Ordered categorical score vs. non-parametric tests or parametric tests, including cross-over design, using a combined binomial distributions as a model for the score.

by Ken-Ichi Adachi .

Abstract: Non-parametric methods of analysis are usually applied to ordered(ordinal) categorical data, rather than normal distribution-based parametric data, since the former data do not follow the normal distribution on which parametric methods are based. There seems to be, however, little evidence addressing whether the non-parametric method is preferable to the parametric method in such cases. In order to clarify this issue, the present study introduced the use of the numbers of successes(m) in each trial when using Bernoulli trials(n), which are generated by the binomial distribution as a model for such discrete ordered categorical data(the m-th score among 0 ~ n). Using this model and a fixed effect balanced cross-over design, the present Monte Carlo simulation revealed that the parametric method is preferable to the non-parametric one, with little inflation of type I error(a) rate(proportion) under the null hypothesis, and more power(=1-type II error(b)) compared to the parametric method under the alternative hypothesis. On the other hand, the non-parametric method resulted in an obvious under-estimation of the type I error under the null hypothesis, and less power compared to the parametric method under the alternative hypothesis, especially in the paired tests. This may lead to statistically non-significant results, even when there is a real difference.

Key Words: ordered(ordinal) categorical data; binomial model for the score; Monte Carlo simulation; fixed effect balanced 2x2 cross-over design; non-parametric methods; parametric method; type I error (alpha) rate(proportion); power

Ken-Ichi Adachi, ken1ada@yahoo.co.jp

Editor: Graf, R.G. , rgraf@sunstroke.sdsu.edu

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