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:
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Calculate your Mann-Whitney U statistic: This involves ranking the combined data set and assigning ranks to each observation based on its group membership.
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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).
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Locate the row with your sample sizes (n1 and n2).
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Find the column with your chosen significance level (α).
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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)
