Handbook of Parametric and Nonparametric Statistical Procedures

Table of Contents......Page 0
Handbook of PARAMETRIC and NONPARAMETRIC STATISTICAL PROCEDURES......Page 2
Preface......Page 4
VII. Additional discussion of the test......Page 5
Endnotes......Page 6
Table of Contents......Page 10
Statistic versus Parameter......Page 31
c) Interval level measurement......Page 32
Measures of Central Tendency......Page 33
b) Quantiles, percentiles, quartiles, and deciles......Page 35
c) The variance and the standard deviation......Page 36
d) The coefficient of variation......Page 39
Measures of Skewness and Kurtosis......Page 40
The Normal Distribution......Page 49
Hypothesis Testing......Page 55
Estimation in Inferential Statistics......Page 60
Basic Concepts and Terminology Employed in Experimental Design......Page 61
Correlational Research......Page 62
Parametric versus Nonparametric Inferential Statistical Tests......Page 63
References......Page 64
Endnotes......Page 65
A. Inferential statistical tests employed with interval/ratio data......Page 68
C. Inferential statistical tests employed with categorical/nominal data......Page 69
B. Inferential statistical tests employed with ordinal/rank-order data......Page 70
B. Measures of correlation/association employed with ordinal/rank order data......Page 71
A. Meta-analytic procedures......Page 72
Guidelines and Decision Tables for Selecting the Appropriate Statistical Procedure......Page 73
Inferential Statistical Tests Employed with a Single Sample......Page 78
III. Null versus Alternative Hypotheses......Page 79
IV. Test Computations......Page 80
V. Interpretation of the Test Results......Page 81
1. The interpretation of a negative z value......Page 82
2. The standard error of the population mean and graphical representation of the results of the single-sample z test......Page 83
4. The z test for a population proportion......Page 87
VIII. Additional Examples Illustrating the Use of the Single- Sample z Test......Page 88
Endnotes......Page 90
I. Hypothesis Evaluated with Test and Relevant Background Information......Page 92
IV. Test Computations......Page 93
V. Interpretation of the Test Results......Page 95
1. Determination of the power of the single-sample t test and the single-sample z test, and the application of Test 2a: Cohen......Page 97
2. Computation of a confidence interval for the mean of the population represented by a sample......Page 105
VII. Additional Discussion of the Single-Sample t Test......Page 111
VIII. Additional Examples Illustrating the Use of the Single- Sample t Test......Page 113
Endnotes......Page 114
I. Hypothesis Evaluated with Test and Relevant Background Information......Page 116
III. Null versus Alternative Hypotheses......Page 117
V. Interpretation of the Test Results......Page 118
1. Large sample normal approximation of the chi-square distribution......Page 121
2. Computation of a confidence interval for the variance of a population represented by a sample......Page 122
VIII. Additional Examples Illustrating the Use of the Single- Sample Chi-Square Test for a Population Variance......Page 125
Endnotes......Page 127
I. Hypothesis Evaluated with Test and Relevant Background Information......Page 128
III. Null versus Alternative Hypotheses......Page 129
IV. Test Computations......Page 130
V. Interpretation of the Test Results......Page 132
1. Exact tables for the single-sample test for evaluating population skewness......Page 133
References......Page 134
I. Hypothesis Evaluated with Test and Relevant Background Information......Page 135
III. Null versus Alternative Hypotheses......Page 136
IV. Test Computations......Page 137
1. Test 5a: The D’Agostino–Pearson test of normality......Page 139
References......Page 141
Endnotes......Page 142
II. Example......Page 143
IV. Test Computations......Page 144
V. Interpretation of the Test Results......Page 146
1. The normal approximation of the Wilcoxon T statistic for large sample sizes......Page 148
2. The correction for continuity for the normal approximation of the Wilcoxon signed-ranks test......Page 150
3. Tie correction for the normal approximation of the Wilcoxon test statistic......Page 151
1. Power-efficiency of the Wilcoxon signed-ranks test and the concept of asymptotic relative efficiency......Page 152
VIII. Additional Examples Illustrating the Wilcoxon Signed-Ranks Test......Page 153
References......Page 154
Endnotes......Page 155
I. Hypothesis Evaluated with Test and Relevant Background Information......Page 157
II. Example......Page 158
III. Null versus Alternative Hypotheses......Page 159
IV. Test Computations......Page 160
V. Interpretation of the Test Results......Page 163
1. Computing a confidence interval for the Kolmogorov–Smirnov goodness-of-fit test for a single sample......Page 164
2. The power of the Kolmogorov–Smirnov goodness-of-fit test for a single sample......Page 165
