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This is accomplished by first converting the calculated U statistic for the observed data into a Z statistic (assuming a Gaussian distribution). In this situation, Prism will always calculate an approximate P value (regardless of ties). The exception to this approach is when there are more than 100 values in the smaller of the two data sets being compared. The exact P value is equal to this fraction. This number is divided by the total number of possible permutations of the data, yielding a fraction of total U statistics that are equal to or less than the U statistic calculated for the observed data. Then, using the ranks of all of the data, Prism determines how many different permutations of the data would result in a U statistic equal to or less than the U statistic calculated for the observed data. To do this, Prism first calculates the U statistic for the observed data. Instead, Prism uses a technique which calculates an exact P value even in the presence of ties. However, this approach is not widely utilized, and is not the technique that Prism uses to calculate P values. Geyer suggests computing a range of P values, which he calls fuzzy P values. Computing a P value from U (or from the sum of signed ranks the two end up being equivalent) is not so straightforward. Prism uses a standard method to correct for ties when it computes U, and the sum of signed ranks. The test statistic for the Mann-Whitney test is the U statistic. I am dubious about how useful the Mann-Whitney test is in this situation. Rather than do the Mann-Whitney test, consider analyzing the data as categorical data using a chi-square test to compare the two groups. In this situation, there are only a few possible values (the number of categories) so there will be lots of tied ranks. Some people use the Mann-Whitney test to compare categorical outcomes, with the categories coded as numbers. How rare? It depends on how many digits of precision are recorded. The test was developed to analyze data from continuous measurements like enzyme activity or weight or blood pressure. In this situation, ties will be rare.
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This situation complicates calculation of a P value. If two values are identical, they tie for the same rank. It reports a P value testing the null hypothesis that the two populations have identical distributions, so any discrepancy in mean rank is just a matter of random sampling. It does this by ranking all the values from low to high and then comparing the average rank of the two groups.
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The Mann-Whitney compare two groups of values without making any assumption about the distribution the values were sampled from.