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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.
In statistics, the Tukey–Duckworth test is a two-sample location test – a statistical test of whether one of two samples was significantly greater than the other. It was introduced by John Tukey, who aimed to answer a request by W. E. Duckworth for a test simple enough to be remembered and applied in the field without recourse to tables, let alone computers.
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]
Compact Letter Display (CLD) is a statistical method to clarify the output of multiple hypothesis testing when using the ANOVA and Tukey's range tests. CLD can also be applied following the Duncan's new multiple range test (which is similar to Tukey's range test).
For example, Tukey's range test and Duncan's new multiple range test (MRT), in which the sample x 1, ..., x n is a sample of means and q is the basic test-statistic, can be used as post-hoc analysis to test between which two groups means there is a significant difference (pairwise comparisons) after rejecting the null hypothesis that all groups ...
John Wilder Tukey (/ ˈ t uː k i /; June 16, 1915 – July 26, 2000) was an American mathematician and statistician, best known for the development of the fast Fourier Transform (FFT) algorithm and box plot. [2] The Tukey range test, the Tukey lambda distribution, the Tukey test of additivity, and the Teichmüller–Tukey lemma all bear his
In statistics, Tukey's test of additivity, [1] named for John Tukey, is an approach used in two-way ANOVA (regression analysis involving two qualitative factors) to assess whether the factor variables (categorical variables) are additively related to the expected value of the response variable. It can be applied when there are no replicated ...
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.