Visualization of significant differences in somatotopic maps: a distributed t-test

In order to test for differences in the properties of two populations of cells within a somatotopic map we need to be able to compare data sets in which sampled cells are randomly scattered throughout the map, and the variable being compared varies with location in the map. We can describe cell properties as exponentially smoothed surfaces fitted to data in the plane of the map, where all data contribute to the computation of the value of each grid point on the surface, with weights which decline exponentially with distance from the grid point. Means, variances and Student's t values can be computed at all grid points, keeping in mind the fact that grid points' t values are not independent of each other. We used Monte Carlo methods to demonstrate that two random samples of 500 values from two populations of 100,000 values at 4000 grid can provide a very useful picture of regions with significant differences. We recommended this procedure, or analogous approaches using other statistical tests, for any analysis where it is necessary to compare values of dependent variables when matched locations on the independent axis or plane cannot be sampled in the two populations.