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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.
The most common setting for Tukey's test of additivity is a two-way factorial analysis of variance (ANOVA) with one observation per cell. The response variable Y ij is observed in a table of cells with the rows indexed by i = 1,..., m and the columns indexed by j = 1,..., n. The rows and columns typically correspond to various types and levels ...
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.
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 ...
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).
The following table defines the possible outcomes when testing multiple null hypotheses. Suppose we have a number m of null hypotheses, denoted by: H 1, H 2, ..., H m. Using a statistical test, we reject the null hypothesis if the test is declared significant. We do not reject the null hypothesis if the test is non-significant.
where is the grand mean, is the additive main effect of level from the first factor (i-th row in the contingency table), is the additive main effect of level from the second factor (j-th column in the contingency table) and is the non-additive interaction effect of treatment (,) for samples =,..., from both factors (cell at row i and column j ...
[5] [6] Unlike Tukey's range test, the Newman–Keuls method uses different critical values for different pairs of mean comparisons. Thus, the procedure is more likely to reveal significant differences between group means and to commit type I errors by incorrectly rejecting a null hypothesis when it is true.