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Factor Analysis with Structured Means
Here are the girls’ factor mean estimates from the text output:
The girls’ mean spatial ability has a critical ratio of –1.209 and is not significantly
different from 0 ( ). In other words, it is not significantly different from the
boys’ mean.
Turning to verbal ability, the girls’ mean is estimated 0.96 units above the boys’
mean. Verbal ability has a standard deviation of about 2.7 among boys and about 3.15
among girls. Thus, 0.96 verbal ability units is about one-third of a standard deviation
in either group. The difference between boys and girls approaches significance at the
0.05 level ( ).
Model B for Boys and Girls
In the discussion of Model A, we used critical ratios to carry out two tests of
significance: a test for sex differences in spatial ability and a test for sex differences in
verbal ability. We will now carry out a single test of the null hypothesis that there are
no sex differences, either in spatial ability or in verbal ability. To do this, we will repeat
the previous analysis with the additional constraint that boys and girls have the same
mean on spatial ability and on verbal ability. Since the boys’ means are already fixed
at 0, requiring the girls’ means to be the same as the boys’ means amounts to setting
the girls’ means to 0 also.
The girls’ factor means have already been named mn_s and mn_v. To fix the means at 0:
E From the menus, choose Analyze > Manage Models.
E In the Manage Models dialog box, type Model A in the Model Name text box,
E Leave the Parameter Constraints box empty.
Means: (Girls - Default model)
Estimate S.E. C.R. P Label
spatial
-1.066 .881 -1.209 .226 mn_s
verbal
.956 .521 1.836 .066 mn_v
p 0.226=
p 0.066=