Mann-Whitney U Test
Non-parametric alternative to the two-sample t-test. No normality assumption required — ideal for process comparisons with small samples, skewed distributions, or outliers.
After switching to a new O-ring supplier, QA wants to compare hardness (Shore A) between new and old batches. The hardness data is skewed with only 15 samples per group, violating the t-test normality assumption — so Mann-Whitney non-parametric statistics are used instead. This tool is also commonly used to compare quality performance across operators, shifts, or machines — ideal for shop-floor evaluations with small samples or unknown distributions.
New batch (n=15) hardness: 65, 68, 70, 63, 72, 66, 69, 71, 64, 73, 67, 70, 68, 65, 74 Old batch (n=15) hardness: 60, 62, 64, 58, 65, 61, 63, 66, 59, 67, 62, 64, 61, 58, 68 U statistic = 195 (max possible = 225) Standardized Z = 3.42 p = 0.0006 < 0.05 → Reject null hypothesis: new batch hardness is significantly higher → Recommend re-evaluating material spec or adjusting assembly torque
FAQ
Related Tools
Box Plot
Before running Mann-Whitney, visualize the medians and distribution shapes of both groups with a box plot to confirm a statistical test is warranted.
Open toolOne-Way ANOVA
Mann-Whitney compares two groups non-parametrically; for three or more non-normal groups, consider Kruskal-Wallis (the non-parametric ANOVA).
Open toolHistogram & Normality Test
Use the Anderson-Darling normality test to verify whether data is normally distributed — the key basis for choosing between t-test and Mann-Whitney.
Open tool