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.