# To use a two-sample t-test or to use a Mann-Whitney U-test on spatial data?

I have obtained some mean summer temperature records (June 1st- September 30th) for all years within the 1930s (1930-1939) and I have obtained summer temperature records for all years within the 2000s (2000-2009), for all regions in Great Britain (i.e. South West Scotland, South East Scotland, Midlands..).

I want to know whether the mean temperature values recorded in the 1930s significantly differ from the mean temperatures values for the same period in the 2000s.

The data is skewed because naturally I have greater temperature values for the South East and Southern England compared to temperature values in the North (Scotland). Therefore, my data does not meet the t-tests normality assumption.

However, because I am literally comparing one variable (1930s mean temperatures) against another variable (2000s mean temperatures), I am not sure whether the alternative non-parametric Mann-Whitney U-test, is appropriate? Because the data is continuous and not ordinal?

I am not sure what other tests to conduct, and would really appreciate some guidance!

• You don't have independent data; they're matched by region (if you have the same regions for both you can look at the temperature differences for each region leading to some paired test; failing that it may still be possible to do something) Commented Mar 13, 2016 at 13:00
• Oh so not a Mann-Whitney U-test then! I think the Wilcoxon-signed ranked test is a better shout then. Commented Mar 13, 2016 at 13:03
• Its a possibility -- but you specifically ask about change in means, which the signed rank test doesn't test for (at least not without additional assumptions). I'll attempt to come up with an answer. Commented Mar 13, 2016 at 13:04
• This appears to need a model with spatial correlations, and be sure to treat time as a continuous variable, using a flexible modeling approach without assuming linearity. Commented Mar 13, 2016 at 13:05
• I have edited the title and tags to make it clear that the data set is spatial in nature, I think that's a key point in this question. Feel free to revert or improve my edits. Commented Mar 13, 2016 at 13:40