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The value q s is the sample's test statistic. (The notation | x | means the absolute value of x; the magnitude of x with the sign set to +, regardless of the original sign of x.) This q s test statistic can then be compared to a q value for the chosen significance level α from a table of the studentized range distribution.
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 ...
The Tukey-Kramer test outputs a q-statistic (lowercase), also called the studentized range statistic, which follows the studentized range distribution Topics referred to by the same term This disambiguation page lists articles associated with the title Q-statistic .
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;
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.
John Wilder Tukey (/ ˈ t uː k i / [2]; 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. [3]
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).
Because the number of means within a range changes with each successive pairwise comparison, the critical value of the q statistic also changes with each comparison, which makes the Neuman-Keuls method more lenient and hence more powerful than Tukey's range test. Thus, if a pairwise comparison was found to be significantly different using the ...