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Estimating and Testing Hypotheses about Means
sample. So, taking both samples together, there are 10 sample moments. As for the
parameters to be estimated, there are seven of them, namely var_rec (the variance of
recall1), var_cue (the variance of cued1), cov_rc (the covariance between recall1 and
cued1), the means of recall1 among young and old people (2), and the means of cued1
among young and old people (2).
The number of degrees of freedom thus works out to be:
The chi-square statistic here is also the same as in Model B of Example 10. The
hypothesis that old people and young people share the same variances and covariance
would be accepted at any conventional significance level.
Here are the parameter estimates for the 40 young subjects:
Here are the estimates for the 40 old subjects:
Chi-square = 4.588
Degrees of freedom = 3
Probability level = 0.205
Computation of degrees of freedom (Default model)
Number of distinct sample moments: 10
Number of distinct parameters to be estimated: 7
Degrees of freedom (10 - 7): 3
Means: (young subjects - Default model)
Estimate S.E. C.R. P Label
recall1
10.250 .382 26.862 ***
cued1
11.700 .374 31.292 ***
Covariances: (young subjects - Default model)
Estimate S.E. C.R. P Label
recall1
<-->
cued1
4.056 .780 5.202 *** cov_rc
Variances: (young subjects - Default model)
Estimate S.E. C.R. P Label
recall1
5.678 .909 6.245 *** var_rec
cued1
5.452 .873 6.245 *** var_cue
Means: (old subjects - Default model)
Estimate S.E. C.R. P Label
recall1
8.675 .382 22.735 ***
cued1
9.575 .374 25.609 ***
Covariances: (old subjects - Default model)
Estimate S.E. C.R. P Label
recall1
<-->
cued1
4.056 .780 5.202 *** cov_rc
Variances: (old subjects - Default model)
Estimate S.E. C.R. P Label
recall1
5.678 .909 6.245 *** var_rec
cued1
5.452 .873 6.245 *** var_cue