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Tukey's range test
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<p>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, is a single-step <a href="/facts/Multiple_comparison/lAItaL18">multiple comparison</a> procedure and <a href="/facts/Statistical_test/yv9RPF6U">statistical test</a>. It can be used to correctly interpret the <a href="/facts/Statistical_significance/PMxjdlAu">statistical significance</a> of the difference between means that have been selected for comparison because of their extreme values. </p><p>The method was initially developed and introduced by <a href="/facts/John_Tukey/2a5FbPWb">John Tukey</a> for use in <a href="/facts/Analysis_of_Variance/HHR2jkDk">Analysis of Variance</a> (ANOVA), and usually has only been taught in connection with ANOVA. However, the <a href="/facts/Studentized_range_distribution/SU7PMqgJ">studentized range distribution</a> used to determine the level of significance of the differences considered in Tukey's test has vastly broader application: It is useful for researchers who have searched their collected data for remarkable differences between groups, but then cannot validly determine <a href="/facts/P-value/InnYd1bz">how significant</a> their discovered stand-out difference is using standard statistical distributions used for other conventional statistical tests, for which the data must have been selected at random. Since when stand-out data is compared it was by definition <i>not</i> selected at random, but rather specifically chosen because it was extreme, it needs a different, stricter interpretation provided by the likely frequency and size of the <a href="/facts/Studentized_range_distribution/SU7PMqgJ">studentized range</a>; the modern practice of "<a href="/facts/Data_mining/AH53q5ac">data mining</a>" is an example where it is used. </p>