ABSTRACT
The student who, at this point, may be familiar only with exploratory uses of statistics, such as the descriptive statistics of means, regression, and exploratory factor analysis, will now be introduced to a new way of using statistical models. The emphasis will be on testing hypothesized models in which certain “overidentifying” constraints on the model’s parameters have been imposed. The aim is to test whether models with these constraints fit data to which they are applied. The closest example to this in the statistics of means would be a test of the null hypothesis that a mean is equal to a specific value prespecified by the researcher. Exploring is when you simply estimate the mean of a variable without any constraints on it other than those minimally necessary to make the estimate possible. In regression we estimate regression coefficients without placing constraints on them. In exploratory factor analysis we estimate factor loadings and factor correlations, with only minimal constraints necessary to achieve unique values for them. Hypothesis testing involves prespecifying certain parameters and performing tests of these values. We will not dwell on hypothesis testing now, but it is important that the student keep this generally in mind as we begin considering structural equation models.
