# Creating a reference group to have equal sample sizes for Wilcoxon signed rank test

I am analyzing three years' worth of data. For some descriptive analysis, I want to know if there is a difference in the median between, $$year_1$$ and $$year_2$$ compared to $$year_3$$. To do this, I planned to average $$year_1$$ and $$year_2$$, creating a comparable 12-month reference group with $$year_3$$. I would then use the Wilcoxon signed rank test. Would this be a fair way to understand the data? The data is considered paired.

Thank you for your feedback. Let me first state, this is a preliminary analysis for a larger interrupted time series analysis in which autocorrelation is account for (using ARIMA).

Knowing this, would you still suggest the the Wilcoxon Mann-Whitney two sampled ranked sum test (from this initial phase)? And if so, it is acceptable to have unequal groups ($$n=24$$ and $$n=12$$)?Also, the rate are coming from one distinct location, which is why I first instinctively considered them paired.

Edit: or is the creation of the (pre 12-month reference group still applicable)

I appreciate your continued input and support.

• The Mann-Whitney Wilcoxon rank sum test is not properly a test for median difference. Rather, it is a test for evidence that $Pr(X_1 > X_2) \ne 0.5$. With additional stringent assumptions that groups 1 & 2 have (i) the same shape distribution, and (ii) the same variance, you can interpret a rejected rank sum null hypothesis as evidence for median difference (and for mean difference also). Tests for median difference in 2 or more groups are a variation of Pearson's $\chi^2$ test; e.g., see Conover's Practical Nonparametric Statistics section 4.3: The Median Test. Commented Dec 9, 2022 at 18:20
• Also: Welcome to CV, Levi. Commented Dec 9, 2022 at 18:21
• what about a test such as this? (blogs.sas.com/content/iml/2017/02/22/…) Quantile regression Commented Dec 9, 2022 at 21:46