The Studentized Range Distribution

Usage

ptukey(q, nmeans, df, nranges = 1)
qtukey(p, nmeans, df, nranges = 1)

Arguments

q vector of quantiles.
p vector of probabilities.
nmeans sample size for range (same for each group).
df degrees of freedom for s (see below).
nranges number of groups whose maximum range is considered.

Description

These functions provide information about the distribution of the studentized range, R/s, where R is the range of a standard normal sample of size n and s^2 is independently distributed as chi-squared with df degrees of freedom, see pchisq.

If ng =nranges is greater than one, R is the maximum of ng groups of nmeans observations each.

Value

ptukey gives the distribution function and qtukey its inverse, the quantile function.

Note

A Legendre 16-point formula is used for the integral of ptukey. The computations are relatively expensive, especially for qtukey which uses a simple secant method for finding the inverse of ptukey. qtukey(..) will be accurate to the 4th decimal place.

References

Copenhaver, Margaret Diponzio & Holland, Burt S. (1988).
Multiple comparisons of simple effects in the two-way analysis of variance with fixed effects. Journal of Statistical Computation and Simulation, 30, 1-15.

See Also

pnorm and qnorm for the corresponding functions for the normal distribution.

Examples

system.time(curve(ptukey(x, nm=6, df=5), from=-1, to=8, n=101))
(ptt <- ptukey(0:10, 2, df= 5))
(qtt <- qtukey(.95, 2, df= 2:11))
## The precision may be not much more than about 8 digits:
summary(abs(.95 - ptukey(qtt,2, df = 2:11)))

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