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Mann-Whitney U Test Calculator

Calculate the Mann-Whitney U statistic and z-score for comparing two independent groups using rank sums.

Inputs

Results

U Statistic

165

Z-Score

2.16

P-Value (two-tailed, approx)

0.03

U' Statistic60
U (min)60
Significant at α=0.05 (1=Yes)1
Effect Size (r)0.39
U Max165
How to Use This Calculator
  1. Enter Group 1 Size (n₁), Group 2 Size (n₂), and Rank Sum for Group 1 (R₁).
  2. Review U Statistic, Z-Score, and P-Value (two-tailed, approx).
  3. Use U and U (min) to inform your decision.
  4. Use the chart to visualize the results and explore different scenarios by adjusting inputs.

How the result changes with Group 1 Size (n₁)

Group 1 Size (n₁)U StatisticZ-ScoreP-Value (two-tailed, approx)
1,002517,353451.510
3,5016,182,5861,569.220
6,50121,232,0862,910.890
9,00040,639,3204,028.480

What each input means

Group 1 Size (n₁)
Number of observations in the first group.
Group 2 Size (n₂)
Number of observations in the second group.
Rank Sum for Group 1 (R₁)
Sum of ranks assigned to Group 1 after ranking all observations together.

How this is calculated

Worked example, using the default values

  1. Identify Input Parameters
    Group 1 Size (n₁) = 15, Group 2 Size (n₂) = 15, Rank Sum for Group 1 (R₁) = 180 = 3 input(s) provided
  2. Calculate U Statistic
    U Statistic
    165 = 165
  3. Calculate Z-Score
    Z-Score
    2.1569 = 2.1569
  4. Calculate P-Value
    P-Value = Math
    0.031 = 0.031
  5. Calculate U' Statistic
    U' Statistic
    60 = 60
  6. Calculate U
    U
    60 = 60

Engine last updated . Checked against 2 independently-derived tests — how we verify calculators.

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