Robustness of the two independent samples t-test when applied to ordinal scaled data

Abstract

One may encounter the application of the two independent samples t-test to ordinal scaled data (for example, data that assume only the values 0, 1, 2, 3) from small samples. This situation clearly violates the underlying normality assumption for the t-test and one cannot appeal to large sample theory for validity. In this paper we report the results of an investigation of the t-test's robustness when applied to data of this form for samples of sizes 5 to 20. Our approach consists of complete enumeration of the sampling distributions and comparison of actual levels of significance with the significance level expected if the data followed a normal distribution. We demonstrate under general conditions the robustness of the t-test in that the maximum actual level of significance is close to the declared level.