The non-parametric alternative to ANOVA for comparing three or more independent groups.
The Kruskal-Wallis Test is essentially a One-Way ANOVA performed on ranked data. It checks if there's a significant difference in the **median** distributions of three or more independent groups. Think of it as ANOVA's rugged, all-terrain cousin—it works even when the ground (your data) isn't perfectly smooth (normal).
Use this test when you want to compare three or more groups, but your data is **not normally distributed** or your sample sizes are very small. It's the perfect tool for situations where ANOVA's assumptions are violated.
This test is ideal for comparing the central tendency of multiple groups when dealing with skewed data, like trade returns or algorithmic performance metrics.
Example: A trading firm wants to compare the profitability of three different trading bots: a machine learning bot, a traditional rule-based bot, and a hybrid model. The profit-per-trade data for each bot is heavily skewed. They use the Kruskal-Wallis test to determine if there is a statistically significant difference in the median profit among the three bots.