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CONFIDENCE INTERVALS AND P-VALUES FOR WILLIAMSí 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 Dunnettís test, are used, p-values and confidence intervals can be reported. However, Williamsí 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 Williamsí test, Dunnettís 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.