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?
 A: 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).
But the autocorrelation makes it non-trivial to find the standard error of this estimate. Some ideas:

*

*Estimate the autocorrelation function and use it to find the se.


*Use moving block bootstrap?


*Calculate an autocorrelation-resistant standard error?
Related Qs on site with interesting answers:
Determining standard error of the mean from a correlated, stationary time series using known autocorrelation without block averaging,
How to estimate confidence interval of the sample mean of a non-stationary time series?,
T-test in the presence of autocorrelation,
Estimating accurately the mean of an autocorrelated bounded integer time series,
Calculating error of mean of time series,
Newey-West t-statistics
