There are actually two U-values, and they are connected by U1+U2=n1*n2 (so just one needs to be actually calculated). The test used the *lower* of these two values. So also in the case that the calculated U-value is just maximal (n1*n2), then the other U-value must be 0, and this 0 is taken for the test.

Btw: I wonder what the relevance of this hypothesis test in the paper is. They divided the data with respect to this variable - what insigt should a test add? And what if the test would have been "non-significant"? Further, the variable was "income". I doubt that the distributions in both groups are equal (except for the location), so the test they performed is not specifically a test for a difference in the (median) incomes.

There are actually two U-values, and they are connected by U1+U2=n1*n2 (so just one needs to be actually calculated). The test used the *lower* of these two values. So also in the case that the calculated U-value is just maximal (n1*n2), then the other U-value must be 0, and this 0 is taken for the test.

Btw: I wonder what the relevance of this hypothesis test in the paper is. They divided the data with respect to this variable - what insigt should a test add? And what if the test would have been "non-significant"? Further, the variable was "income". I doubt that the distributions in both groups are equal (except for the location), so the test they performed is not specifically a test for a difference in the (median) incomes.

Thank you Jochen. That makes a lot more sense. The MWU was not a statistical hypothesis test. It really was to show that the two groups that they created were different based on 'income' which in this context (now I understand the significance of 0) would mean that Group 1 had values below the values of the largest group. I believe the U is used essentially to 'validate' the median split despite the uneven sample sizes to begin with and the large SD in group 2.

Thank you for your answer.

Hi Jan,

Thank you for the insight and the questions. I agree the focus on this minor point in the paper does detract from the value of the overall finding but the fact that I did not quite understand it's relevance was frustrating, so I had to ask. Also, the logic of using a median split on three groups that were already heavily skewed baffled me a little - I don't think it really solved a problem but rather that the large SD in the 'high' group would likely mask any potential effect in the context of the ANOVA. Personally, I think a multiple regression would have better answered their question given the uneven distribution of their original sample.

Just as an aside, there is an emerging literature on neuropsychological and neurophysiological differences associated with differing levels of SES. However, SES (where it is taken into account) is a) often held constant or b) not appropriately measured/parsed out as a between-subject factor in studies with bilingual participants, leading to the assumption that SES is an unimportant factor. Bilingualism does have protective effects but I think there is a more complex relationship between SES and language status than is presently elucidated in the literature.