3. Test 7a: The Lilliefors test for normality......Page 166
1. Effect of sample size on the result of a goodness-of-fit test......Page 167
References......Page 168
Endnotes......Page 170
I. Hypothesis Evaluated with Test and Relevant Background Information......Page 171
III. Null versus Alternative Hypotheses......Page 172
IV. Test Computations......Page 173
1. Comparisons involving individual cells when k > 2......Page 175
2. The analysis of standardized residuals......Page 178
3. Computation of a confidence interval for the chi-square goodness-of-fit test......Page 179
6. Application of the chi-square goodness-of-fit test for assessing goodness-of-fit for a theoretical population distribution......Page 181
8. Heterogeneity chi-square analysis......Page 185
1. Directionality of the chi-square goodness-of-fit test......Page 188
VIII. Additional Examples Illustrating the Use of the Chi-Square Goodness-of-Fit Test......Page 191
References......Page 193
Endnotes......Page 194
I. Hypothesis Evaluated with Test and Relevant Background Information......Page 197
III. Null versus Alternative Hypotheses......Page 198
IV. Test Computations......Page 199
V. Interpretation of the Test Results......Page 201
1. Test 9a: The z test for a population proportion......Page 202
2. Test 9b: The single-sample test for the median......Page 209
3. Computing the power of the binomial sign test for a single sample......Page 212
1. Evaluating goodness-of-fit for a binomial distribution......Page 213
VIII. Additional Example Illustrating the Use of the Binomial Sign Test for a Single Sample......Page 214
1. The multinomial distribution......Page 215
2. The negative binomial distribution......Page 218
3. The hypergeometric distribution......Page 220
4. The Poisson distribution......Page 223
5. The matching distribution......Page 228
References......Page 230
Endnotes......Page 231
I. Hypothesis Evaluated with Test and Relevant Background Information......Page 237
III. Null versus Alternative Hypotheses......Page 238
V. Interpretation of the Test Results......Page 239
1. The normal approximation of the single-sample runs test for large sample sizes......Page 240
2. The correction for continuity for the normal approximation of the single-sample runs test......Page 241
3. Extension of the runs test to data with more than two categories......Page 242
4. Test 10a: The runs test for serial randomness......Page 243
1. Additional discussion of the concept of randomness......Page 246
VIII. Additional Examples Illustrating the Single-Sample Runs Test......Page 247
1. The generation of pseudorandom numbers......Page 250
2. Alternative tests of randomness 9......Page 254
5) Tests of trend analysis/time series analysis......Page 263
References......Page 264
Endnotes......Page 265
Inferential Statistical Tests Employed with Two Independent Samples (and Related Measures of Association/Correlation)......Page 268
II. Example......Page 269
IV. Test Computations......Page 270
V. Interpretation of the Test Results......Page 272
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......Page 274
2. Test 11a: Hartley’s Fmax test for homogeneity of variance/F test for two population variances: Evaluation of the homogeneity of variance assumption of the t test for two independent samples......Page 275
3. Computation of the power of the t test for two independent samples and the application of Test 11b: Cohen’s d index......Page 280
4. Measure of magnitude of treatment effect for the t test for two independent samples: Omega squared (Test 11c)......Page 285
5. Computation of a confidence interval for the t test for two independent samples......Page 287
6. Test 11d: The z test for two independent samples......Page 288
1. Unequal sample sizes......Page 290
2. Robustness of the t test for two independent samples......Page 291
3. Outliers (Test 11e: Procedures for identifying outliers) and data transformation......Page 292
4. Hotelling’s T2......Page 302
VIII. Additional Examples Illustrating the Use of the t Test for Two Independent Samples......Page 303
References......Page 304
Endnotes......Page 305
I. Hypothesis Evaluated with Test and Relevant Background Information......Page 310
III. Null versus Alternative Hypotheses......Page 311
IV. Test Computations......Page 312
V. Interpretation of the Test Results......Page 314
1. The normal approximation of the Mann–Whitney U statistic for large sample sizes......Page 315
3. Tie correction for the normal approximation of the Mann–Whitney U statistic......Page 317
2. Equivalency of the normal approximation of the Mann–Whitney U test and the t test for two independent samples with rank-orders......Page 318
VIII. Additional Examples Illustrating the Use of the Mann– Whitney U Test......Page 319
IX. Addendum......Page 320
References......Page 332
Endnotes......Page 334
I. Hypothesis Evaluated with Test and Relevant Background Information......Page 339
