Alternative ranked set sampling protocols for the sign test

In this paper we investigate the effects of different ranked set sampling protocols on the sign test statistic. Sampling protocols considered include sequential, mid-range and fixed sampling designs. We show that in all of these sampling protocols the introduction of any correlation structure on the quantified observations leads to a reduction in the Pitman efficiency of the sign test. In the fixed sampling protocol, design optimality is achieved when only the middle observation is quantified from each set.