A monte carlo investigation of a statistic for a bivariate missing data problem |
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Authors: | R.F. Woolson J.D. Leeper J.W.L. Cole W.R. Clarke |
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Affiliation: | Department of Preventive Medicine and Environmental Health , University of Iowa , Iowa City, Iowa |
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Abstract: | Testing the equal means hypothesis of a bivariate normal distribution with homoscedastic varlates when the data are incomplete is considered. If the correlational parameter, ρ, is known, the well-known theory of the general linear model is easily employed to construct the likelihood ratio test for the two sided alternative. A statistic, T, for the case of ρ unknown is proposed by direct analogy to the likelihood ratio statistic when ρ is known. The null and nonnull distribution of T is investigated by Monte Carlo techniques. It is concluded that T may be compared to the conventional t distribution for testing the null hypothesis and that this procedure results in a substantial increase in power-efficiency over the procedure based on the paired t test which ignores the incomplete data. A Monte Carlo comparison to two statistics proposed by Lin and Stivers (1974) suggests that the test based on T is more conservative than either of their statistics. |
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Keywords: | bivariate normal distribution t statistics likelihood ratio tests Monte Carlo methods missing values |
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