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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.
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;
Some common post hoc tests include: [6] [7] Holm-Bonferroni Procedure; Newman-Keuls; Rodger’s Method; Scheffé’s Method; 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.
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).
This procedure is often used as a post-hoc test whenever a significant difference between three or more sample means has been revealed by an analysis of variance (ANOVA). [1] The Newman–Keuls method is similar to Tukey's range test as both procedures use studentized range statistics.
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]
Tukey's procedure is only applicable for pairwise comparisons. It assumes independence of the observations being tested, as well as equal variation across observations ( homoscedasticity ).
The problem of multiple comparisons received increased attention in the 1950s with the work of statisticians such as Tukey and Scheffé. Over the ensuing decades, many procedures were developed to address the problem. In 1996, the first international conference on multiple comparison procedures took place in Tel Aviv. [3]