Ing-Haur Liu

Date of Award


Degree Type


Degree Name

Master of Science (MS)


Mathematics and Statistics

First Advisor

Ronald V. Canfield


Comparison of the means of two normal populations is a simpler problem when the variance (if unknown) are assumed to be equal than it is when they are not equal. The main concern of this report is the latter case also called the Behrens [4] - Fisher [5] problem.

In this report the solutions proposed by Behrens-Fisher, Scheffe [10], Welch [12], Banerjee [3] and Hajek [8], will be described and compared. To this problem Scheffe proposed a solution which has the advantage that no special table is necessary for its use, since the variate has an exact "Student's t" distribution. It may therefore be used for large sample sizes, but Welch's method will presumably give shorter intervals for very small sample sizes, where the loss of efficiency of Scheffe's statistic is greatest [9].

A Monte Carlo study was undertaken to compare these methods for large and small sample sizes. The results are reported in the Conclusion.

The main objective of this report is to present the efficient solutions to the reader who is familiar with statistical methods but not with theories.