On Neutral Responses (Zeros) in the Sign Test and Ties in the Wilcoxon–Mann–Whitney Test

An alternative treatment of neutral responses in the sign test is proposed that makes explicit use of the probability of a neutral response in the hypotheses being tested. It permits a more conservative (liberal) interpretation of neutral responses in the context of a test with good power properties for the hypotheses chosen. The extension of this formulation to treating ties in the Wilcoxon–Mann–Whitney problem setting is also discussed.