I am a neuroscientist, and have neuronal response measurements for a large range of stimuli delivered to my subjects. I use this data to construct receptive fields (RFs), which show the mean response magnitude as a function of stimulus value. So, two RFs, for two different neurons, when they are shown stimuli from a 2-d stimulus space, might look like this:
I have multiple presentations of each stimulus (here I am representing each stimulus as an $(x,y)$ pair: you can consider it as the location of a light presented to the eye, and the height is the mean neuronal response to the light presented at that location).
Note that the two receptive fields above are not probabilities, but the height represents the mean response to the stimulus.
I want to test whether the receptive field centers are different for the two neurons. That is, is the location of the peak in the above two bumps different? Let's say we assume the two bumps are Gaussian in shape: what is the best way to test the null hypothesis that the two RF centers are identical?
If all else fails, I could do some kind of bootstrap, where I sample with replacement from the set of all $(x_i, y_i, r_i)$ triplets from each group. But even then, I would be back to square one of figuring out what statistical test to apply to these two samples of the original data.
Potentially Relevant Links: