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Biometrika 1974 61(2):325-334; doi:10.1093/biomet/61.2.325
© 1974 by Biometrika Trust
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On difference of means with incomplete data

PI-ERH LIN and LAWRENCE E. STIVERS

Department of Statistics, The Florida State University Tallahassee

An estimate of the difference of means is obtained when sampling from a bivariate normal distribution with variances {sigma}21 and {sigma}22 and correlation p, where some observations on either of the variables are missing. It is shown that this estimate has desirable properties. In this paper a test of the hypothesis of the equality of means is also considered. The above estimate is adopted and three new statistics based on the difference of sample means are proposed for the test. Their empirical powers are computed for different values of p and {sigma}21/{sigma}22.

Key Words: Asymptotic efficiency • Conservative test • Empirical powers • Likelihood ratio test • Maximum likelihood estimate • Missing data • Preferred test • Probabilities of type I error • Unbiased-ness • Weak consistency • Welch approximate test


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