III. Null versus Alternative Hypotheses......Page 340
IV. Test Computations......Page 342
V. Interpretation of the Test Results......Page 344
2. Computing sample confidence intervals for the Kolmogorov–Smirnov test for two in-dependent samples......Page 345
1. Additional comments on the Kolmogorov–Smirnov test for two independent samples......Page 346
VIII. Additional Examples Illustrating the Kolmogorov–Smirnov Test for Two Independent Samples......Page 347
Endnotes......Page 348
I. Hypothesis Evaluated with Test and Relevant Background Information......Page 350
III. Null versus Alternative Hypotheses......Page 351
IV. Test Computations......Page 352
1. The normal approximation of the Siegel–Tukey test statistic for large sample sizes......Page 355
2. The correction for continuity for the normal approximation of the Siegel–Tukey test for equal variability......Page 356
4. Adjustment of scores for the Siegel–Tukey test for equal variability when   1     2......Page 357
1. Analysis of the homogeneity of variance hypothesis for the same set of data with both a parametric and nonparametric test, and the power-efficiency of the Siegel–Tukey test for equal variability......Page 359
2. Alternative nonparametric tests of dispersion In Section I it is noted that the Siegel– Tukey test for equal variability......Page 360
VIII. Additional Examples Illustrating the Siegel–Tukey Test for Equal Variability......Page 361
References......Page 362
Endnotes......Page 363
I. Hypothesis Evaluated with Test and Relevant Background Information......Page 364
III. Null versus Alternative Hypotheses......Page 365
IV. Test Computations......Page 367
V. Interpretation of the Test Results......Page 369
1. The normal approximation of the Moses test statistic for large sample sizes......Page 370
2. Issue of repetitive resampling......Page 371
VIII. Additional Examples Illustrating the Moses Test for Equal Variability......Page 372
References......Page 375
Endnotes......Page 376
I. Hypothesis Evaluated with Test and Relevant Background Information......Page 378
II. Examples......Page 380
III. Null versus Alternative Hypotheses......Page 381
IV. Test Computations......Page 383
V. Interpretation of the Test Results......Page 385
1. Yates’ correction for continuity......Page 387
2. Quick computational equation for a 2 x 2 table......Page 388
3. Evaluation of a directional alternative hypothesis in the case of a 2 x 2 contingency table......Page 389
4. Test 16c: The Fisher exact test......Page 390
5. Test 16d: The z test for two independent proportions......Page 395
6. Computation of confidence interval for a difference between proportions......Page 400
7. Test 16e: The median test for independent samples......Page 401
8. Extension of the chi-square test for r x c tables to contingency tables involving more than two rows and/or columns, and a......Page 403
9. The analysis of standardized residuals......Page 409
11. Heterogeneity chi-square analysis for a 2 x 2 contingency table......Page 411
12. Measures of association for r x c contingency tables......Page 415
1. Simpson’s paradox......Page 426
2. Analysis of multidimensional contingency tables......Page 428
VIII. Additional Examples Illustrating the Chi-Square Test for r x c Tables......Page 439
References......Page 443
Endnotes......Page 445
Inferential Statistical Tests Employed with Two Dependent Samples (and Related Measures of Association/Correlation)......Page 450
I. Hypothesis Evaluated with Test and Relevant Background Information......Page 451
III. Null versus Alternative Hypotheses......Page 452
IV. Test Computations......Page 453
V. Interpretation of the Test Results......Page 455
1. Alternative equation for the t test for two dependent samples......Page 456
3. Test 17a: The t test for homogeneity of variance for two dependent samples: Evaluation of the homogeneity of variance assumption of the t test for two dependent samples......Page 460
4. Computation of the power of the t test for two dependent samples and the application of Test 17b: Cohen’s d index......Page 463
5. Measure of magnitude of treatment effect for the t test for two dependent samples: Omega squared (Test 17c)......Page 467
6. Computation of a confidence interval for the t test for two dependent samples......Page 468
7. Test 17d: Sandler’s A test......Page 469
8. Test 17e: The z test for two dependent samples......Page 470
1. The use of matched subjects in a dependent samples design......Page 473
2. Relative power of the t test for two dependent samples and the t test for two independent samples......Page 476
3. Counterbalancing and order effects......Page 477
4. Analysis of a before-after design with the t test for two dependent samples......Page 478
VIII. Additional Example Illustrating the Use of the t Test for Two Dependent Samples......Page 479
Endnotes......Page 480
