 Structural Equation Modeling: Sample Size Parameters - Quick Tab

Select the Quick tab of the Structural Equation Modeling: Sample Size Parameters dialog box to access options to establish the basic parameters for analyzing sample size for structural equation modeling.

Fixed Parameters. The entries in the boxes under Fixed Parameters establish the fixed, or baseline, parameters for subsequent sample size calculations and graphs. Parameters that are not varied explicitly as the independent (X-axis) variables in a graphical analysis will be set equal to these values.

RMSEA (R). In the RMSEA (R) box, enter the population RMSEA. This coefficient is a "badness of fit" coefficient, i.e., small values represent good fit, large values bad fit. Rough guidelines suggested by MacCallum, Browne and Sugawara (1996) are that a good fit represented by a value of R less than or equal to .05.

Null RMSEA (R0). In the Null RMSEA (R0) box, enter the RMSEA specified under the null hypothesis. The traditional chi-square test of perfect fit in structural equation modeling is equivalent to a test that R = 0. A test of "close fit" involves testing the hypothesis that R is less than or equal to a "reasonable value" (like .05) representing good fit, as opposed to an alternative value (say, .08) representing mediocre fit. MacCallum, Browne and Sugawara (1996) provide power tables based on a test of "close fit" where R = .08, R0 = .05, and the null hypothesis is that R is less than or equal to R0. These authors also suggest a test of "not close fit," which involves testing the hypothesis that the fit coefficient is greater than a "reasonable value." Rejecting this hypothesis, in favor of the alternative that the value of R is small, constitutes strong evidence that a model fits very well. MacCallum, Browne and Sugawara (1996) provide power tables based on a test of "not close fit" where R = .01, R0 = .05, and the null hypothesis is that R is greater than or equal to R0.

Df. In the Df box, enter the number of degrees of freedom for the chi-square statistic.

Alpha. In the Alpha box, enter the type I error rate for the overall significance test.

Power Goal. In the Power Goal box, enter the minimum acceptable power, for which a minimum sample size is calculated. If the search for an acceptable sample size is successful, the actual power of the statistical test will be greater than or equal to this value.

Type of Hypothesis. The choice of option buttons under Type of Hypothesis determines the type of null hypothesis tested.

1-tailed (R <= R0). Select the 1-tailed (R <= R0) option button to test null and alternative hypotheses of the form

H0: R  ≤; R0  H1: R > R0

1-tailed (R >= R0). Select the 1-tailed (R >= R0) option button to test null and alternative hypotheses of the form

H0: R   R0  H1: R < R0

1-tailed (R = 0). Select the 1-tailed (R = 0) option button to test null and alternative hypotheses of the form

H0: R  = R0  H1: R > R0