Studentized Range (Paperback)

PMHigh Quality Content by WIKIPEDIA articles! In statistics, the studentized range computed from a list x1, ..., xn of numbers is frac{max{,x_1,dots,x_n,} - min{,x_1,dots,x_n,}}{s}, where s^2 = frac{1}{n - 1}sum_{i=1}^n (x_i - overline{x})^2, is the sample variance and overline{x} = frac{x_1 + cdots + x_n}{n} is the sample mean. Generally, studentized means adjusted by dividing by an estimate of a population standard deviation; see also studentized residual. The concept is named after William Sealey Gosset, who wrote under the pseudonym "Student". The fact that the variance is a sample variance rather than the population variance, and thus something that differs from one random sample to the next, is essential to the definition, and complicates the problem of finding the probability distribution of any statistic that is studentize