Studentized Range Distribution Calculator

Compute the lower and upper tail probabilities of the studentized range Q for a given number of groups k and degrees of freedom nu. Useful for Tukey HSD critical values.

Input

The distribution of the statistic Q, the range of k sample means divided by a standard error with nu degrees of freedom. Enter q, the number of groups k, and the degrees of freedom nu.

Studentized range q

The statistic value q whose probability you want (0 or more)

Number of groups k

The number of groups compared. An integer of at least 2

Degrees of freedom nu

Degrees of freedom of the standard error estimate. A positive number

Result

Lower tail probability P(Q at most q) for q = 3.5, groups k = 3, df nu = 12

0.93000446

Lower tail P(Q at most q)

0.93000446

Upper tail 1 minus P(Q at most q)

0.06999554

Cumulative distribution P(Q at most q)

How it works

The studentized range Q divides the range of k sample means from normal populations with equal variance by an independent standard error estimate with nu degrees of freedom.
Its cumulative distribution is found by convolving the range distribution CDF with the scaling density via numerical integration.
In Tukey HSD multiple comparisons, the q whose upper tail probability equals the significance level is the critical value.
Enter the number of groups k as an integer of at least 2 and the degrees of freedom nu as a positive number.

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