09 SOC 681Estimating and Testing Hypotheses about Means

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Estimating and Testing

Hypotheses about Means

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Estimating Means

• SEM is usually used to estimate

variances, covariances and regression weights

• Example 13 demonstrates how to estimate and test hypotheses about means

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,var_rec

recall1

,var_cue

cued1

cov_rc

Example 13: Model A

Homogenous covariance structures Attig (1983) young subjects

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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

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Results

• Chi Square = 4.588 • Df = 3

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Output

• Means (Young subjects/old subjects)

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mn_rec, var_rec

recall1

mn_cue, var_cue

cued1

cov_rc

Example 13: Model B

Invariant means and (co-)variances Attig (1983) young subjects

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Results

• Chi Square = 19.267 • Df = 5

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Conclusions

• Hypothesis of equal variances and covariances is accepted

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Regression with an Explicit

Intercept

• SEM usually does not estimate the intercept for the linear equations

• Example 14 demonstrates how to estimate intercepts

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value knowledge

performance

satisfaction

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error

1

Example 14

Job Performance of Farm Managers Regression with an explicit intercept

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Analysis Properties Dialog Box

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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

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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

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mn_s,

Example 15: Model A

Factor analysis with structured means

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Analysis Properties Dialog Box

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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

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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

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Results

• Chi Square = 22.593 • Df = 24

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Means for Girls

FACTOR Estimate SE CR Prob.

Spatial -1.066 0.881 -1.209 0.226