That is not an ideal name for the independent variable, but neither I nor the study’s authors
have a better suggestion. Within each group of composite photographs were three male and
three female faces, but we will ignore gender for this example. (There were no significant
gender differences, and the overall test on group differences is not materially affected by
ignoring that variable.)
Langlois and Roggman presented different groups of subjects with composite faces and
asked them to rate the attractiveness of the faces on a 1–5 scale, where 5 represents “very at-
tractive.” The individual data points in their analysis were actually the means averaged across
raters for the six different composites in each condition. The data are given in Table 12.9.
These data are fictional, but they have been constructed to have the same mean and variance
as those reported by Langlois and Roggman, so the overall Fand the tests on trend will be
the same as those they reported.
A standard one-way analysis of variance on these data would produce the following
summary table:Source df SS MS F
Composite 4 2.1704 0.5426 3.13*
Error 25 4.3281 0.1731
Total 29 6.4985
*p , .05From the summary table it is apparent that there are significant differences among the five
groups, but it is not clear how these differences are manifested. One way to examine these
differences would be to plot the group means as a function of the number of individual pic-
tures that were averaged to create the composite. An important problem that arises if we
try to do this concerns the units on the abscissa. We could label the groups as “2, 4, 8, 16,
and 32,” on the grounds that these values correspond to the number of elements over which
the average was taken. However, it seems unlikely that rated attractiveness would increase
directly with those values. We might expect that a picture averaged over 32 items would be
more attractive than one averaged over 2 items, but I doubt that it would be 16 times more
attractive. But notice that each value of the independent variable is a power of 2. In other
words, the values of 2, 4, 8, 16, and 32 correspond to. (Put another way,
taking the of 2, 4, 8, 16, and 32 would give us 1, 2, 3, 4, and 5.) For purposes of ana-
lyzing these data, I am going to represent the groups with the numbers 1 to 5 and refer to
these as measuring the degree of the composite. (If you don’t like my approach, and there
is certainly room to disagree, be patient and we will soon see a solution using unequallylog 221 ,2^2 ,2^3 ,2^4 , and 2^5404 Chapter 12 Multiple Comparisons Among Treatment Means
Table 12.9 Data on rated attractiveness (from left to right the groups
represent averaging across 2, 4, 8, 16, or 32 faces)
Group 1 Group 2 Group 3 Group 4 Group 5
2.201 1.893 2.906 3.233 3.200
2.411 3.102 2.118 3.505 3.253
2.407 2.355 3.226 3.192 3.357
2.403 3.644 2.811 3.209 3.169
2.826 2.767 2.857 2.860 3.291
3.380 2.109 3.422 3.111 3.290
Mean 2.6047 2.6450 2.8900 3.1850 3.2600