Multiple comparisons by rerandomization tests

Abstract Classical methods of simultaneous inference cannot be used with rerandomization tests without risking excessive type I errors. This is illustrated by examples that show some published methods to be invalid for multiple comparisons. However, the use of stepwise procedures is shown to remain valid with rerandomization tests. In particular, this article advocates an adaptation of Begun and Gabriel's (1981) technique and provides the algorithm for using it.

[1]  Bert F. Green,et al.  A Practical Interactive Program for Randomization Tests of Location , 1977 .

[2]  K. R. Gabriel A Procedure for Testing the Homogeneity of All Sets of Means in Analysis of Variance , 1964 .

[3]  Chin-Fei Hsu,et al.  Evaluation of the Power of Rerandomization Tests, with Application to Weather Modification Experiments , 1983 .

[4]  E. Pitman Significance Tests Which May be Applied to Samples from Any Populations , 1937 .

[5]  Power Differences Between Pairwise Multiple Comparisons: Rejoinder , 1978 .

[6]  K. Ruben Gabriel,et al.  Closure of the Newman-Keuls Multiple Comparisons Procedure , 1981 .

[7]  Juliet Popper Shaffer Control of Directional Errors with Stagewise Multiple Test Procedures , 1980 .

[8]  W. J. Hall,et al.  Rerandomization Inference on Regression and Shift Effects: Computationally Feasible Methods , 1983 .

[9]  Rupert G. Miller Simultaneous Statistical Inference , 1966 .

[10]  B. L. Welch ON THE z-TEST IN RANDOMIZED BLOCKS AND LATIN SQUARES , 1937 .

[11]  D. Newman,et al.  THE DISTRIBUTION OF RANGE IN SAMPLES FROM A NORMAL POPULATION, EXPRESSED IN TERMS OF AN INDEPENDENT ESTIMATE OF STANDARD DEVIATION , 1939 .

[12]  K. Ruben Gabriel,et al.  Some statistical issues in weather experimentation , 1979 .

[13]  H. O. Hartley,et al.  Some recent developments in analysis of variance , 1955 .

[14]  M. Dwass Modified Randomization Tests for Nonparametric Hypotheses , 1957 .

[15]  E. J. G. Pitman,et al.  Significance Tests Which May be Applied to Samples from Any Populations. II. The Correlation Coefficient Test , 1937 .

[16]  K. Gabriel,et al.  A Study of the Powers of Several Methods of Multiple Comparisons , 1975 .

[17]  Karl Pearson,et al.  On the "z" Test , 1931 .

[18]  Oscar Kempthorne,et al.  THE RANDOMIZATION THEORY OF' EXPERIMENTAL INFERENCE* , 1955 .

[19]  O. L. Davies,et al.  The Design and Analysis of Experiments , 1953 .

[20]  Gerard E. Dallal,et al.  Double Dual Histograms , 1977 .

[21]  The Design and Analysis of Experiments. , 1955 .

[22]  T. A. Ryan,et al.  Significance tests for multiple comparison of proportions, variances, and other statistics. , 1960, Psychological bulletin.

[23]  T. A. Ryan Multiple comparison in psychological research. , 1959 .

[24]  R. A. Fisher,et al.  Design of Experiments , 1936 .

[25]  J. Shuster,et al.  Nonparametric Multiple Comparison Procedures , 1979 .

[26]  Philip H. Ramsey Power Differences between Pairwise Multiple Comparisons , 1978 .

[27]  K. Gabriel,et al.  SIMULTANEOUS TEST PROCEDURES-SOME THEORY OF MULTIPLE COMPARISONS' , 1969 .