Experimental evaluation of the efficiencies of certain non- parametric statistics

The purpose of this thesis is the determination of the efficiency of a particular small sample of observations and to gain therefrom an insight into the approximate efficiency of these rank order tests for small samples when the population means of the two groups differ by fixed amounts. This problem will be approached experimentally because all attempts to use mathematics in the solution have thus far been held at an impasse because of the difficulties encountered in the integration of portions of the expression which result when the various consideration and relationships involved in the problem are expressed in mathematical terms.

In the analysis of the results of this experiment, the 10% level will be considered as the level of significance in the computation of the efficiency since the sample size selected does lend itself to the use of the 5% level of significance. The reader may possibly wish to consider half of the efficiency at the 10% level of significance as roughly indicative of what the efficiency at the 5% level would be. The use of the 10% level of significance in non-parametric tests does seem unrealistic, because, in general, non-parametric statistics tend to be more conservative than parametric statistics. In case non-parametric methods are applied to samples from a population which is normally distributed, the conservativistic tendencies of non-parametric inference validate the use of the higher significance level.

The results of this experiment should prove helpful in the setting up of non-parametric quality control systems for such activities as subjective testing between a control group and a group receiving some particular treatment, the effects of which cannot be measured in any definite units.

In addition to information of a general nature concerning these tests, this thesis also hopes to provide relatively concrete information about the particular test in which three observations are taken from each group. Some insight into the efficiency of these tests for this particular sample size is of interest because in industrial applications of non-parametric quality control limits, it is frequently possible to fix the sample size.