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My goal is to take a world population grid (2.5 arcmin) and perform zonal statistics as table inside country borders (and also inside the cells of a 1-degree fishnet intersected with country borders). I see on the tool description that one shouldn't use geographic coordinate systems for Zonal Statistics as Table. However, I just tried to project my input raster to an equal-area projection and it seemed like it would never finish - also projecting required me to choose a "resample" option - I want the same values that I started with!

So, will I be okay if I perform ZS as table in my starting system (which I think is WGS 84)? I just want to add up pixels inside shapes. I'm most concerned about allocation happening properly across borders - of the countries and fishnet. And I don't understand why projection matters in this case, as my raster grid cells have a specific location and my polygons do too, so no matter what projection, wouldn't their relative placing remain the same?

Bonus question: does projection matter for plain Zonal statistics, too? What about for converting a polygon to a raster?

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The projection matters a lot, as the statistics are weighted by number of cells, and if the data are not projected the areas are in square degrees depending on where you are the ground area of a cell is different. This is true for Zonal Statistics tools.

Highly recommend you project your raster data if you want your statistics to have meaning. There are several equal area world projections that would work, depending on your needs.

To successfully project you may want to convert your raw population to density, you can resample that bilinear and the data will smear around, then you can do an average population density and multiple it by zonal area.

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