TukeyHSD
Compute Tukey Honest Significant Differences
Create a set of confidence intervals on the differences between the means of the levels of a factor with the specified familywise probability of coverage. The intervals are based on the Studentized range statistic, Tukey's ‘Honest Significant Difference’ method.
Usage
TukeyHSD(x, which, ordered = FALSE, conf.level = 0.95, ...)
Arguments
 x
 A fitted model object, usually an
aov
fit.  which
 A character vector listing terms in the fitted model for which the intervals should be calculated. Defaults to all the terms.
 ordered
 A logical value indicating if the levels of the factor
should be ordered according to increasing average in the sample
before taking differences. If
ordered
is true then the calculated differences in the means will all be positive. The significant differences will be those for which thelwr
end point is positive.  conf.level
 A numeric value between zero and one giving the familywise confidence level to use.
 ...
 Optional additional arguments. None are used at present.
Details
This is a generic function: the description here applies to the method
for fits of class "aov"
.
When comparing the means for the levels of a factor in an analysis of
variance, a simple comparison using ttests will inflate the
probability of declaring a significant difference when it is not in
fact present. This because the intervals are calculated with a
given coverage probability for each interval but the interpretation of
the coverage is usually with respect to the entire family of
intervals.
John Tukey introduced intervals based on the range of the sample means rather than the individual differences. The intervals returned by this function are based on this Studentized range statistics.
The intervals constructed in this way would only apply exactly to balanced designs where there are the same number of observations made at each level of the factor. This function incorporates an adjustment for sample size that produces sensible intervals for mildly unbalanced designs.
If which
specifies nonfactor terms these will be dropped with
a warning: if no terms are left this is an error.
Value

A list of class
c("multicomp", "TukeyHSD")
,
with one component for each term requested in which
.
Each component is a matrix with columns diff
giving the
difference in the observed means, lwr
giving the lower
end point of the interval, upr
giving the upper end point
and p adj
giving the pvalue after adjustment for the multiple
comparisons.There are print
and plot
methods for class
"TukeyHSD"
. The plot
method does not accept
xlab
, ylab
or main
arguments and creates its own
values for each plot.
References
Miller, R. G. (1981) Simultaneous Statistical Inference. Springer.
Yandell, B. S. (1997) Practical Data Analysis for Designed Experiments. Chapman & Hall.
See Also
aov
, qtukey
, model.tables
,
glht
in package \href{https://CRAN.Rproject.org/package=#1}{\pkg{#1}}multcompmultcomp.
Examples
library(stats)
require(graphics)
summary(fm1 < aov(breaks ~ wool + tension, data = warpbreaks))
TukeyHSD(fm1, "tension", ordered = TRUE)
plot(TukeyHSD(fm1, "tension"))