Mann-Whitney u-test
Regular test¶
#
HypothesisTests.MannWhitneyUTest
— Function.
1 2 | 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.
Pooled test¶
#
UncertainData.UncertainStatistics.MannWhitneyUTestPooled
— Function.
1 2 | 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.
Element-wise test¶
#
UncertainData.UncertainStatistics.MannWhitneyUTestElementWise
— Function.
1 2 | 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.