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Example 2
Notice the word \format in the bottom line of the figure caption. Words that begin with
a backward slash, like
\format, are called text macros. Amos replaces text macros with
information about the currently displayed model. The text macro \format will be
replaced by the heading Model Specification, Unstandardized estimates, or
Standardized estimates, depending on which version of the path diagram is displayed.
Hypothesis Testing
The implied covariances are the best estimates of the population variances and
covariances under the null hypothesis. (The null hypothesis is that the parameters
required to have equal estimates are truly equal in the population.) As we know from
Example 1, the sample covariances are the best estimates obtained without making any
assumptions about the population values. A comparison of these two matrices is
relevant to the question of whether the null hypothesis is correct. If the null hypothesis
is correct, both the implied and sample covariances are maximum likelihood estimates
of the corresponding population values (although the implied covariances are better
estimates). Consequently, you would expect the two matrices to resemble each other.
On the other hand, if the null hypothesis is wrong, only the sample covariances are