTREME
STUDENTIZED DEVIATE OUTLIER STATISTIC 1703 TABLE A27. TABLE OF
DURBIN-WATSON TEST STATISTIC 1704 INDEX 1707 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Sheskin, David J. 1941- |
| author_GND | (DE-588)1013718429 |
| author_facet | Sheskin, David J. 1941- |
| author_role | aut |
| author_sort | Sheskin, David J. 1941- |
| author_variant | d j s dj djs |
| building | Verbundindex |
| bvnumber | BV022386740 |
| callnumber-first | Q - Science |
| callnumber-label | QA276 |
| callnumber-raw | QA276.25 |
| callnumber-search | QA276.25 |
| callnumber-sort | QA 3276.25 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 830 |
| classification_tum | MAT 620b MAT 626b MAT 625b |
| ctrlnum | (OCoLC)71266496 (DE-599)BVBBV022386740 |
| dewey-full | 519.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 |
| dewey-search | 519.5 |
| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 4. ed. |
| format | Book |
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| id | DE-604.BV022386740 |
| illustrated | Illustrated |
| index_date | 2024-07-02T17:12:56Z |
| indexdate | 2024-07-09T20:56:29Z |
| institution | BVB |
| isbn | 9781584888147 1584888148 |
| language | English |
| lccn | 2006029391 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015595655 |
| oclc_num | 71266496 |
| open_access_boolean | |
| owner | DE-473 DE-BY-UBG DE-92 DE-20 DE-91 DE-BY-TUM DE-634 DE-83 |
| owner_facet | DE-473 DE-BY-UBG DE-92 DE-20 DE-91 DE-BY-TUM DE-634 DE-83 |
| physical | XXX, 1736 graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Chapman & Hall/CRC |
| record_format | marc |
| spelling | Sheskin, David J. 1941- Verfasser (DE-588)1013718429 aut Handbook of parametric and nonparametric statistical procedures David J. Sheskin 4. ed. Boca Raton [u.a.] Chapman & Hall/CRC 2007 XXX, 1736 graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Statistiek gtt Statistik Statistique mathématique - Guides, manuels, etc Mathematical statistics Handbooks, manuals, etc Statistische Schlussweise (DE-588)4182963-3 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Inferenzstatistik (DE-588)4247120-5 gnd rswk-swf Parametrisches Verfahren (DE-588)4205938-0 gnd rswk-swf Nichtparametrisches Verfahren (DE-588)4339273-8 gnd rswk-swf Statistische Schlussweise (DE-588)4182963-3 s Parametrisches Verfahren (DE-588)4205938-0 s DE-604 Statistik (DE-588)4056995-0 s Nichtparametrisches Verfahren (DE-588)4339273-8 s Inferenzstatistik (DE-588)4247120-5 s http://www.loc.gov/catdir/toc/ecip0620/2006029391.html Table of contents only http://www.loc.gov/catdir/enhancements/fy0668/2006029391-d.html Publisher description HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015595655&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sheskin, David J. 1941- Handbook of parametric and nonparametric statistical procedures Statistiek gtt Statistik Statistique mathématique - Guides, manuels, etc Mathematical statistics Handbooks, manuals, etc Statistische Schlussweise (DE-588)4182963-3 gnd Statistik (DE-588)4056995-0 gnd Inferenzstatistik (DE-588)4247120-5 gnd Parametrisches Verfahren (DE-588)4205938-0 gnd Nichtparametrisches Verfahren (DE-588)4339273-8 gnd |
| subject_GND | (DE-588)4182963-3 (DE-588)4056995-0 (DE-588)4247120-5 (DE-588)4205938-0 (DE-588)4339273-8 |
| title | Handbook of parametric and nonparametric statistical procedures |
| title_auth | Handbook of parametric and nonparametric statistical procedures |
| title_exact_search | Handbook of parametric and nonparametric statistical procedures |
| title_exact_search_txtP | Handbook of parametric and nonparametric statistical procedures |
| title_full | Handbook of parametric and nonparametric statistical procedures David J. Sheskin |
| title_fullStr | Handbook of parametric and nonparametric statistical procedures David J. Sheskin |
| title_full_unstemmed | Handbook of parametric and nonparametric statistical procedures David J. Sheskin |
| title_short | Handbook of parametric and nonparametric statistical procedures |
| title_sort | handbook of parametric and nonparametric statistical procedures |
| topic | Statistiek gtt Statistik Statistique mathématique - Guides, manuels, etc Mathematical statistics Handbooks, manuals, etc Statistische Schlussweise (DE-588)4182963-3 gnd Statistik (DE-588)4056995-0 gnd Inferenzstatistik (DE-588)4247120-5 gnd Parametrisches Verfahren (DE-588)4205938-0 gnd Nichtparametrisches Verfahren (DE-588)4339273-8 gnd |
| topic_facet | Statistiek Statistik Statistique mathématique - Guides, manuels, etc Mathematical statistics Handbooks, manuals, etc Statistische Schlussweise Inferenzstatistik Parametrisches Verfahren Nichtparametrisches Verfahren |
| url | http://www.loc.gov/catdir/toc/ecip0620/2006029391.html http://www.loc.gov/catdir/enhancements/fy0668/2006029391-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015595655&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT sheskindavidj handbookofparametricandnonparametricstatisticalprocedures |