72 lines
1.4 KiB
Go
72 lines
1.4 KiB
Go
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package onlinestats
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// https://en.wikipedia.org/wiki/Mann%E2%80%93Whitney_U
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import (
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"math"
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"sort"
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)
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// MannWhitney performs a Matt-Whitney U test for the two samples xs and ys.
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// It returns the two-tailed p-value for the null hypothesis that the medians
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// of the two samples are the same. This uses the normal approximation which
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// is more accurate if the number of samples is >30.
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func MannWhitney(xs, ys []float64) float64 {
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// floats in a map.. this feels dubious?
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data := make(map[float64][]int)
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for _, x := range xs {
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data[x] = append(data[x], 0)
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}
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for _, y := range ys {
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data[y] = append(data[y], 1)
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}
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floats := make([]float64, 0, len(data))
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for k := range data {
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floats = append(floats, k)
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}
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sort.Float64s(floats)
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var r [2]float64
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var idx = 1
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for _, f := range floats {
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dataf := data[f]
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l := len(dataf)
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var rank float64
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if l == 1 {
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rank = float64(idx)
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} else {
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rank = float64(idx) + float64(l-1)/2.0
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}
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for _, xy := range dataf {
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r[xy] += rank
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}
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idx += l
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}
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n1n2 := len(xs) * len(ys)
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idx = 0
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u := float64(n1n2+(len(xs)*(len(xs)+1))/2.0) - r[0]
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if u1 := float64(n1n2+(len(ys)*(len(ys)+1))/2.0) - r[1]; u > u1 {
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idx = 1
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u = u1
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}
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mu := float64(n1n2) / 2.0
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sigu := math.Sqrt(float64(n1n2*(len(xs)+len(ys)+1)) / 12.0)
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zu := math.Abs(float64(u)-mu) / sigu
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return 2 - 2*cdf(0, 1, zu)
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}
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func cdf(mean, stddev, x float64) float64 {
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return 0.5 + 0.5*math.Erf((x-mean)/(stddev*math.Sqrt2))
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}
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