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Tukey's range test, also known as Tukey's test, Tukey method, Tukey's honest significance test, or Tukey's HSD (honestly significant difference) test, [1] is a single-step multiple comparison procedure and statistical test.
Hochberg's procedure is more powerful than Holm's. Nevertheless, while Holm’s is a closed testing procedure (and thus, like Bonferroni, has no restriction on the joint distribution of the test statistics), Hochberg’s is based on the Simes test, so it holds only under non-negative dependence.
Tukey’s Test (see also: Studentized Range Distribution) However, with the exception of Scheffès Method, these tests should be specified "a priori" despite being called "post-hoc" in conventional usage. For example, a difference between means could be significant with the Holm-Bonferroni method but not with the Turkey Test and vice versa.
Thus, The Hochberg procedure is uniformly more powerful than the Holm procedure. However, the Hochberg procedure requires the hypotheses to be independent or under certain forms of positive dependence, whereas Holm–Bonferroni can be applied without such assumptions. A similar step-up procedure is the Hommel procedure, which is uniformly more ...
The problem of multiple comparisons received increased attention in the 1950s with the work of statisticians such as Tukey and Scheffé. Over the ensuing decades, many procedures were developed to address the problem. In 1996, the first international conference on multiple comparison procedures took place in Tel Aviv. [3]
With respect to FWER control, the Bonferroni correction can be conservative if there are a large number of tests and/or the test statistics are positively correlated. [9] Multiple-testing corrections, including the Bonferroni procedure, increase the probability of Type II errors when null hypotheses are false, i.e., they reduce statistical power.
Tukey's test is either: Tukey's range test , also called Tukey method, Tukey's honest significance test, Tukey's HSD (Honestly Significant Difference) test Tukey's test of additivity
Its statistical distribution is the studentized range distribution, which is used for multiple comparison procedures, such as the single step procedure Tukey's range test, the Newman–Keuls method, and the Duncan's step down procedure, and establishing confidence intervals that are still valid after data snooping has occurred. [4]