Estimating and Testing Hypotheses about Means

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Estimating and Testing Hypotheses about Means

• James G. Anderson, Ph.D.
• Purdue University

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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
• The data are from Attg-yng.xls and Attg_old.xls

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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 estimate two means, two
  variances and a covariance for each group.

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Results

• Chi Square 4.588
• Df 3
• Probability level 0.205

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Output

• Means (Young subjects/old subjects)
• Covariances (Young subjects/old subjects)
• Variances (Young subjects/old subjects)

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Results

• Chi Square 19.267
• Df 5
• Probability level 0.002

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Conclusions

• Hypothesis of equal variances and covariances is
  accepted
• Hypothesis of equal means is rejected

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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
• The data are from Warren5v.xls

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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 estimate a mean for each
  predictor and the intercept for the linear
  equation.

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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
• 1 error variance
• Total 14

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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
• The data are from Grnt_fem.sav and Grnt_mal.sav

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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 estimate two means, two
  variances and a covariance for each group.

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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
• Continue in the same manner to give names to the
  five other intercepts

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Procedures

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

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Results

• Chi Square 22.593
• Df 24
• Probability level 0. 544

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Means for Girls