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! 
 A: It would be better to go back to the design of your study.  You have taken two time periods as examples, but much more data are available than that.  I suggest obtaining a sample that encompasses at least 100 years, using calendar time as a continuous variable, and that incorporates highly localized geographical location in the model, plus allows for spatial correlations between locations.  Once you have the best sample and a well-specified model you can look at the model assumptions.   Here normality of residuals is at issue, not normality or symmetry of raw temperatures.
The time trend can be modeled using a flexible approach such as regression splines with lots of knots to allow for complexity.  A primary focus would be estimation of the time effect, with confidence bands.  You can extend this analysis by adding seasonal trends into the mean model, e.g., you can have one spline function for long-term trends and another for repeated yearly trends.
Once you are comfortable with the type of main effects model described above, you can allow time to interact to location to estimate and test for different temperature trends by region.
Note that nonparametric tests work very well on continuous data.  All continuous variables are ordinal.  The limitation of Wilcoxon and other tests is their inability to incorporate covariates.  That's why their generalizations (e.g., proportional odds ordinal logistic model) are gaining in popularity.
