Tukey {stats} | R Documentation |
Functions of the distribution of the studentized range, R/s
,
where R
is the range of a standard normal sample and
df \times 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 |
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
|
If n_g =
nranges
is greater than one, R
is
the maximum of n_g
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)))