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Example 15
Here are the boys’ estimates:
Girls have an estimated mean spatial ability of –1.07. We fixed the mean of boys’
spatial ability at 0. Thus, girls’ mean spatial ability is estimated to be 1.07 units below
boys’ mean spatial ability. This difference is not affected by the initial decision to fix
the boys’ mean at 0. If we had fixed the boys’ mean at 10.000, the girls’ mean would
have been estimated to be 8.934. If we had fixed the girls’ mean at 0, the boys’ mean
would have been estimated to be 1.07.
What unit is spatial ability expressed in? A difference of 1.07 verbal ability units
may be important or not, depending on the size of the unit. Since the regression weight
for regressing visperc on spatial ability is equal to 1, we can say that spatial ability is
expressed in the same units as scores on the visperc test. Of course, this is useful
information only if you happen to be familiar with the visperc test. There is another
approach to evaluating the mean difference of 1.07, which does not involve visperc. A
portion of the text output not reproduced here shows that spatial has an estimated
variance of 15.752 for boys, or a standard deviation of about 4.0. For girls, the variance
of spatial is estimated to be 21.188, so that its standard deviation is about 4.6. With
standard deviations this large, a difference of 1.07 would not be considered very large
for most purposes.
The statistical significance of the 1.07 unit difference between girls and boys is easy
to evaluate. Since the boys’ mean was fixed at 0, we need to ask only whether the girls’
mean differs significantly from 0.
0, 15.75
spatial
30.14
visperc
25.12
cubes
16.60
lozenges
16.22
wordmean
9.45
paragrap
18.26
sentence
0, 31.87
err_v
0, 15.31
err_c
0, 40.71
err_l
0, 2.35
err_p
0, 6.02
err_s
0, 20.33
err_w
0, 7.03
verbal
1.00
.56
1.37
1.00
1.28
2.21
1
1
1
1
1
1
6.98