Estimating and Testing Hypotheses about Means

1. Estimating and Testing Hypotheses about Means James G. Anderson, Ph.D. Purdue University

2. Estimating Means • SEM is usually used to estimate variances, covariances and regression weights • Example 13 demonstrates how to estimate and test hypotheses about means • The data are from Attg-yng.xls and Attg_old.xls

4. Analysis Properties Dialog Box • Check the box for Estimate means and intercepts. • The path diagram shows a means, variance pair of parameters for each exogenous variable. • When you choose Calculate Estimates from the Analyze Menu, AMOS will estimate two means, two variances and a covariance for each group.

5. Results • Chi Square = 4.588 • Df = 3 • Probability level = 0.205

6. Output • Means (Young subjects/old subjects) • Covariances (Young subjects/old subjects) • Variances (Young subjects/old subjects)

8. Results • Chi Square = 19.267 • Df = 5 • Probability level = 0.002

9. Conclusions • Hypothesis of equal variances and covariances is accepted • Hypothesis of equal means is rejected

10. Regression with an Explicit Intercept • SEM usually does not estimate the intercept for the linear equations • Example 14 demonstrates how to estimate intercepts • The data are from Warren5v.xls

12. Analysis Properties Dialog Box • Check the box for Estimate means and intercepts. • The path diagram shows a means, variance pair of parameters for each exogenous variable. • When you choose Calculate Estimates from the Analyze Menu, AMOS will estimate a mean for each predictor and the intercept for the linear equation.

13. Results • Sample Moments: • 4 sample means • 4 sample variances • 6 sample covariances • Df= 14 • Parameters to be Estimated: • 3 means • 3 variances • 3 covariances • 3 regression weights • 1 intercept • 1 error variance • Total = 14

14. Factor Analysis with Structured Means • SEM can not estimate the means of comm0on factors in a single-sample factor analysis • Example 15 demonstrates how to estimate differences in factor means across populations • The data are from Grnt_fem.sav and Grnt_mal.sav

16. Analysis Properties Dialog Box • Check the box for Estimate means and intercepts. • The path diagram shows a means, variance pair of parameters for each exogenous variable. • When you choose Calculate Estimates from the Analyze Menu, AMOS will estimate two means, two variances and a covariance for each group.

17. Procedure • Constrain the intercepts to be equal across groups • Right click on one of the observed variables (e.g., visperc) • Choose Object Properties • Click the Parameters Tab • Enter a Parameter Name in the intercept text box • Select All Groups so that the intercept is named the same in both groups • Continue in the same manner to give names to the five other intercepts

18. Procedures • Fix the factor means in one group at a constant. For example, fix the means of the boy’s spatial and verbal factors at 0. • Next assign names to the girls’ factor means

19. Results • Chi Square = 22.593 • Df = 24 • Probability level = 0. 544

20. Means for Girls