<p><strong>Count data.</strong></p>

<p>Quantitative data that varies discretely and arbitrarily along some scale can be called <strong>count</strong> data. </p>

<p>Nick Chrisman (1995; Beyond Stevens: A revised approach to measurement for geographic information, presented at Auto-Carto; see <a href="http://mapcontext.com/autocarto/proceedings/auto-carto-12/pdf/beyond-stevens-a-revised-approach-to-measurement.pdf" rel="nofollow">this PDF</a> 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 <em><a href="https://en.wikipedia.org/wiki/Level_of_measurement" rel="nofollow">Typologies of measurement</a></em> article.</p>

<p>None of the measurement typologies are rigid or prescriptive, but Crisman is not alone in recognizing counts as an important <a href="https://en.wikipedia.org/wiki/Statistical_data_type" rel="nofollow">statistical data type</a>:</p>

<blockquote>
  <p>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). </p>
</blockquote>

<p>Mosteller and Tukey also called them <em>counts</em> (see Mosteller's book, <em>Data Analysis and Regression</em>).</p>

<p>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.</p>

<p><em>This answer was edited after clarification in the comments.</em></p>

CC BY-SA 3.0
2015-11-02T22:31:19.860Z
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
CC BY-SA 3.0
2015-11-02T22:45:42.877Z
Hm, not sure I follow. Can you edit your question with one or two specific examples of what you mean by 'summing on aggregation'?
Matt Hall
CC BY-SA 3.0
2015-11-03T01:28:08.560Z
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
CC BY-SA 3.0
2015-11-03T13:31:30.657Z
I edited the question and the answer after you kindly helped me understand what you are asking. Interesting question!
Matt Hall
CC BY-SA 3.0
2015-11-02T16:33:00.237Z
2015-11-03T13:30:46.230Z
2015-11-03T13:30:46.230Z
Matt Hall
<p>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? <em>Categorical</em> for the latter, perhaps, but what for the former? </p>

<p>To illustrate <em>aggregation by sum</em>: 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.</p>

CC BY-SA 3.0
2015-11-20T13:11:55.913Z
@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
CC BY-SA 3.0
2015-11-20T13:17:06.863Z
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.
Matt Hall
<remote-sensing><terminology><statistics><cartography>
What is the technical term for spatially aggregated measures?
J Kelly
# What is the technical term for spatially aggregated measures?

(Asked by: username_0 on 2015-11-02)

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.

**Tags:** remote-sensing, terminology, statistics, cartography

> **Comments:**
> **username_0**: @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.  
> **username_1**: 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.  

---

## 1 answers

### Answer by username_1 on 2015-11-02. Score: 3

**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](http://mapcontext.com/autocarto/proceedings/auto-carto-12/pdf/beyond-stevens-a-revised-approach-to-measurement.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](https://en.wikipedia.org/wiki/Level_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](https://en.wikipedia.org/wiki/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.*

> **Comments:**
> **username_0**: 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.  
> **username_1**: Hm, not sure I follow. Can you edit your question with one or two specific examples of what you mean by 'summing on aggregation'?  
> **username_0**: 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.  
> **username_1**: I edited the question and the answer after you kindly helped me understand what you are asking. Interesting question!  

---

