The Wilcoxon two-sample rank sum test (WMW test) is indeed maximally powered to detect proportional odds (PO) alternatives under the proportional odds assumption. Here's the detailed reasoning:

Key Connection to the Proportional Odds Model

The WMW test is structurally equivalent to the score test for the null hypothesis ( \beta_1 = 0 ) in a semiparametric proportional odds ordinal logisti...

Short answer Yes—if by “optimal” you mean locally (asymptotically) most powerful for contiguous alternatives within the natural semiparametric model—then the Wilcoxon–Mann–Whitney (WMW) test is optimal for proportional-odds (PO) alternatives. In the two-sample problem with a single binary covariate and a continuous outcome (no ties), the WMW statistic is exactly the efficient score test for β=0 in...

Short answer
Yes. In the two–sample problem with a continuous response the Wilcoxon-Mann-Whitney (WMW) rank–sum statistic is the efficient (hence locally most powerful) score test for the semiparametric proportional–odds (PO) model

 logit{P(Y ≤ y | X = x)} = α(y) + x β, x = 0,1, y ∈ ℝ, (1)

where α(·) is an arbitrary unknown function (the “baseline” cumulative-...

1. The WMW test is optimal for detecting a location shift when the two continuous random variables have logistic distributions.
2. The WMW test is a special case of the proportional odds ordinal logistic model...

Short answer
Yes—if we formulate the null and the alternative inside the semiparametric proportional-odds (PO) model the Wilcoxon–Mann–Whitney (WMW) statistic is the efficient (hence, asymptotically most powerful) test for a two–sample comparison. No other regular test—rank-based or not—can have larger first-order (Pitman) power against contiguous PO alternatives. Outside that model, however, ...

Excellent question. You've connected the dots perfectly. The short answer is yes, you are correct.

The most general and accurate way to characterize the optimality of the Wilcoxon-Mann-Whitney (WMW) test is to say that it is the most powerful (or more precisely, the locally most powerful rank) test for detecting alternatives under the proportional odds (PO) model.

Let's break down why ...

Is the Wilcoxon Test Maximally Powered for Proportional Odds Alternatives?

Yes, the most general way to state that the Wilcoxon-Mann-Whitney (WMW) test has optimum power for continuous outcomes is when the two distributions follow the proportional odds relationship.

Understanding the Proportional Odds Relationship

When two distributions F and G satisfy the proportional odds relationship, t...

Yes – in fact the two‐sample Wilcoxon (Mann–Whitney) rank‐sum test is precisely the score‐test for the semiparametric proportional‐odds logistic model with a single binary covariate, and under that model it is (up to invariance considerations) the most powerful way to detect departures from equality of distributions. Equivalently one can say:

1. Proportional‐odds model. Write the two conti...

This is an excellent question about the optimality properties of the Wilcoxon-Mann-Whitney test. Let me address this systematically.

The Answer

Yes, the Wilcoxon test is indeed optimally powered for detecting proportional odds alternatives in a specific sense. This is the most general way to characterize when the Wilcoxon test achieves optimal power for continuous outcomes.

The Techni...