# What is the technical term for spatially aggregated measures?

Is there an adjective to describe data that has areal weight, like area, biomass, population, etc. — data that has to be aggregated by sum for example — vs. data that doesn't, such as landcover classification? Categorical for the latter, perhaps, but what for the former?

To illustrate aggregation by sum: if you had rasters of biomass and elevation on 200 m $\times$ 200 m cells, and you wanted to re-scale it to 400 m $\times$ 400 m, you'd give each new, larger cell the average elevation on the 4 smaller cells that comprise it, but the sum of the 4 biomass values.

• @kwinkunks, what do you think of "pycnophylactic" as a term to describe this type of data? It's not generally used to describe the nature of data, but rather a property that, as best I understand it, requires the sum of the parts to be the total of the whole. – J Kelly Nov 20 '15 at 13:11
• OK, that's my new favourite word, but do remember what Twain or EB White or whoever said about \$10 words... Srsly though, whatever you call it, you're going to have to define it carefully. – kwinkunks Nov 20 '15 at 13:17

Count data.

Quantitative data that varies discretely and arbitrarily along some scale can be called count data.

Nick Chrisman (1995; Beyond Stevens: A revised approach to measurement for geographic information, presented at Auto-Carto; see this PDF for a transcript) pointed out that there are many more typologies of measurement than the 'classic' four proposed by Stevens and outlined in Wikipedia's Typologies of measurement article.

None of the measurement typologies are rigid or prescriptive, but Crisman is not alone in recognizing counts as an important statistical data type:

Another class of geographic measurements consist of counts aggregated over some region in space. Counts are discrete, since there is no half person to count, but a count captures more mathematical structure than the other discrete levels (nominal and ordinal).

Mosteller and Tukey also called them counts (see Mosteller's book, Data Analysis and Regression).

It's clear to me that the concept is a good fit for, say, population, but your biomass example seems intuitively less clear-cut. The point is that it's a countable quantity, as opposed to a ratio scale, so it might just be a matter of being careful how you define the term.

This answer was edited after clarification in the comments.

• Not continuous, but it's a good thought. Elevation, for example, would be continuous but not summed on aggregation, having no "mass." Whereas something like population is discrete, and only continuous by illusion. – J Kelly Nov 2 '15 at 22:31
• Hm, not sure I follow. Can you edit your question with one or two specific examples of what you mean by 'summing on aggregation'? – kwinkunks Nov 2 '15 at 22:45
• If you had rasters of biomass and elevation on 200m x 200m cells, and you wanted to re-scale it to 400m x 400m, you'd give each new, larger cell the average elevation on the 4 smaller cells that comprise it, but the sum of the 4 biomass values. – J Kelly Nov 3 '15 at 1:28
• I edited the question and the answer after you kindly helped me understand what you are asking. Interesting question! – kwinkunks Nov 3 '15 at 13:31