| Tukey {base} | R Documentation |
The Studentized Range Distribution
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 n_g =nranges is greater than one, R is
the maximum of n_g groups of nmeans
observations each.
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 |
nranges |
number of groups whose maximum range is considered. |
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)))