Combined Nonparametric Tests for the Social Sciences

The nonparametric framework is very often considered in the social sciences because the hypothesis of normality is generally not tenable. In this context, combined testing has been very useful for comparing means/medians, variability and for the location/scale problem. The aim of the paper is to see whether combined testing is useful also for general two-sample problems that arise in the social sciences. The framework of combined testing for the general two-sample problem is presented. Some tests are developed according to it. Size and power of the combined tests are investigated in a simulation study and compared to non combined tests. It is shown that the new tests compare favorably with the former ones. In particular, the new tests can be very useful when the practitioner, as very often happens when analyzing social data, has no clear idea on parent population distributions. An example of social experiment is discussed.