Multiple Comparison Procedures - Analysis of Variance Designs - page 130

satscore

Tukev HSD

Subset for alpha = 0.05

months of
study

N 1 2 3 4

Means alone in a
homogeneous subset
differ significantly
from all other means.

zero months
two months
four months
six months
eight months
Sig.

7
7
7
7
7

412.8571

474.2857

552.8571

614.2857
622.8571
.992

These two means are in
the same homogeneous
subset-we therefore
know that they do not
differ significantly.

1.000 1.000 1.000

Means for groups in homogeneous subsets are displayed.

Figure 7.5 The Tukey results in homogeneous subsets.

Here is how to read the display. Means inside a column do not differ
from each other. Column 4 shows means of 614.2857 (for the six month
study group) and 622.8571 (for the eight month study group). Because
these means are in the same column, we know that the Tukey test indicated
that they are not significantly different. That is why the term homogeneous
subsets is used - the subsets are composed of groups whose means are
comparable. The other columns each show only a single mean. Thus,
there is no mean that is comparable to them - they are significantly
different from all of the other means.
Given such a structure, we can read the homogeneous output (using
more words than are needed to make everything explicit) from left to right
in the following way:

The zero month study group is in its own subset and has the low-
est mean; it has therefore scored significantly lower than all other
groups.
The two month study group is in its own subset and is therefore
significantly different from all other groups; that group has scored
significantly higher than the zero month study group but signifi-
cantly lower than the other groups.
The four month study group is in its own subset and is therefore
significantly different from all other groups; that group has scored
significantly higher than than the zero month and two month study
groups but significantly lower than the six month and eight month
study groups.
The six month and eight month study groups are together in a subset
and therefore do not differ; however, those two groups scored higher
than all of the other groups.

The homogeneous subset display summarizes the more complete
information in the Multiple Comparisons output shown in Figure 7.6.
The structure of Figure 7.6 is a very common sort of configuration that