Premium
Robustness of the two independent samples t ‐test when applied to ordinal scaled data
Author(s) -
Heeren Timothy,
D'Agostino Ralph
Publication year - 1987
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.4780060110
Subject(s) - ordinal data , statistics , robustness (evolution) , normality , mathematics , normality test , econometrics , computer science , statistical hypothesis testing , biochemistry , chemistry , gene
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.