A One–Sample Non-Parametric Location Test Statistic for Classified Normally Distributed Data

Abstract

Hypothesis testing about the location parameter of normal distribution is often tested using parametric test statistics including t and Z statistics. In this research, the rank version of the one-sample parametric test statistics was obtained, and it resulted into the proposed test statistic for testing the hypothesis about the location parameter when normally distributed data are ranked or classified. The test statistic is the average rank of the first p observations closest to the hypothesized mean value. Monte Carlo experiments were conducted at eight (8) levels of sample sizes to ascertain the distribution of the proposed statistic, investigate its type 1 error and power rates, and examine its agreement with both existing parametric and non-parametric equivalent test statistics. The proposed test statistic is symmetric, and the values of p at which its type 1 error rate is not different from the pre-selected levels of significance were obtained, as well as their power rates and measures of agreement. The power and measures of agreement of the proposed statistic are better than that of the Sign test and compete favorably with that of the Wilcoxon Signed Rank test. A numerical example was used to illustrate the usage of the proposed statistic.