Summary
For testing the significance of the difference between the unknown means of two normal populations having different unknown variances, we have the known Fisher-Behren’s-Welch test statistic. Several expressions for the distribution of this test statistic are available, and this paper is yet another attempt in the same direction. However, the expression given here appears to be, perhaps, more elegant and straight-forward than the ones available at present.
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References
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Ray, W. D. andPitman, A. E.N.T.: An exact distribution of the Fisher-Behren’s-Welch statistic for testing the difference between the means of two normal populations with unknown variances. J. Roy. Statist. Soc. B23, 377 (1961).
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Kabe, D.G. On the exact distribution of the Fisher-Behren’-Welch statistic. Metrika 10, 13–15 (1966). https://doi.org/10.1007/BF02613414
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DOI: https://doi.org/10.1007/BF02613414