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CONFIDENCE
INTERVALS AND P-VALUES FOR WILLIAMS’ AND OTHER STEP-DOWN MULTIPLE COMPARISON
TESTS AGAINST CONTROL
Journal of Biopharmaceutical Statistics
2001, 11, 45-63
ABSTRACT
When single-step multiple comparison tests
against control, such as Dunnett’s test, are used, p-values and confidence
intervals can be reported. However, Williams’ test and other step-down
multiple comparison tests only provide results in terms of statistical
significance. In this paper, approximate confidence intervals are proposed for
some step-down multiple comparison tests and their coverage properties are
assessed by simulation; p-values are readily calculated. The proposed
simultaneous confidence intervals associated with Williams’ test, Dunnett’s
step-down test and the closed t test are all found to have good coverage,
typically between 94% and 96% for a nominal value of 95%. Thus practising
statisticians can now quote p-values for these tests and use simple confidence
intervals to aid interpretation of test results.
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