## Mann-Whitney U Test

Mann-Whitney U Test Calculator | ||
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Group 1 : X | Group 2 : Y | |

Enter Data (Separated by comma ,) | ||

Level of Significance ($\alpha$) | ||

Tail | Left tailed Right tailed Two tailed | |

Results | ||

Number of Observations (n): | ||

Ranks for Group 1: | ||

Ranks for Group 2: | ||

Ranks sum for Group 1: | ||

Ranks sum for Group 2: | ||

U Statistic : | ||

U Critical Value : | ||

## Mann-Whitney U Test

Define

```
$$
\begin{aligned}
U_1 & = n_1n_2 + \frac{n_1(n_1+1)}{2}-R_1\\
U_2 & = n_1n_2 + \frac{n_2(n_2+1)}{2}-R_2\\
\end{aligned}
$$
```

The test statistic is $U=min{U_1,U_2 }$.

The critical value of U is $U_{\alpha, n1,n2}$