Tukey {stats} | R Documentation |
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
.
ptukey(q, nmeans, df, nranges = 1, lower.tail = TRUE, log.p = FALSE) qtukey(p, nmeans, df, nranges = 1, lower.tail = TRUE, log.p = FALSE)
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]. |
If ng =nranges
is greater than one, R is
the maximum of ng groups of nmeans
observations each.
ptukey
gives the distribution function and qtukey
its
inverse, the quantile function.
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.
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.
pnorm
and qnorm
for the corresponding
functions for the normal distribution.
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)))