Robustness of the two independent samplest‐test when applied to ordinal scaled data

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Abstract
One may encounter the application of the two independent samplest‐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 thet‐test and one cannot appeal to large sample theory for validity. In this paper we report the results of an investigation of thet‐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 thet‐test in that the maximum actual level of significance is close to the declared level.

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