I. Hypothesis Evaluated with Test and Relevant Background Information......Page 484
III. Null versus Alternative Hypotheses......Page 485
IV. Test Computations......Page 486
V. Interpretation of the Test Results......Page 487
1. The normal approximation of the Wilcoxon T statistic for large sample sizes......Page 489
2. The correction for continuity for the normal approximation of the Wilcoxon matched-pairs signed-ranks test......Page 490
3. Tie correction for the normal approximation of the Wilcoxon test statistic......Page 491
1. Power-efficiency of the Wilcoxon matched-pairs signed-ranks test......Page 492
References......Page 493
Endnotes......Page 494
I. Hypothesis Evaluated with Test and Relevant Background Information......Page 495
III. Null versus Alternative Hypotheses......Page 496
IV. Test Computations......Page 497
V. Interpretation of the Test Results......Page 499
1. The normal approximation of the binomial sign test for two dependent samples with and without a correction for continuity......Page 500
2. Computation of a confidence interval for the binomial sign test for two dependent samples......Page 502
2. Equivalency of the Friedman two-way analysis variance by ranks and the binomial sign test for two dependent samples when k = 2......Page 504
Endnotes......Page 505
I. Hypothesis Evaluated with Test and Relevant Background Information......Page 507
II. Examples......Page 508
III. Null versus Alternative Hypotheses......Page 510
IV. Test Computations......Page 511
V. Interpretation of the Test Results......Page 512
1. Alternative equation for the McNemar test statistic based on the normal distribution......Page 513
3. Computation of the exact binomial probability for the McNemar test model with a small sample size......Page 514
4. Additional analytical procedures for the McNemar test......Page 516
1. Alternative format for the McNemar test summary table and modified test equation......Page 517
VIII. Additional Examples Illustrating the Use of the McNemar Test......Page 518
IX. Addendum......Page 520
References......Page 522
Endnotes......Page 523
Inferential Statistical Tests Employed with Two or More Independent Samples (and Related Measures of Association/Correlation)......Page 525
I. Hypothesis Evaluated with Test and Relevant Background Information......Page 526
III. Null versus Alternative Hypotheses......Page 527
IV. Test Computations......Page 528
V. Interpretation of the Test Results......Page 532
1. Comparisons following computation of the omnibus F value for the single-factor between-subjects analysis of variance......Page 533
2. Comparing the means of three or more groups when k 4......Page 561
3. Evaluation of the homogeneity of variance assumption of the single-factor between- subjects analysis of variance......Page 562
4. Computation of the power of the single-factor between-subjects analysis of variance......Page 565
5. Measures of magnitude of treatment effect for the single-factor between-subjects analysis of variance: Omega squared (Test......Page 568
6. Computation of a confidence interval for the mean of a treatment population......Page 571
1. Theoretical rationale underlying the single-factor between-subjects analysis of variance......Page 573
2. Definitional equations for the single-factor between-subjects analysis of variance......Page 575
3. Equivalency of the single-factor between-subjects analysis of variance and the t test for two independent samples when k = 2......Page 576
4. Robustness of the single-factor between-subjects analysis of variance......Page 577
6. Multivariate analysis of variance (MANOVA)......Page 578
VIII. Additional Examples Illustrating the Use of the Single-Factor Between-Subjects Analysis of Variance......Page 579
IX. Addendum......Page 580
References......Page 596
Endnotes......Page 598
I. Hypothesis Evaluated with Test and Relevant Background Information......Page 609
III. Null versus Alternative Hypotheses......Page 610
IV. Test Computations......Page 611
V. Interpretation of the Test Results......Page 612
1. Tie correction for the Kruskal–Wallis one-way analysis of variance by ranks......Page 613
2. Pairwise comparisons following computation of the test statistic for the Kruskal–Wallis one-way analysis of variance by ra......Page 614
1. Exact tables of the Kruskal–Wallis distribution......Page 617
3. Power-efficiency of the Kruskal–Wallis one-way analysis of variance by ranks......Page 618
VIII. Additional Examples Illustrating the Use of the Kruskal– Wallis One-Way Analysis of Variance by Ranks......Page 619
References......Page 620
Endnotes......Page 621
I. Hypothesis Evaluated with Test and Relevant Background Information......Page 624
III. Null versus Alternative Hypotheses......Page 625
IV. Test Computations......Page 626
V. Interpretation of the Test Results......Page 628
1. Pairwise comparisons following computation of the test statistic for the van der Waerden normal-scores test for k independent samples......Page 629
