A Monte Carlo Comparison of the Type I Error Rates of the Likelihood Ratio Chi-square Test Statistic and Hotelling's Two-sample T2 on Testing the Differences Between Group Means PDF Download

Author: John R. Boulet
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Languages : en
Pages : 0

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Book Description
The present paper demonstrates how Structural Equation Modelling (SEM) can be used to formulate a test of the difference in means between groups on a number of dependent variables. A Monte Carlo study compared the Type I error rates of the Likelihood Ratio (LR) Chi-square ($\chi\sp2$) statistic (SEM test criterion) and Hotelling's two-sample T$\sp2$ statistic (MANOVA test criterion) in detecting differences in means between two independent samples. Seventy-two conditions pertaining to average sample size ((n$\sb1$ + n$\sb2$)/2), extent of inequality of sample sizes (n$\sb1$:n$\sb2$), number of variables (p), and degree of inequality of variance-covariance matrices ($\Sigma\sb1$:$\Sigma\sb2$) were modelled. Empirical sampling distributions of the LR $\chi\sp2$ statistic and Hotelling's T$\sp2$ statistic consisted fo 2000 samples drawn from multivariate normal parent populations. The actual proportion of values that exceeded the nominal levels are presented. The results indicated that, in terms of maintaining Type I error rates that were close to the nominal levels, the LR $\chi\sp2$ statistic and Hotelling's T$\sp2$ statistic were comparable when $\Sigma\sb1$ = $\Sigma\sb2$ and (n$\sb1$ + n$\sb2$)/2:p was relatively large (i.e., 30:1). However, when $\Sigma\sb1$ = $\Sigma\sb2$ and (n$\sb1$ + n$\sb2$)/2:p was small (i.e., 10:1) Hotelling's T$\sp2$ statistic was preferred. When $\Sigma\sb{1} \not=\Sigma\sb2$ the LR $\chi\sp2$ statistic provided more appropriate Type I error rates under all of the simulated conditions. The results are related to earlier findings, and implications for the appropriate use of the SEM method of testing for group mean differences are noted.