Tukey {Devore5} | R Documentation |
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(x, which=seq(along = tabs), ordered=FALSE, conf.level=0.95, ...)
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.
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.
D. M. Bates
data(xmp10.01) fm1 <- aov(strength ~ type, data = xmp10.01) Tukey(fm1) Tukey(fm1, ord = TRUE, conf = 0.9)