1. Alternative normal-scores tests......Page 631
VIII. Additional Examples Illustrating the van der Waerden Normal-Scores test for k Independent Samples......Page 632
Endnotes......Page 633
Inferential Statistical Tests Employed with Two or More Dependent Samples (and Related Measures of Association/Correlation)......Page 636
I. Hypothesis Evaluated with Test and Relevant Background Information......Page 637
II. Example......Page 638
IV. Test Computations......Page 639
V. Interpretation of the Test Results......Page 644
1. Comparisons following computation of the omnibus F value for the single-factor within-subjects analysis of variance......Page 645
2. Comparing the means of three or more conditions when k   4......Page 653
3. Evaluation of the sphericity assumption underlying the single-factor within-subjects analysis of variance......Page 655
4. Computation of the power of the single-factor within-subjects analysis of variance......Page 659
5. Measures of magnitude of treatment effect for the single-factor within-subjects analysis of variance: Omega squared (Test 24g) and Cohen’s f index (Test 24h)......Page 661
6. Computation of a confidence interval for the mean of a treatment population......Page 663
1. Theoretical rationale underlying the single-factor within-subjects analysis of variance......Page 665
2. Definitional equations for the single-factor within-subjects analysis of variance......Page 667
3. Relative power of the single-factor within-subjects analysis of variance and the single-factor between-subjects analysis of variance......Page 670
4. Equivalency of the single-factor within-subjects analysis of variance and the t test for two dependent samples when k = 2......Page 671
5. The Latin square design......Page 672
VIII. Additional Examples Illustrating the Use of the Single-Factor Within-Subjects Analysis of Variance......Page 673
References......Page 676
Endnotes......Page 677
I. Hypothesis Evaluated with Test and Relevant Background Information......Page 681
III. Null versus Alternative Hypotheses......Page 682
IV. Test Computations......Page 683
V. Interpretation of the Test Results......Page 684
1. Tie correction for the Friedman two-way analysis of variance by ranks......Page 685
2. Pairwise comparisons following computation of the test statistic for the Friedman two-way analysis of variance by ranks......Page 686
1. Exact tables of the Friedman distribution......Page 690
2. Equivalency of the Friedman two-way analysis of variance by ranks and the binomial sign test for two dependent samples when k = 2......Page 691
5. Relationship between the Friedman two-way analysis of variance by ranks and Kendall’s coefficient of concordance......Page 692
VIII. Additional Examples Illustrating the Use of the Friedman Two-Way Analysis of Variance by Ranks......Page 693
Endnotes......Page 694
I. Hypothesis Evaluated with Test and Relevant Background Information......Page 697
IV. Test Computations......Page 698
1. Pairwise comparisons following computation of the test statistic for the Cochran Q test......Page 700
1. Issues relating to subjects who obtain the same score under all of the experimental conditions......Page 704
2. Equivalency of the Cochran Q test and the McNemar test when k = 2......Page 705
3. Alternative nonparametric procedures for categorical data for evaluating a design involving k dependent samples......Page 706
VIII. Additional Examples Illustrating the Use of the Cochran Q Test......Page 707
References......Page 711
Endnotes......Page 712
Inferential Statistical Test Employed with Factoral Design (and Related Measures of Association/Correlation)......Page 714
I. Hypothesis Evaluated with Test and Relevant Background Information......Page 715
III. Null versus Alternative Hypotheses......Page 716
Set 3: Hypotheses for interaction......Page 717
IV. Test Computations......Page 718
V. Interpretation of the Test Results......Page 724
b) One or both main effects are significant, but the interaction is not significant......Page 728
c) A significant interaction is present with or without one or more of the main effects being significant......Page 729
2. Evaluation of the homogeneity of variance assumption of the between-subjects factorial analysis of variance......Page 738
3. Computation of the power of the between-subjects factorial analysis of variance......Page 739
4. Measures of magnitude of treatment effect for the between-subjects factorial analysis of variance: Omega squared (Test 27g) and Cohen’s f index (Test 27h)......Page 741
1. Theoretical rationale underlying the between-subjects factorial analysis of variance......Page 745
2. Definitional equations for the between-subjects factorial analysis of variance......Page 746
3. Unequal sample sizes......Page 748
4. Final comments on the between-subjects factorial analysis of variance......Page 749
