## Abstract

An exact solution is given for the Behrens-Fisher distribution under the independent normal model. The cumulative distribution function (cdf) and the probability density function (pdf) are expressed as infinite series of non-central t-distributions cdfs and pdfs, respectively. It is then observed that if the means are equal the distribution depends only on the ratio of the two population variances and the sample sizes. When the means are not equal, the distribution depends on the difference of the two means, the two population variances, and the two sample sizes. Methods are given for using the exact distribution to obtain an estimated confidence interval and an estimated * p * -value.

Original language | American English |
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State | Published - Apr 24 2015 |

## Keywords

- Comparing two population means
- Confidence interval
- Welsh’s approximation
- p-value

## DC Disciplines

- Statistical Methodology