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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. If the q s value is larger than the critical value q α obtained from the distribution, the two means are said to be significantly different at level α : 0 ≤ α ≤ 1 . {\displaystyle \ \alpha ...
The value of the studentized range, most often represented by the variable q, can be defined based on a random sample x 1, ..., x n from the N(0, 1) distribution of numbers, and another random variable s that is independent of all the x i, and νs 2 has a χ 2 distribution with ν degrees of freedom.
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 ...
For ->∞, a tabulation exists for an exact value of Q (see link). A word of caution is needed here: notations for Q and R are not the same throughout literature, where Q is sometimes denoted as the shortest significant interval, and R as the significant quantile for studentized range distribution (Duncan's 1955 paper uses both notations in ...
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 .
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 ...
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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.