Studentized range

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 The concept was later presented by a number of actual students, Newman (1939) and Keuls (1952) and John Tukey in some unpublished notes.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.