## 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 language | English |
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Pages (from-to) | 681-688 |

Number of pages | 8 |

Journal | Communications in Statistics - Theory and Methods |

Volume | 5 |

Issue number | 7 |

DOIs | |

State | Published - Jan 1 1976 |

## Keywords

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