I'm wondering if anyone can tell me whether using the spatial statistics tools such as Getis Ord Gi* "hot spot" analysis in ArcView is advisable when your input data is an averaged value, e.g. the average income in a census tract. I don't know enough about the mathematics going on under the hood in the spatial statistics toolset to determine whether using averaged census data would introduce error into the analysis.
I'm looking for clusters of high income and low income dissemination areas (slightly smaller than census tracts) within a Census Metropolitan Area. Ideally, I would like to create a series of maps that compare the location of high/low income dissemination areas across 3 census years, but median income values are not provided for one of them, meaning I would have to rely on average income in order to do so. I have run the Getis Ord Gi* tool on average income for these three censuses, as well as median income for the years where it is available and the spatial patterns produced do not seem to differ much. However, this question is still of general interest, as I haven't been able to track down any studies that use Hot Spot Analysis directly on average income for comparison.