Mastering the Mann-Whitney U Test: Theory and Practice with Python
Introduction
Welcome to lesson two on Hypothesis Testing with Python! Today's focus is on the Mann-Whitney U test. We've previously discussed T-tests, but now we're shifting attention to the Mann-Whitney U test, used to compare two independent samples. This tool helps when data doesn't meet the normality assumption for T-tests. In this lesson, we explore the ins and outs of the Mann-Whitney U test, applying it to a real-life dataset using SciPy.
Mann-Whitney U Test Overview
Let's start with non-parametric tests. These are also called distribution-free tests; they work with data that doesn't fit a normal distribution. We use them when our data is skewed, ordinal, or has outliers. Here, ordinal means a type of data where the order of the data points matters, but not the difference between the data points. For example, the sequence in which participants finish matters in a race, but the exact time difference between each runner does not.
The Mann-Whitney U test compares two independent groups when the dependent variable is ordinal or continuous but doesn't follow a normal distribution. It ranks the values from the two groups and adds the ranks. Similar sums of ranks indicate the two groups are not significantly different.
The Mann-Whitney U test provides two values: the U-statistic and the p-value. The U-statistic signifies the rank sum difference between two groups regarding their observed data values. In everyday language, a very small or very large U-statistic means more separation or difference between the two groups' data. The p_value here means the same as in the T-test: If the p-value is less than 0.05, we conclude that the difference is statistically significant and unlikely to be due to randomness alone.
Performing the Test in Python
The mannwhitneyu() function from SciPy runs the U test, taking two data samples as input and returning a test statistic (U) and a p-value (p). Here's what the code looks like:
If the p-value is less than 0.05, we consider it evidence against the null hypothesis, leading to its rejection.
