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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.
Since the null hypothesis for Tukey's test states that all means being compared are from the same population (i.e. μ 1 = μ 2 = μ 3 = ... = μ k), the means should be normally distributed (according to the central limit theorem) with the same model standard deviation σ, estimated by the merged standard error, , for all the samples; its ...
Download as PDF; Printable version; In other projects ... Tukey's test is either: Tukey's range test, also called Tukey method, Tukey's honest ...
Tukey–Duckworth test: tests equality of two distributions by using ranks. Wald–Wolfowitz runs test: tests whether the elements of a sequence are mutually independent/random. Wilcoxon signed-rank test: tests whether matched pair samples are drawn from populations with different mean ranks.
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]
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] The Tukey range test, the Tukey lambda distribution, the Tukey test of additivity, and the Teichmüller–Tukey lemma all bear
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.
This means that if we test the null hypothesis that the center of a Gaussian scale mixture distribution is 0, say, then t n G (x) (x ≥ 0) is the infimum of all monotone nondecreasing functions u(x) ≥ 1/2, x ≥ 0 such that if the critical values of the test are u −1 (1 − α), then the significance level is at most α ≥ 1/2 for all ...