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This page is maintained by the Multiplicity
Advisory Board ( Alex
Dmitrienko). Parametric multiple tests
Parametric multiple tests make explicit assumptions
about the joint distribution of the individual test statistics
(for example, the test statistics follow a multivariate normal
or t distribution). These tests are more powerful than multiple
tests based on marginal p-values.
Papers and books
Dunnett, C.W. (1955). A multiple comparison
procedure for comparing several treatments with a control. Journal
of the American Statistical Association. 50, 1096-1121.
This paper introduced the famous Dunnett
test for performing multiplicity adjustments in problems involving
the comparison of multiple groups to a commo control.
Dunnett, C.W., Tamhane, A.C. (1992). A step-up
multiple test procedure. Journal of the American Statistical Association.
87, 162-170.
Dunnett, C.W., Tamhane, A.C. (1995). Step-up multiple testing
of parameters with unequally correlated estimates. Biometrics.
51, 217-227.
These papers discussed a step-up version
of the Dunnett test which is uniformly more powerful than the
standard Dunnett test. This test is also more powerful than the
step-down Dunnett test (Naik, 1975) when most of the mean treatment-control
differences in a dose-finding study are significantly different
from zero. Note that the step-down Dunnett test is analogous to
the Holm test whereas the step-up Dunnett test can be viewed as
a parametric version of the Hochberg test.
Naik, U.D. (1975). Some selection rules for
comparing p processes with a standard. Communications in Statistics.
Series A. 4, 519-535.
A step-down version of the Dunnett test was
discussed in this paper. This test serves as a parametric extension
of the Holm test.
Stefansson, G., Kim, W.-C., Hsu, J.C. (1988).
On confidence sets in multiple comparisons. Statistical Decision
Theory and Related Topics IV. Gupta, S.S., Berger, J.O. (Editors).
Academic Press, New York, 89-104.
Simultaneous confidence intervals for the
step-down Dunnett test (Naik, 1975) were proposed in this paper.
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