| Tukey {base} | R Documentation |
The Studentized Range Distribution
Description
Functions on 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.
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 |
nranges |
number of groups whose maximum range is considered. |
log, log.p |
logical; if TRUE, probabilities p are given as log(p). |
lower.tail |
logical; if TRUE (default), probabilities are
|
Details
If n_g =nranges is greater than one, R is
the maximum of n_g 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
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)))