Statistical Comparison of Eight Alternative Methods for the Analysis of Paired Sample Data with Applications

This paper presents and statistically compares eight alternative methods that could possibly be used in the analysis of matched or paired sample data, including situations in which the data being analyzed satisfy the usual assumptions of normality and continuity necessary for the use of parametric tests as well as when the data are numeric and non-numeric measurements on as low as the ordinal scale. It is shown that only the modified sign tests based on only the raw observations or their assigned ranks may be used with non numeric measurement on the ordinal scale. If the ordinary sign test, the Wilcoxon signed rank sum test and the modified sign tests can be equally used in data analysis, then it is shown that the modified sign tests are more efficient and hence more powerful than the ordinary sign tests because the two test statistics are intrinsically and structurally modified for the possible presence of tied observations between the sampled populations for both using raw and simulated data. Of all the non-parametric methods presented, the modified Wilcoxon’s signed rank sum test when applicable is the most efficient and powerful, followed in this order by the modified sign test by ranks and the modified sign test based on only raw scores for raw data while using simulation, modified sign test by ranks is the most efficient and powerful, followed in this order by modified Wilcoxon’s signed rank sum test and modified sign test. Each of the non-parametric methods presented can be easily modified and re-specified for use with one sample data by simply re-designating the observations from one of the sampled populations to correspond with a hypothesized value of some measure of central tendency. The methods are illustrated with some raw data as well as simulated data and their relative performances compared.