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In statistics, the studentized range is the difference between the largest and smallest data in a sample measured in units of sample standard deviations. The studentized range, ''q'', is named for William Sealy Gosset (who wrote under the pseudonym "''Student''"), and was initially evoked by him (1927). The concept was later presented by a number of actual ''students'', Newman (1939) and Keuls (1952) and John Tukey in some unpublished notes. ''q'' is the basic statistic for 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. == Description == The value of the studentized range is most often represented by the variable ''q''. The studentized range computed from a list ''x''1, ..., ''x''''n'' of numbers is given by the formulas : where : is the sample variance, an unbiased estimator of the population variance and the square of the sample standard deviation ''s'', and : is the sample mean. The critical value of ''q'' is based on three factors: #α (the probability of rejecting a true null hypothesis) #''n'' (the number of observations or groups) #''v'' (the degrees of freedom used to estimate the sample variance) 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Studentized range」の詳細全文を読む スポンサード リンク
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