In statistics, the studentized range, denoted q, is the difference between the largest and smallest data in a sample normalized by the sample standard deviation.
It is named after William Sealy Gosset (who wrote under the pseudonym "Student"), and was introduced by him in 1927.[1]
The concept was later discussed by Newman (1939),[2] Keuls (1952),[3] and John Tukey in some unpublished notes.
Its statistical distribution is 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.[4]
^Newman D. (1939). "The Distribution of Range in Samples from a Normal Population Expressed in Terms of an Independent Estimate of Standard Deviation". Biometrika. 31 (1–2): 20–30. doi:10.1093/biomet/31.1-2.20.
^Keuls M. (1952). "The Use of the "Studentized Range" in Connection with an Analysis of Variance". Euphytica. 1 (2): 112–122. doi:10.1007/bf01908269. S2CID 19365087.
^John A. Rafter (2002). "Multiple Comparison Methods for Means". SIAM Review. 44 (2): 259–278. Bibcode:2002SIAMR..44..259R. CiteSeerX 10.1.1.132.2976. doi:10.1137/s0036144501357233.
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