Author : Mohamed Ismail
CoAuthors : Halperin, M., Lan, K. K. G., and Hamdy, M. I.
Source : Biometrika
Date of Publication : 06/1988
Abstract :
An approach to multiple comparisons defines the error control objective as assuring
with given probability that k or fewer out of N specified linear combinations of p means
are significant when an overall null hypothesis is true, or that k or fewer confidence
interval statements are incorrect. The case fc = 0 is basically the Scheffe (1953) method
except for the consideration of a specified set of N linear combinations rather than all
possible linear combinations. A theoretical result is obtained under normal theory and
we assume an infinite number of linear combinations with normalized coefficients, that
is the sum of squares is unity, uniformly distributed over the unit p-sphere. For a finite
number N of specified linear combinations the problem is reformulated in a way which
in principle would allow computation of the exact distributions required to provide
critical values. In general, the computations required are so complex that they are
impractical, but a Monte Carlo approach is straightforward.
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