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Example 18
The parameter estimates and standard errors for young subjects are:
The parameter estimates and standard errors for old subjects are:
The estimates for the mean of vocab are 56.891 in the young population and 65.001 in
the old population. Notice that these are not the same as the sample means that would
have been obtained from the 10 young and 10 old subjects who took the vocab test. The
sample means of 58.5 and 62 are good estimates of the population means (the best that
can be had from the two samples of size 10), but the Amos estimates (56.891 and
65.001) have the advantage of using information in the v_short scores.
How much more accurate are the mean estimates that include the information in the
v_short scores? Some idea can be obtained by looking at estimated standard errors. For
the young subjects, the standard error for 56.891 shown above is about 1.765, whereas
the standard error of the sample mean, 58.5, is about 2.21. For the old subjects, the
standard error for 65.001 is about 2.167 while the standard error of the sample mean,
Means: (young subjects - Default model)
Estimate
S.E.
C.R. P Label
vocab
56.891
1.765
32.232 *** m1_yng
v_short
7.950
.627
12.673 *** par_4
Covariances: (young subjects - Default model)
Estimate
S.E. C.R. P Label
vocab
<-->
v_short
32.916
8.694 3.786 *** par_3
Correlations: (young subjects - Default model)
Estimate
vocab
<-->
v_short .920
Variances: (young subjects - Default model)
Estimate
S.E.
C.R. P Label
vocab
83.320
25.639
3.250 .001 par_7
v_short
15.347
3.476
4.416 *** par_8
Means: (old subjects - Default model)
Estimate
S.E.
C.R. P Label
vocab
65.001
2.167
29.992 *** m1_old
v_short
10.025
.526
19.073 *** par_6
Covariances: (old subjects - Default model)
Estimate
S.E. C.R. P Label
vocab
<-->
v_short
31.545
8.725 3.616 *** par_5
Correlations: (old subjects - Default model)
Estimate
vocab
<-->
v_short .896
Variances: (old subjects - Default model)
Estimate
S.E.
C.R. P Label
vocab
115.063
37.463
3.071 .002 par_9
v_short
10.774
2.440
4.416 *** par_10