\Header{TukeyHSD}{Compute Tukey Honest Significant Differences}
\alias{plot.TukeyHSD}{TukeyHSD}
\alias{print.TukeyHSD}{TukeyHSD}
\methalias{TukeyHSD.aov}{TukeyHSD}
\keyword{models}{TukeyHSD}
\keyword{design}{TukeyHSD}
\begin{Description}\relax
Create a set of confidence intervals on the differences between the
means of the levels of a factor with the specified family-wise
probability of coverage.  The intervals are based on the Studentized
range statistic, Tukey's \sQuote{Honest Significant Difference}
method.  There is a \code{plot} method.
\end{Description}
\begin{Usage}
\begin{verbatim}
TukeyHSD(x, which, ordered = FALSE, conf.level = 0.95, ...)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{x}] A fitted model object, usually an \code{\Link{aov}} fit.
\item[\code{which}] A list of terms in the fitted model for which the
intervals should be calculated.  Defaults to all the terms.
\item[\code{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 \code{ordered} is true then
the calculated differences in the means will all be positive.  The
significant differences will be those for which the \code{lwr} end
point is positive.
\item[\code{conf.level}] A numeric value between zero and one giving the
family-wise confidence level to use.
\item[\code{...}] Optional additional arguments.  None are used at present.
\end{ldescription}
\end{Arguments}
\begin{Details}\relax
When comparing the means for the levels of a factor in an analysis of
variance, a simple comparison using t-tests 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.

Technically the intervals constructed in this way would only apply 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.
\end{Details}
\begin{Value}
A list with one component for each term requested in \code{which}.
Each component is a matrix with columns \code{diff} giving the
difference in the observed means, \code{lwr} giving the lower
end point of the interval, and \code{upr} giving the upper end point.
\end{Value}
\begin{Author}\relax
Douglas Bates
\end{Author}
\begin{References}\relax
Miller, R. G. (1981)
\emph{Simultaneous Statistical Inference}. Springer.

Yandell, B. S. (1997)
\emph{Practical Data Analysis for Designed Experiments}.
Chapman \& Hall.
\end{References}
\begin{SeeAlso}\relax
\code{\Link{aov}}, \code{\Link{qtukey}}, \code{\Link{model.tables}}
\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
data(warpbreaks)
summary(fm1 <- aov(breaks ~ wool + tension, data = warpbreaks))
TukeyHSD(fm1, "tension", ordered = TRUE)
plot(TukeyHSD(fm1, "tension"))
\end{ExampleCode}
\end{Examples}

