# Thread: What is the p-value in a rank-biserial correlation?

1. ## What is the p-value in a rank-biserial correlation?

Hello, can someone tell me how to compute the p-value in a rank-biserial correlation?

I understand the rank-biserial correlation coefficient is a function of the Mann–Whitney U test, and is a special case of Somers' d where one variable is dichotomous and the other is ordinal or continuous, but am not sure how to derive the p-value when doing rank-biserial correlations.

In SPSS, the output of Mann–Whitney produces a different p-value to Somers' d (in the latter case an "approximate significance" is generated) and I'd like to better understand the difference, as well as which of these—or neither?—would be best use when doing a rank-biserial correlation.

Any advice/guidance would be most greatly appreciated.

Many thanks in advance for any guidance!

2. ## Re: What is the p-value in a rank-biserial correlation?

Originally Posted by marklee_csu
Hello, can someone tell me how to compute the p-value in a rank-biserial correlation?

I understand the rank-biserial correlation coefficient is a function of the Mann–Whitney U test, and is a special case of Somers' d where one variable is dichotomous and the other is ordinal or continuous, but am not sure how to derive the p-value when doing rank-biserial correlations.

In SPSS, the output of Mann–Whitney produces a different p-value to Somers' d (in the latter case an "approximate significance" is generated) and I'd like to better understand the difference, as well as which of these—or neither?—would be best use when doing a rank-biserial correlation.

Any advice/guidance would be most greatly appreciated!

Many thanks in advance for any guidance!

Kind regards,

Mark Lee
Australia
Yes, the Rank-Biserial correlation is a linear function of the U statistic - to be more precise. I believe you can find the answer to your question if you look at the following article:

Willson, V. L. (1976). Critical values of the rank-biserial correlation coefficient. Educational and Psychological Measurement, Vol. 36, pp. 297-300.

3. ## Re: What is the p-value in a rank-biserial correlation?

Many thanks, Dragan, for your response! I've taken a look at the article you referenced, and also note that Cureton (1956), who first came up with the rank-biserial correlation, states that "The hypothesis that rrb differs only by chance from prb = 0 may be tested by the Mann-Whitney extension of the Wilcoxon test."

My dilemma is that all of the following generate different p-values, and I don't know which would be most appropriate to use:

1. The Somers' d option in SPSS (under Crosstabs);
2. The somersd package in Stata;
3. The Mann–Whitney U option in SPSS and the corresponding command (ranksum) in Stata.

Any additional guidance you or anyone else is able to provide would be most welcomed and appreciated!

4. ## Re: What is the p-value in a rank-biserial correlation?

Originally Posted by marklee_csu
Many thanks, Dragan, for your response! I've taken a look at the article you referenced, and also note that Cureton (1956), who first came up with the rank-biserial correlation, states that "The hypothesis that rrb differs only by chance from prb = 0 may be tested by the Mann-Whitney extension of the Wilcoxon test."

My dilemma is that all of the following generate different p-values, and I don't know which would be most appropriate to use:

1. The Somers' d option in SPSS (under Crosstabs);
2. The somersd package in Stata;
3. The Mann–Whitney U option in SPSS and the corresponding command (ranksum) in Stata.

Any additional guidance you or anyone else is able to provide would be most welcomed and appreciated!
Well, I'm not looking at your (ostensibly disparate) computational results. For example, you could just generalize and say that if all p-values - from the various statistical software packages - are less than 0.05, then just say that....unless they are giving you results such as: p=0.20, p=0.001, and p=0.055....then, for sure, I see a problem.

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