It's common in many aspects of science to want to determine if the trends shown in spatial data are significant. In my field of familiarity, climate science, authors often show the trends in temperature data, for example, and overlay stippling to show trend significance at 5%. For example see Rotstayn et al. (2013) (open access) Fig. 1:
Rotstayn et al. mention that
statistical significance of ensemble means is assessed using a two-sided t-test [Sect. 2]
For the example above, let's assume they have three data sets: model1 --> temperature climatology; model2 --> temperatures from an alternative model and model3 --> temperatures from another alternative model. (a) and (b) are then model2 - model1 and model3 - model1 respectively. In this case, the plot is latitude-pressure (height), but plots may be lat-lon, lon-pressure etc. Ultimately, you're working with a set of 2d matrices [x,y].
How do you obtain significance at each discrete data point rather than obtaining one t/p statistic for the comparison of the entire data set, such that you can plot of field of 5% significance.
I plot and process data in Python, so bonus points for discussion how this can be implemented in Python.
Also feel free to discuss the merits of t-tests and/or suggest alternative tests that may be better suited to data that is not normally distributed.
A similar question has been asked on Stackover flow here: Test for statistically significant difference between two arrays but I don't understand how the answers help me.