Tukey                 package:stats                 R Documentation

The Studentized Range Distribution

Description:

     Functions of the distribution of the studentized range, R/s, where
     R is the range of a standard normal sample and df*s^2 is
     independently distributed as chi-squared with df degrees of
     freedom, see 'pchisq'.

Usage:

     ptukey(q, nmeans, df, nranges = 1, lower.tail = TRUE, log.p = FALSE)
     qtukey(p, nmeans, df, nranges = 1, lower.tail = TRUE, log.p = FALSE)

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.

   log.p: logical; if TRUE, probabilities p are given as log(p).

lower.tail: logical; if TRUE (default), probabilities are P[X <= x],
          otherwise, P[X > x].

Details:

     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 and 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:

     if(interactive())
       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)))

