Using the Bernoulli trial approaches for detecting ordered alternatives

Background: Diagnostic problems in clinical trials are sometimes ordinal. For example, colon tumor staging was performed according to the TNM classification. However, clinical data are limited by markedly small sample sizes in some stage. Methods: We propose a distribution-free test for detecting ordered alternatives in a completely randomized design. The new statistic is based on summing all correctly (ascending) ordered samples. Results: The exact mean and variance of the null distribution are derived and it is shown that this distribution is asymptotically normal. Furthermore, we show using Monte Carlo simulation that the proposed test is a significant improvement over the Terpstra-Magel test. That is, power is decreased where the investigator falsely assumes an a priori ordering relationship. Conclusions: We conclude that these tests frequently detect an ordered trend when, in fact, one does not exist. However, the new test can reduce the error rate, at least not to the extent in which the Jonckheere-Terpstra test does.