A monte carlo investigation of a statistic for a bivariate missing data problem

R. F. Woolson, J. D. Leeper, J. W.L. Cole, W. R. Clarke

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

Testing the equal means hypothesis of a bivariate normal distribution with homoscedastic variates when the data are incomplete is considered. If the correlational parameter, p, 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 p unknown is proposed by direct analogy to the likelihood ratio statistic when p 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.

Original languageEnglish
Pages (from-to)681-688
Number of pages8
JournalCommunications in Statistics - Theory and Methods
Volume5
Issue number7
DOIs
StatePublished - Jan 1 1976

Keywords

  • Monte Carlo methods
  • bivariate normal distribution
  • likelihood ratio tests
  • missing values
  • t statistics:

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