# Example of Mann-Whitney Test

A state highway department uses two brands of paint for painting stripes on roads. A highway official wants to know whether the durability of the two brands of paint are different. For each paint, the official records the number of months the paint persists on the highway.

The official performs a Mann-Whitney test to determine whether the median number of months that the paint persists differs between the two brands.

1. Open the sample data, HighwayPaint.MTW.
2. Open the Mann-Whitney Test dialog box.
• Mac: Statistics > 2-Sample Inference > Mann-Whitney
• PC: STATISTICS > Two Samples > Mann-Whitney
3. From the drop-down list, select Each sample is in its own column.
4. In Sample 1 enter Brand A.
5. In Sample 2, enter Brand B.
6. Click OK.

## Interpret the results

The null hypothesis states that the difference in the median number of months that the paint persists between the two brands is 0. Because the p-value is 0.0019, which is less than the significance level of 0.05, the official rejects the null hypothesis. The official concludes that the difference in the median number of months the paints persists between the two brands is not 0. The 95.5 Percent CI indicates that the population median of Brand B is likely to be greater than Brand A.

 Method
 η₁: median of Brand A η₂: median of Brand B Difference: η₁ - η₂
 Descriptive Statistics
 Sample N Median Brand A 11 36.0 Brand B 10 37.6
 Estimation for Difference
 Difference CI for Difference Achieved Confidence -1.85 (-3.0, -0.9) 95.52%
 Test
 Null hypothesis H₀: η₁ - η₂ = 0 Alternative hypothesis H₁: η₁ - η₂ ≠ 0
 Method W-Value P-Value Not adjusted for ties 76.50 0.0019 Adjusted for ties 76.50 0.0019
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