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Analyze/Stats: Mann-Whitney U Test

What is the Mann-Whitney U Test?

The Mann-Whitney U (also called Wilcoxon rank-sum test) test is a non-parametric statistical method used to compare differences between two independent groups. It evaluates whether one group tends to have higher or lower values than the other, without assuming a normal distribution. This test serves as the non-parametric alternative to the independent samples t-test and is ideal when working with ordinal data or non-normal continuous data.

Why Use This Test?

Unlike the t-test which compares group means assuming normality, the Mann-Whitney U test works by comparing ranked values between the two groups. This makes it suitable for:

  • Non-normal data distributions (no normality assumption)
  • Ordinal data or non-normal continuous data
  • Small sample sizes (especially with n ≤ 20)
  • Large sample sizes, where non-parametric robustness is still desired
  • Presence of outliers (robust to violations of parametric assumptions)

It is commonly used in clinical studies, biology data, behavioral research, or market comparisons involving two distinct groups (e.g., treatment vs. control, male vs. female, A vs. B).

When Should You Use the Mann-Whitney U Test?

  • You are comparing two independent groups
  • Your data is ordinal or continuous but not normally distributed
  • Sample sizes are small or unequal
  • You prefer a non-parametric alternative to the t-test
  • The two groups are unrelated (independent observations)

Common Alternatives (When Mann-Whitney U Isn’t the Best Fit)

How to Interpret the Results

The Mann-Whitney U test returns two key numbers:

  1. U-statistic: Reflects the difference in ranks between the two groups
  2. p-value: Determines statistical significance of the difference
Mann-Whitney results with SimpliStats

This is how you see the Mann-Whitney U test results with SimpliStats

Decision Rule:
  • If p-value < 0.05: Reject the null hypothesis (assuming p < 0.05, there is a significant difference between groups).
  • If p-value ≥ 0.05: No strong evidence of a difference (No significant difference detected between groups).

Note: A significant result tells you a difference exists, but not the direction. Use descriptive statistics to explore further.

Example:

Suppose we are comparing the age at diagnosis of :

When Mann-Whitney test, example data

The data: Type II diabetes between males and females.

When Mann-Whitney settings

Mann-Whitney settings with SimpliStats: Select the groups, customize the options if needed, click in “Analyze”.

Results:

p-value: 0.010

Since p = 0.010 < 0.05, we conclude:

“There is a statistically significant difference in diagnosis age between males and females.”

Advanced options

P-value Calculation Method and Continuity Correction

When performing the Mann-Whitney U test, you can adjust how the p-value is computed depending on the sample size and the presence of ties between groups:

Use Continuity (Continuity Correction)
The continuity correction (adding 0.5) is applied when approximating the distribution of the test statistic using a normal distribution (asymptotic method).

This option is relevant only when method=’asymptotic’. The default is True in this case. It has no effect if other methods are used.

Method:
You can choose how the p-value is calculated using the method parameter:

  • Asymptotic:
    Uses a normal approximation to compute the p-value, with corrections for ties. Recommended for large samples or when ties are present.
  • Exact:
    Calculates the exact distribution of the test statistic under the null hypothesis and compares the observed statistic to it. No correction for ties is made. This method is more accurate for small sample sizes and when no ties are present.
  • Auto (default):
    Automatically chooses the best method based on the data: Uses ‘exact’ when both samples have size ≤ 8 and there are no ties. Uses ‘asymptotic’ otherwise.

How the Function is Called

				
					from scipy.stats import mannwhitneyu

statistic, pvalue = mannwhitneyu(x, y, method='auto', use_continuity = True, alternative='two-sided')

Input

  • x and y: arrays of samples. Each arrays is one data column.
  • alternative: The alternative hypothesis (“two-sided”, “less”, “greater”).
  • method: ‘exact’, ‘asymptotic’, or ‘auto’
  • use_continuity: True/False

Output

  • statistic: The Mann-Whitney U value
  • pvalue: The associated p-value

Conclusion

The Mann-Whitney U test is a robust and flexible non-parametric method for comparing two independent groups. It is especially useful when data doesn’t meet the assumptions of the t-test (e.g., normality, equal variance). Researchers across medical, social, and business fields use it to evaluate differences when working with ranks, medians, or skewed data.

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