For each element of x, compute the cumulative distribution function (CDF) of the studentized range distribution for k groups and df degrees of freedom. The size of p is the common size of x, k and df. A scalar input functions as a constant matrix of the same size as the other inputs.

The studentized range is the range of k independent standard normal variables divided by an independent sqrt (chi2 / df), where chi2 has a chi-square distribution with df degrees of freedom. It is the distribution behind Tukey’s honestly significant difference and the Tukey-Kramer multiple comparison procedure. k must be an integer of at least 2 and df positive, Inf included, which gives the range of k standard normals; otherwise p is NaN.

p = stdrcdf (x, k, df, "upper") computes the upper tail probability of the studentized range distribution at the values in x. Each tail is computed directly, so a small upper tail probability keeps its relative accuracy.

The distribution is evaluated by numerical integration, accurate to about 1e-13 relative to the tail probability for df up to 1e4, and to about 1e-8 for df of 1e8.

MATLAB has no public counterpart of this function.

Further information about the studentized range distribution can be found at https://en.wikipedia.org/wiki/Studentized_range_distribution

Input arguments must be double or single; integer, logical, and character arrays are rejected.

See also: stdrinv, stdrpdf, stdrrnd, stdrstat, multcompare

Source Code: stdrcdf