<P> Under the general formulation, the test is only consistent when the following occurs under H: </P> <Ol> <Li> The probability of an observation from population X exceeding an observation from population Y is different (larger, or smaller) than the probability of an observation from Y exceeding an observation from X; i.e., P (X> Y) ≠ P (Y> X) or P (X> Y) + 0.5 P (X = Y) ≠ 0.5 . </Li> </Ol> <Li> The probability of an observation from population X exceeding an observation from population Y is different (larger, or smaller) than the probability of an observation from Y exceeding an observation from X; i.e., P (X> Y) ≠ P (Y> X) or P (X> Y) + 0.5 P (X = Y) ≠ 0.5 . </Li> <P> Under more strict assumptions than the general formulation above, e.g., if the responses are assumed to be continuous and the alternative is restricted to a shift in location, i.e., F (x) = F (x + δ), we can interpret a significant Mann--Whitney U test as showing a difference in medians . Under this location shift assumption, we can also interpret the Mann--Whitney U test as assessing whether the Hodges--Lehmann estimate of the difference in central tendency between the two populations differs from zero . The Hodges--Lehmann estimate for this two - sample problem is the median of all possible differences between an observation in the first sample and an observation in the second sample . </P>

What is the null hypothesis for mann whitney test