Definition 1: Suppose that we take a sample of size n from each of k populations with the same normal distribution N(μ, σ) and suppose that x̄min is the smallest of these sample means and x̄max is the largest of these sample means, and suppose s2 is the pooled sample variance from these samples. Then the following random variable has a Studentized range distribution.
This distribution is related to the t distribution and is very useful especially in follow up testing for ANOVA such as Tukey’s HSD (see Unplanned Comparisons).
Tables of critical values for this distribution can be found in Studentized Range q Table.
Real Statistics Functions: The following functions are supplied by the Real Statistics Resource Pack
QDIST(q, k, df) = value at q of the studentized range distribution with k independent variables and df degrees of freedom
QINV(p, k, df, tails) = inverse of the studentized q distribution, i.e. the critical value for the studentized q range; tails = the number of tails and takes on the value 1 or 2 (default); QINV(p, k, df) has the value q such that QDIST(q, k, df) = p.
QCRIT(k, df, α, tails) = the critical value for the studentized q range based on the entries in the tables found in Studentized Range q Table, making a linear interpolation for entries between entries in the table; α is a number between 0 and 1 (default .05); tails = the number of tails and takes on the value 1 or 2 (default).
Note that theoretically QINV(p, k, df) = QCRIT(k, df, p), but whereas QCRIT does a table lookup, QINV makes a calculation of the critical value. Generally for values shown in the tables QCRIT is more accurate, while for values outside the table QINV is usually preferred.