Despite a plethora of asymptotic and small samples Monte Carlo studies on the failure of the rank transform in designed experiments, Choi in 1998 published a paper praising the technique. The purpose of this reaction is to (a) examine Choi's literature review on the rank transform, (b) provide some “new” results on the rank transform, and (c) summarize the failures of the rank transform.
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References
1.
AkritasM. G. (1991) Limitations of the rank transform procedure: A study of repeated measures designs, Part I. Journal of the American Statistical Association, 86, 457–460.
2.
BlairR. C.HigcinsJ. J. (1985) A comparison of the power of the paired samples rank transform statistic to that of Wilcoxon's signed rank statistic. Journal of Educational Statistics, 10, 368–583.
3.
BlairR. C.SawilowskyS. S.HigginsJ. J. (1987) Limitations of the rank transform in factorial ANOVA. Communications in Statistics–Simulation and Computation, 16, 1133–1145.
4.
BradstreetT. E. (1997) A Monte Carlo study of Type I error rates for the two-sample Behrens-Fisher problem with and without rank transformation. Computational Statistics and Data Analysis, 25, 167–179.
5.
BrunnerE.DetteH. (1992) Rank procedures for the two factor mixed model. Journal of the American Statistical Association, 87, 884–888.
6.
ChoiY. H. (1994) Rank transform F statistic in a 2 × 2 factorial designJournal of the Korean Statistical Society, 23, 103–114.
7.
ChoiY. H. (1998) A study of the power of the rank transform test in a 23 factorial experiment. Communications in Statistics–Simulation and Computation, 27, 259–274.
8.
ConoverW. J. (1999) Practical nonparametric statistics. New York: Wiley.
9.
ConoverW. J.ImanR. (1976) On some alternative procedures using ranks for the analysis of experimental designs. Communications in Statistics–Simulation and Computation, 5, 1349–1368.
10.
ConoverW. J.ImanR. (1981) Rank transformations as a bridge between parametric and nonparametric statistics. American Statistician, 35, 124–129.
11.
FlignerM. A. (1981) Comment. American Statistician, 35, 131–132.
12.
HarwellM.SerlinR. C. (1989) A nonparametric test statistic for the general linear model. Journal of Educational Statistics, 14, 351–371.
13.
HarwellM.SerlinR. C. (1997) An empirical study of five multivariate tests for the single-factor repeated measures model. Communications in Statistics-Simulation and Computation, 26, 605–618.
14.
HeadrickT. (1997) Type I error and power of the rank transform analysis of covariance (ANCOVA) in a 3 × 4 factorial layout. Unpublished doctoral dissertation, Wayne State Univer., Detroit, MI.
15.
HigcinsJ. J.TashtoushS. (1994) An aligned rank transform for interaction. Nonlinear World, 1, 201–211.
16.
ImanR. L. (1974) A power study of a rank transform for the two-way classification model when interactions may be present. Canadian Journal of Statistics, 2, 227–239.
17.
ImanR. L.ConoverW. J. (1976) A comparison of several rank tests for the two-way layout. (SAND76–0631) Albuquerque, NM: Sandia Laboratories.
18.
JuddC. M.McClellandG. H.CulhaneS. E. (1995) DATA ANALYSIS: Continuing issues in the everyday analysis of psychological data. Annual Review of Psychology, 46, 433–465.
19.
KelleyD. L. (1994) The comparative power of several nonparametric alternatives to the analysis of variance test for interaction in a 2 × 2 × 2 layout. Unpublished doctoral dissertation, Wayne State Univer., Detroit, MI.
20.
KepnerJ. L.WackerlyD. D. (1996) On rank transformation techniques for balanced incomplete repeated-measures designs. Journal of the American Statistical Association, 91, 1619–1625.
21.
KeselmanH. J.CarriereK. C.LixL. M. (1995) Robust and powerful nonorthogonal analyses. Psychometrika, 60, 395–418.
