TukeyHSD                package:stats                R Documentation

Compute Tukey Honest Significant Differences

Description:

     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 'Honest Significant
     Difference' method.  There is a 'plot' method.

Usage:

     TukeyHSD(x, which, ordered = FALSE, conf.level = 0.95, ...)

Arguments:

       x: A fitted model object, usually an 'aov' fit.

   which: A list of 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 the 'lwr'
          end point is positive.

conf.level: A numeric value between zero and one giving the family-wise
          confidence level to use.

     ...: Optional additional arguments.  None are used at present.

Details:

     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.

Value:

     A list 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, and 'upr' giving the upper end point.

Author(s):

     Douglas Bates

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'

Examples:

     data(warpbreaks)
     summary(fm1 <- aov(breaks ~ wool + tension, data = warpbreaks))
     TukeyHSD(fm1, "tension", ordered = TRUE)
     plot(TukeyHSD(fm1, "tension"))

