Using Binning before Mann–Whitney for Temperature Data

I have daily temperature for 2 cities, and I am trying to see if we can conclude that one city is warmer than the other. I could use a Mann–Whitney for a whole year, or I can bin the temperature into maybe weeks or 2–3 days at a time. Maybe I can use a Chi-squared? Are there also technical issues (not related to area knowledge, i.e., how temperature is experienced) to consider when binning?

• If you're comparing the two cities for the same year, then I wonder if you have paired data. If so, you want Wilcoxon signed rank test for 365 days. If you want to compare 'how temperature is experienced' maybe you want a temperature index that takes humidity and wind into account: 'feels-like' temperatures. // Your description is sketchy and telegraphic, but just from what you say, I see no advantage to binning. Nov 19, 2019 at 21:09
• @BruceET: I don't get it, if I have data for each city taken at each day, how is not paired data?
– MSIS
Nov 19, 2019 at 21:11
• I'm saying I think it is paired data. But don't use Mann-Whitney-Wilcoxon 2-sample test for paired data. Nov 19, 2019 at 21:12
• Beware; these are time series; the temperature differences are not going to be independent. I agree with "don't bin" advice; it's rarely beneficial. Sometimes it doesn't hurt much. Nov 20, 2019 at 2:15
• @Glen_b-ReinstateMonica: I worry too about variance of individual data points being high-enough that ranks may be flipped, e.g., if the difference in one day is 0.8 but variance is 1. How would we address this?
– MSIS
Nov 20, 2019 at 19:30

Since this is temperature time series, there is certainly autocorrelation, which must be taken into account. Let the time series be $$Y_{jt}, j=1,2;\quad t=1,2 \dotsc, T$$. Since the interest is in the paired comparison calculate the difference time series $$D_t = Y_{2t}-Y_{1t}$$. The mean temperature difference can be estimated by the mean of $$D_t$$ (other estimators as the median or some trimmed mean ... could replace the mean).