Structural Equation Modeling: Power Calculation Parameters - Quick Tab

Select the Quick tab of the Structural Equation Modeling: Power Calculation Parameters dialog box to access options to enter baseline parameters for sample size calculations for structural equation modeling. These power calculations are based on the RMSEA index of fit. For a discussion of the use of the RMSEA in assessing power and sample size in structural equation modeling, see MacCallum, Browne, and Sugawara, (1996).

Fixed Parameters. The entries in the boxes under Fixed Parameters establish the fixed, or baseline, parameters for subsequent power 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.

N.  In the N box, enter N, the sample size.

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

Type of Hypothesis. The choice of option buttons in the Type of Hypothesis box 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