title: Using the Bernoulli trial approaches for detecting ordered alternatives.
abstract: 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.
authors.affiliation: Department of Nursing, Chang Gung University of Science and Technology, Chiayi Campus, Chiayi, Taiwan 61363. howellchang@gmail.com.
authors.forename: Chia-Hao
authors.initials: CH
authors.lastname: Chang
authors.forename: Chih-Chien
authors.initials: CC
authors.lastname: Chin
authors.forename: Weichieh Wayne
authors.initials: WW
authors.lastname: Yu
authors.forename: Ying-Yu
authors.initials: YY
authors.lastname: Huang
mesh_terms: D000230:Adenocarcinoma / Q000145:classification / Q000473:pathology; D000465:Algorithms; D003110:Colonic Neoplasms / Q000145:classification / Q000473:pathology; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D006801:Humans; D009010:Monte Carlo Method; D009367:Neoplasm Staging / Q000379:methods; D018709:Statistics, Nonparametric