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 FACTOREstimateSECRProb. Spatial-1.0660.881-1.2090.226 Verbal0.9560.5211.8360.066