Two-sample inference based on one-sample ranked set sample sign statistics

A two-sample sign test is developed for ranked set samples. It is shown that the testing procedure is distribution free but requires evaluation of the incomplete beta function. Efficiency and type I error, in general, depend on the measured observations and the ratio of cycle sites, It is shown that there is a substantial gain in the efficiency of the test even when there are ranking errors. On the other hand, the type I error is inflated for imperfect ranking. The proposed test is superior to the two-sample Mann-Whitney-Wilcoxon ranked set sample test when the underlying probability model has heavy and long tail distribution, and the number of quantified observations in each cycle is small. We provide a simple way to implement the procedure.