In this paper we present a first general proof of Tukey's (1953) conjecture concerning the extension of the Tukey multiple comparisons procedure to the case of unequal sample sizes, thereby proving that the so-called Tukey-Kramer procedure is conservative in all cases. Also a brief history of the conjecture is given and some extensions and further problems concerning the procedure are discussed.
@article{1176346392,
author = {Hayter, Anthony J.},
title = {A Proof of the Conjecture that the Tukey-Kramer Multiple Comparisons Procedure is Conservative},
journal = {Ann. Statist.},
volume = {12},
number = {1},
year = {1984},
pages = { 61-75},
language = {en},
url = {http://dml.mathdoc.fr/item/1176346392}
}
Hayter, Anthony J. A Proof of the Conjecture that the Tukey-Kramer Multiple Comparisons Procedure is Conservative. Ann. Statist., Tome 12 (1984) no. 1, pp. 61-75. http://gdmltest.u-ga.fr/item/1176346392/