# Studentized Range (Q) Distribution

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The Studentized range, Q, is a statistic due to Newman (1939) and Keuls (1952) that is used in multiple comparison methods. Q is defined as the range of means divided by the estimated standard error of the mean for a set of samples being compared. The estimated standard error of the mean for a group of samples is usually derived from analysis of variance.

__Technical Validation__

StatsDirect calculates tail areas and percentage points for a given number of samples and sample sizes (Copenhaver and Holland, 1988). These calculations are highly iterative therefore you may notice a delay during their computation. Other software and web sites might produce different results to StatsDirect; this is likely to be due to their use of less precise or more restricted algorithms (Gleason, 1999; Lund and Lund, 1983; Royston, 1987).