Mann-Whitney U Table

The Mann-Whitney U Test is a non-parametric statistical test used to compare two independent groups when the data is not normally distributed or the variances are unequal. The Mann-Whitney U Table provides critical values for interpreting the results of this test.

What it contains:

  • Sample sizes (n1 and n2): The number of observations in each group.
  • Significance level (α): The probability of rejecting the null hypothesis (H0) when it’s actually true, typically set at 0.05 (5%) or 0.01 (1%).
  • Critical values for U: These are specific thresholds for your calculated Mann-Whitney U statistic based on n1, n2, and α. There are separate tables for two-tailed and one-tailed tests.

How to use it:

  1. Calculate your Mann-Whitney U statistic: This involves ranking the combined data set and assigning ranks to each observation based on its group membership.

  2. Identify the appropriate section: Two-tailed table for comparing differences in any direction, one-tailed table if you have a specific direction in mind (e.g., only larger values in one group).

  3. Locate the row with your sample sizes (n1 and n2).

  4. Find the column with your chosen significance level (α).

  5. Compare your calculated U statistic to the critical value:

    • Two-tailed test: If your U is less than or equal to the critical value, reject the null hypothesis (H0) and conclude that there is a significant difference between the two groups.
    • One-tailed test: Double your chosen α and use the table accordingly. Reject H0 if U is less than or equal to (for lower values in one group) or greater than or equal to (for higher values in one group) the adjusted critical value.

Alpha = .01 (two-tailed)


Alpha = .05 (two-tailed)

Alpha = .10 (two-tailed)