The Third U-test

Let's compare the 'Average Purchase Value' metric for both samples.

We'll start with the distribution plot:

It's difficult to make a conclusive inference about the distribution of both samples. Additionally, the median of the test group appears to be larger. Let's conduct the Shapiro test:

The first Shapiro test did not find statistical evidence of normality in the distribution. However, the second Shapiro test confirmed the normality of the distribution in the test group. In this case, for the U-test, it is not a problem. It is capable of comparing both normal and non-normal distributions. We do not need to be concerned about the variance in this case.

The hypotheses will be:

H₀: The medians of the 'Average Purchase Value' metric in the control and test groups are the same.

Hₐ: The medians of the 'Average Purchase Value' metric differ between the control and test groups.

The obtained test statistic value and the low p-value indicate a statistically significant difference between the medians of the 'Average Purchase Value' metric in the control and test groups. We have sufficient evidence to reject the null hypothesis and accept the alternative hypothesis that the medians are different. The median in the test group is larger.