Mann-Whitney U-test

MannWhitneyUTest(d1::AbstractUncertainValue, d2::AbstractUncertainValue,
    n::Int = 1000) -> MannWhitneyUTest

Let s1 and s2 be samples of n realisations from the distributions furnishing the uncertain values d1 and d2.

Perform a Mann-Whitney U test of the null hypothesis that the probability that an observation drawn from the same population as s1 is greater than an observation drawn from the same population as s2 is equal to the probability that an observation drawn from the same population as s2 is greater than an observation drawn from the same population as s1 against the alternative hypothesis that these probabilities are not equal.

The Mann-Whitney U test is sometimes known as the Wilcoxon rank-sum test. When there are no tied ranks and ≤50 samples, or tied ranks and ≤10 samples, MannWhitneyUTest performs an exact Mann-Whitney U test. In all other cases, MannWhitneyUTest performs an approximate Mann-Whitney U test.

MannWhitneyUTest(d1::UncertainDataset, d2::UncertainDataset,
    n::Int = 1000) -> MannWhitneyUTest

Let $s_{1_{i}}$ be a sample of n realisations of the distribution furnishing the uncertain value d1[i], where $i \in [1, 2, \ldots, N]$ and $N$ is the number of uncertain values in d1. Next, gather the samples for all $s_{1_{i}}$ in a pooled sample $S_1$. Do the same for the second uncertain dataset d2, yielding the pooled sample $S_2$.

Perform a Mann-Whitney U test of the null hypothesis that the probability that an observation drawn from the same population as $S_1$ is greater than an observation drawn from the same population as $S_2$ is equal to the probability that an observation drawn from the same population as $S_2$ is greater than an observation drawn from the same population as $S_1$ against the alternative hypothesis that these probabilities are not equal.

The Mann-Whitney U test is sometimes known as the Wilcoxon rank-sum test. When there are no tied ranks and ≤50 samples, or tied ranks and ≤10 samples, MannWhitneyUTest performs an exact Mann-Whitney U test. In all other cases, MannWhitneyUTest performs an approximate Mann-Whitney U test.

MannWhitneyUTest(d1::UncertainDataset, d2::UncertainDataset,
    n::Int = 1000) -> Vector{MannWhitneyUTest}

Assume d1 and d2 consist of the same number of uncertain values. Let $s_{1_{i}}$ be a sample of n realisations of the distribution furnishing the uncertain value d1[i], where $i \in [1, 2, \ldots, N]$ and $N$ is the number of uncertain values in d1. Let $s_{2_{i}}$ be the corresponding sample for d2[i]. This function

Perform an element-wise Mann-Whitney U test of the null hypothesis that the probability that an observation drawn from the same population as $s_{1_{i}}$ is greater than an observation drawn from the same population as $s_{2_{i}}$ is equal to the probability that an observation drawn from the same population as $s_{2_{i}}$ is greater than an observation drawn from the same population as $s_{1_{i}}$ against the alternative hypothesis that these probabilities are not equal.

The Mann-Whitney U test is sometimes known as the Wilcoxon rank-sum test. When there are no tied ranks and ≤50 samples, or tied ranks and ≤10 samples, MannWhitneyUTest performs an exact Mann-Whitney U test. In all other cases, MannWhitneyUTest performs an approximate Mann-Whitney U test.