22.
LemmerH. H. (1980) Some empirical results on the two-way analysis of variance by ranks. Communications in Statistics–Simulation and Computation, 14, 1427–1438.
23.
MansouriH.ChangG. H. (1995) A comparative study of some rank tests for interaction. Computational Statistics and Data Analysis, 19, 85–96.
24.
MardenJ. I.MuyotM. E. (1995) Rank tests for main and interaction effects in analysis of variance. Journal of the American Statistical Association, 90, 1388–1398.
25.
McKeanJ. W.VidmarT. J. (1994) A comparison of two rank-based methods for the analysis of linear models. The American Statistician, 48, 220–229.
26.
PavurR.NathR. (1986) Parametric versus rank transform procedures in the two-way factorial experiment: A comparative study. Journal of Statistical Computation and Simulation, 23, 231–240.
27.
SawilowskyS. S. (1985) Robust and power analysis of the 2 × 2 × 2 ANOVA, rank transformation, random normal scores, and expected normal scores transformation tests. Unpublished doctoral dissertation, Univer. of South Florida, Tampa, FL.
28.
SawilowskyS. S. (1986) Properties of the rank transformation statistic in factorial ANOVA. Paper presented at the annual meeting of the Florida Educational Research Association, Tampa, FL.
29.
SawilowskyS. S. (1988a) Failure of the random normals scores and expected normals scores transform tests for interactions in the 2 × 2 × 2 ANOVA. MWERA Researcher Abstracts-Abstracts of the 1988 annual meeting of the Mid-Western Educational Research Association, Chicago, IL. Kent, OH: Kent State Univer.
30.
SawilowskyS. S. (1988b) Limitations of the rank transform in analysis of variance. Annual meeting of the American Educational Research Association, SIG/Educational Statisticians, New Orleans, LA.
31.
SawilowskyS. S. (1989) Rank transformation: The bridge is falling down. Annual meeting of the American Educational Research Association, SIG/Educational Statisticians, San Francisco, CA.
32.
SawilowskyS. S.BlairR. C. (1986) An examination of the rank transformation in factorial ANOVA. Invited paper, annual meeting of the Florida Educational Research Association, Tampa, FL.
33.
SawilowskyS. S.BlairR. C. (1987a) An investigation of the Type I error and power properties of the rank transformation procedure in factorial ANOVA. [Educational Resources Information Center (ERIC): ED 322149].
34.
SawilowskyS. S.BlairR. C. (1987b) Properties of the rank transformation statistic. Annual meeting of the American Educational Research Association. Distinguished papers from the state and regional associations: Eleventh annual session, SIG/State and Regional Research Associations, Washington, DC.
35.
SawilowskyS. S.BlairR. C. (1987C) Type I error and power properties of the rank transform procedure in factorial ANOVA. Annual meeting of the American Educational Research Association, SIG/Educational Statisticians, Washington, DC.
36.
SawilowskyS. S.BlairR. C.HigginsJ. J. (1989) An investigation of the Type I error and power properties of the rank transform procedure in factorial ANOVA. Journal of Educational Statistics, 14, 255–267.
37.
SmithW. B. (1999) Comments from the editor-in-chief. Communications in Statistics-Simulation and Computation, 28(1), vii.
38.
ThompsonG. L. (1991) A unified approach to rank tests for multivariate and repeated measures designs. Journal of the American Statistical Association, 86, 410–419.
39.
ToothakerL. E.NewmanD. (1994) Nonparametric competitors to the two-way ANOVA. Journal of Educational and Behavioral Statistics, 19, 237–273.
40.
ZimmermanD. W. (1994) Simplified interaction tests for non-normal data in psychological research. British Journal of Mathematical and Statistical Psychology, 47, 327–335.
41.
ZimmermanD. W. (1996) A note on homogeneity of variance of scores and ranks. The Journal of Experimental Education, 64, 351–362.
