Quantiles of Tukey's Studentized Range Distribution

DESCRIPTION:

Computes a quantile of the studentized range random variable for use in multiple comparisons.

USAGE:

qtukey(p, k, df) 

REQUIRED ARGUMENTS:

p
the probability lying below the desired quantile.
k
a scalar, the number of treatments or quantities to be compared; missing values and Inf's are not accepted.
df
an integer, the error degrees of freedom. Inf is accepted, though if k>2, then df will be set to 1000. Missing values ( NA) are not accepted.

VALUE:

the pth quantile of the studentized range of k independent standard normal variates based on df degrees of freedom.

DETAILS:

This is the random variable as originally defined by Tukey; for example, qtukey(1-alpha, 2, df) equals sqrt(2)*qt(1-alpha/2, df). For many choices of the arguments, the function does a table lookup. For large values of k, df, and/or unusual values of p, the function obtains the critical point by numerical integration and a bisection method.

REFERENCES:

Hochberg, Y. and Tamhane, A. C.(1987). Multiple Comparison Procedures. Wiley, New York.

Hsu, Jason C. (1996). Multiple Comparisons: Theory and Methods. Chapman and Hall, London.

SEE ALSO:

, , , .

EXAMPLES:

qtukey(.95, 2, Inf)/sqrt(2) 
qtukey(.99, 50, 100)