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 tha t 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 imp erfect ranking. The proposed test is superior to the two-sample Mann-Whitne y-Wilcoxon ranked set sample test when the underlying probability model has heavy and long tail distribution, and the number of quantified observation s in each cycle is small. We provide a simple way to implement the procedur e.