One of the most difficult problems occurring with stepwise
multiple test procedures for a set of two-sided hypotheses is the control of
direc-tional errors if rejection of a hypothesis is accomplished with a
directional decision. In this paper we generalize a result for so-called
step-down procedures derived by Shaffer to a large class of stepwise or closed
multiple test procedures. In a unifying way we obtain results for a large class
of order statistics procedures including step-down as well as step-up
procedures (Hochberg, Rom), but also a procedure of Hommel based on critical
values derived by Simes. Our method of proof is also applicable in situations
where directional decisions are mainly based on conditionally independent
$t$-statistics. A closed $F$-test procedure applicable in regression models
with orthogonal design, the modified $S$-method of Scheffé applicable in
the Analysis of Variance and Fisher’s LSD-test for the comparison of
three means will be considered in more detail.
Publié le : 1999-03-14
Classification:
Closed multiple test procedure,
closure principle,
directional error,
F-test,
familywise error rate,
multiple comparisons,
multiple hypotheses testing,
multiple level of significance,
step-down procedure,
step-up procedure,
stepwise multiple test procedure,
totally positive of order 3,
type III error,
unimodality,
variation diminishing property,
62J15,
62F03,
62C99,
62F07
@article{1018031111,
author = {Finner, H.},
title = {Stepwise multiple test procedures and control of directional
errors},
journal = {Ann. Statist.},
volume = {27},
number = {4},
year = {1999},
pages = { 274-289},
language = {en},
url = {http://dml.mathdoc.fr/item/1018031111}
}
Finner, H. Stepwise multiple test procedures and control of directional
errors. Ann. Statist., Tome 27 (1999) no. 4, pp. 274-289. http://gdmltest.u-ga.fr/item/1018031111/