title: Confidence intervals and p-values for Williams' and other step-down multiple comparison tests against control.
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 practicing statisticians can now quote p-values for these tests and use simple confidence intervals to aid interpretation of test results.
authors.affiliation: Biostatistics and Data Management, Knoll Ltd Research and Development, Nottingham, United Kingdom.
authors.forename: E J
authors.initials: EJ
authors.lastname: Channon
authors.forename: D J
authors.initials: DJ
authors.lastname: McEntegart
mesh_terms: D003198:Computer Simulation; D016001:Confidence Intervals; D004305:Dose-Response Relationship, Drug; D016018:Least-Squares Analysis; D008956:Models, Chemical; D012107:Research Design / Q000706:statistics & numerical data*