A/B tests · For studentsMann–Whitney U test calculator
An online Mann–Whitney U test solved step by step: a ranking table of both samples, ties with the mean rank, rank sums and U, an exact p for small samples without ties and the normal approximation with corrections. Effect size r, group medians, and Python and R code. For skewed data, outliers and ordinal scales.
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01
Data
The test compares distributions, not means: it checks whether the values of one group tend to be higher. It suits skewed data, outliers and ordinal scales.
Numbers separated by spaces, semicolons, “, ” or new lines — you can paste a column from Excel. The samples may differ in length.
α = 0.05 · two-sided test
02
Result
The distributions differ
Values in B tend to be higher than in A: U = 24.5, p = 0.0160 (asymptotic). Effect size r = 0.76, large.
U statistic for B
24.5
for A: 0.5
p-value
0.0160
asymptotic, with corrections
Effect size r
0.76
large
Median of A
13
n = 5
Median of B
17
n = 5
Normal approximation, z
2.410
with continuity correction
03
Ranking table
04
Step by step
- 1RankingRank 10 values in ascending order; ties get the mean rank.
- 2Rank sumsRA = 15.5RB = 39.5(check: they add up to 15.5 + 39.5 = 10·11/2 = 55)
- 3The U statisticUA = RA − nA(nA + 1)2 = 15.5 − 5 · 62 = 0.5UB = nAnB − UA = 5 · 5 − 0.5 = 24.5
- 4Normal approximation and p-valueWith ties or large samples — the normal approximation with a tie correction in σ and a continuity correction in z.μ = nAnB2 = 12.5σ = 4.773z = |UB − μ| − 0,5σ = 2.410p = 2 · (1 − Φ(|z|)) = 0.0160
- 5Conclusionp = 0.0160 < 0.05 — reject H₀: the distributions differ, values in B are higher. Effect size r = 0.76, large.
05
Check in Python / R
06
Problems
07
Frequently asked questions
Updated