On a Proposed Test Statistic for Testing Equality of Two Means Under Unequal Population Variances
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Date
2017-04-30
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Publisher
Faculty of Humanities, Umaru Musa Yar'Adua University, Katsina, Nigeria
Abstract
In this paper, we propose a test statistic for testing equality of two independent sample means for unequal variances. When variances differ, the pooled sample variance is inadequate as a single value for the variances. This problem is commonly known as the Behrens-Fisher problem. Instead, the sample harmonic mean of variances is proposed, examined and found to represent the unequal variances better. The distribution of this statistic which is known to be generalized Beta is further approximated by the chi-square distribution with the degrees of freedom related to that of the degrees of freedom of the chi-square distribution of the pooled sample variance. Consequently, it is used to replace the pooled sample variance in the resulting proposed t-test. An application of the test statistic using real-life data is provided.
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Keywords
Harmonic mean of variances, ordered alternative, variance heterogeneity, Chi-square distribution, modified t-test statistic
Citation
Abidoye, A. O., Sanni, O. O. M., Ikoba, N. A. and Job, O. (2017). On a Proposed Test Statistic for Testing Equality of Two Means Under Unequal Population Variances. Taguwa Journal of Humanities, 8 (1), 152-158.