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[1] The concept was later discussed by Newman (1939),[2] Keuls (1952),[3] and John Tukey in some unpublished notes.
[4] The value of the studentized range, most often represented by the variable q, can be defined based on a random sample x1, ..., xn from the N(0, 1) distribution of numbers, and another random variable s that is independent of all the xi, and νs2 has a χ2 distribution with ν degrees of freedom.
In applications, the xi are typically the means of samples each of size m, s2 is the pooled variance, and the degrees of freedom are ν = n(m − 1).
This complicates the problem of finding the probability distribution of any statistic that is studentized.