Mann-Whitney U test

Expected difference between two populations' median

tails:
tutorial

Hypotheses

H0: var1 ≥ var2 H0: var1 = var2 H0: var1 ≤ var2
H1: var1 < var2 H1: var1 ≠ var2 H1: var1 > var2

Test statistic

Z statistic

Normal Distribution

Normal distribution two tailed Normal distribution two tailed Normal distribution two tailed
c - continuity correction, when U > μ: c = -0.5, when U < μ: c = 0.5

Test calculation

The tool uses the critical value tables when ni ≤ 20 and a normal approximation for a larger sample size
When ni ≤ 20 the normal distribution chart is only for demonstration.

Unlike t-test that compares the means, the Mann-Whitney U test compares a randomly selected value from group1 to a randomly selected value from group1.
When the two distributions have a similar shape you can use the test to compare also the medians.
When the two distributions have a similar symmetrical shape, you can use the test to compare also the means.

Statistic Data

α:significant level (0-1), maximum chance allowed rejecting H0 while H0 is correct (Type1 Error)
outliers:this test is robust for outliers. It is not recommended to exclude outliers unless you know the reasons
methodwhen n1≤20 and n2≤20 uses the exact value from table, otherwise uses the z approximation
distribution:continuity correction for discrete distribution (relevent only for normal approximation)

Enter raw data directly
Enter raw data from excel

Enter sample data directly

Header: You may change groups' name to the real names.
Data: When entering data, press Enter after each value.

It is okay to leave empty cells, empty cells or non numeric cells won't be counted

Enter sample data from excel

You may copy data from Excel, Google sheets or any tool that separate data with Tab and Line Feed.
Copy the data, one block of consecutive columns includes the header, and paste below. . click to see example: example from excel


It is okay to leave empty cells, empty cells or non numeric cells won't be counted


Results

 
 
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