Date of Award
Master of Science (MS)
Mathematics and Statistics
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  - Fisher  problem.
In this report the solutions proposed by Behrens-Fisher, Scheffe , Welch , Banerjee  and Hajek , 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 .
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.
Liu, Ing-Haur, "Solutions of the Problem of Finding Confidence Intervals for the Two Normal Population with Unequal Variances" (1970). All Graduate Plan B and other Reports. 1132.
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