  Measures of the non-Gaussianity of a random field depend on how accurately
one is able to measure the field. If a signal measured at a certain point is to
be averaged with its surroundings, or coarse-grained, the magnitude of its
non-Gaussian component can vary. In this article, we investigate the variation
of the "apparent" non-Gaussianity, as a function of the coarse-graining length,
when we measure non-Gaussianity using the statistics of extrema in the field.
We derive how the relative difference between maxima and minima -- which is a
geometrical measure of the field's non-Gaussianity -- behaves as the field is
coarse-grained over increasingly larger length scales. Measuring this function
can give extra information about the non-Gaussian statistics and facilitate its
detection.