VIII. Additional Examples Illustrating the Use of the Between- Subjects Factorial Analysis of Variance......Page 750
1. Test 27i: The factorial analysis of variance for a mixed design......Page 751
2. Test 27j: The within-subjects factorial analysis of variance......Page 755
Endnotes......Page 761
Measures of Association/Correlation......Page 766
I. Hypothesis Evaluated with Test and Relevant Background Information......Page 767
II. Example......Page 769
III. Null versus Alternative Hypotheses......Page 770
IV. Test Computations......Page 771
V. Interpretation of the Test Results......Page 772
1. Derivation of a regression line......Page 775
2. The standard error of estimate......Page 784
3. Computation of a confidence interval for the value of the criterion variable......Page 785
4. Computation of a confidence interval for a Pearson product-moment correlation coefficient......Page 786
5. Test 28b: Test for evaluating the hypothesis that the true population correlation is a specific value other than zero......Page 788
6. Computation of power for the Pearson product-moment correlation coefficient......Page 789
7. Test 28c: Test for evaluating a hypothesis on whether there is a significant difference between two independent correlatio......Page 790
8. Test 28d: Test for evaluating a hypothesis on whether k independent correlations are homogeneous......Page 792
9. Test 28e: Test for evaluating the null hypothesis H0 :   XZ =   YZ......Page 794
10. Tests for evaluating a hypothesis regarding one or more regression coefficients......Page 795
1. The definitional equation for the Pearson product-moment correlation coefficient......Page 798
2. Residuals......Page 799
3. Covariance......Page 800
4. The homoscedasticity assumption of the Pearson product-moment correlation coefficient......Page 801
5. The phi coefficient as a special case of the Pearson product-moment correlation coefficient......Page 802
6. Autocorrelation/serial correlation......Page 803
IX. Addendum......Page 807
1. Bivariate measures of correlation that are related to the Pearson-product moment correlation coefficient......Page 808
2. Multiple regression analysis......Page 818
3. Additional multivariate procedures involving correlational analysis......Page 831
4. Meta-analysis and related topics......Page 840
References......Page 859
Endnotes......Page 862
I. Hypothesis Evaluated with Test and Relevant Background Information......Page 870
III. Null versus Alternative Hypotheses......Page 872
IV. Test Computations......Page 873
V. Interpretation of the Test Results......Page 874
1. Tie correction for Spearman’s rank-order correlation coefficient......Page 876
2. Spearman’s rank-order correlation coefficient as a special case of the Pearson product-moment correlation coefficient......Page 878
3. Regression analysis and Spearman’s rank-order correlation coefficient......Page 879
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......Page 880
2. Power efficiency of Spearman’s rank-order correlation coefficient......Page 883
References......Page 884
Endnotes......Page 885
I. Hypothesis Evaluated with Test and Relevant Background Information......Page 887
II. Example......Page 888
III. Null versus Alternative Hypotheses......Page 889
IV. Test Computations......Page 890
V. Interpretation of the Test Results......Page 892
1. Tie correction for Kendall’s tau......Page 895
4. Sources for computing a confidence interval for Kendall’s tau......Page 897
VIII. Additional Examples Illustrating the Use of Kendall’s Tau......Page 898
Endnotes......Page 899
I. Hypothesis Evaluated with Test and Relevant Background Information......Page 901
III. Null versus Alternative Hypotheses......Page 902
IV. Test Computations......Page 903
V. Interpretation of the Test Results......Page 904
1. Tie correction for Kendall’s coefficient of concordance......Page 905
1. Relationship between Kendall’s coefficient of concordance and Spearman’s rank-order correlation coefficient......Page 907
2. Relationship between Kendall’s coefficient of concordance and the Friedman two-way analysis of variance by ranks......Page 908
VIII. Additional Examples Illustrating the Use of Kendall’s Coefficient of Concordance......Page 910
Endnotes......Page 911
I. Hypothesis Evaluated with Test and Relevant Background Information......Page 913
II. Example......Page 914
III. Null versus Alternative Hypotheses......Page 915
IV. Test Computations......Page 916
V. Interpretation of the Test Results......Page 919
1. The computation of a confidence interval for the value of Goodman and Kruskal’s gamma......Page 920
3. Sources for computing a partial correlation coefficient for Goodman and Kruskal’s gamma......Page 921
VIII. Additional Examples Illustrating the Use of Goodman and Kruskal’s Gamma......Page 922
Endnotes......Page 924
Acknowledgments and Sources for Tables in Appendix......Page 926