*Box Plots and Mosaic Plots* |

## Multiple Comparison Options

Box plots enable you to examine means in different groups.
Statistical questions you might have about the group means
include
- Which underlying group means are likely
to be different?
- Which group means are better than the mean of a
standard group?
- Which group means are statistically indistinguishable
from the best?

From the **Multiple Comparison Options** dialog, you can
select a multiple comparison of means test and a confidence level
for the test.
Multiple comparison tests enable you to infer differences between
means and also to construct simultaneous confidence intervals
for these differences.
All of the tests implemented in SAS/INSIGHT software are
constructed assuming that the displayed variables are independent
and normally distributed with identical variance. For details,
refer to Hsu (1996).
Each of the tests available in SAS/INSIGHT software is described below.
In the descriptions that follow,
*k* is the number of categories
(that is, the number of boxes in the box plot),
*n*_{i} is the number of observations for the *i*th category,
is the true mean for the *i*th category, is the
sample mean for the *i*th category, is the
total degrees of freedom, and is the root mean square
error, also known as the pooled standard deviation. Each test creates
a table showing
confidence intervals for the difference
, , *i* = 1 ... *k*.

**Figure 33.8:** Multiple Comparison Options

The **Pairwise ***t*-test is not a true simultaneous comparison
test, but rather uses a pairwise *t* test to provide confidence intervals
about the difference between two means. These intervals
have a half-width equal to . Although each confidence interval
was computed at the level, the probability that
all of your confidence intervals are correct *simultaneously*
is less than .The actual simultaneous confidence for the *t*-based intervals is
approximately . For example, for five groups the
actual simultaneous confidence for the *t*-based intervals is
approximately only 75%.
The **Tukey-Kramer** method is a true "multiple comparison" test,
appropriate when all pairwise comparisons are of interest; it is
the default test used.
The test is an exact -level test if the sample sizes are
the same, and it is slightly conservative for unequal sample sizes.
The confidence interval around the point-estimate
has half-width . It is a common
convention to report the quantity as the Tukey-Kramer
quantile, rather than just *q*^{*}.
The **Pairwise Bonferroni** method is also appropriate when all
pairwise comparisons are of interest. It is conservative; that is,
Bonferroni tests performed at a nominal significance level of actually have a somewhat greater level of significance. The
Bonferroni method uses the *t* distribution, like the pairwise
*t* test, but returns smaller intervals with half-width
.Note that the *t* probability (, since this is a two-sided
test) is divided by the total number of pairwise comparisons
(*k*(*k*-1)/2). The Bonferroni test
produces wider confidence intervals than the Tukey-Kramer
test.
**Dunnett's Test with Control** is a two-sided multiple comparison
method used to
compare a set of categories to a control group. The quantile that
scales the confidence interval is usually denoted |*d*|. If the *i*th
confidence interval does not include zero, you may infer that the
*i*th group is significantly different from the control. A
control group may be a placebo or null treatment, or it may be a
standard treatment. While the interactive nature of SAS/INSIGHT
enables you to select any category to use as the basis of comparison in
Dunnett's test, you should select a category only if it truly is the
control group. To select a category, click on the corresponding
comparison circle.
**Hsu's Test for Best** can be used to screen out group means that
are statistically less than the (unknown) largest true mean. It
forms *nonsymmetric* confidence intervals around the difference
between the largest sample mean and each of the others. If an
interval does not properly contain zero in its interior, then you may
infer that the associated group is not among the best.
Similary, **Hsu's Test for Worst** can be used to screen out group
means that are statistically greater than the (unknown) smallest
true mean. If an interval does not properly contain zero in its
interior, then you may infer that the true mean of that group
is not equal to the (unknown) smallest true mean.

Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.