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When reporting estimates you should always include the margin of error. There are conventional ways of reporting margin of error in a table, text or graph. But, how do you report margin of error for data visualized on a map?

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I didn't have the option of making this a community wiki. @Mods, please change to community wiki if you deem it appropriate. I expect this may have more than one 'correct' answer. – Sean Aug 1 '11 at 14:58
converted to community wiki. – Mapperz Aug 1 '11 at 16:41
Margin of error of what? Position? Something you're plotting? – whuber Aug 1 '11 at 20:50
It seems he is referring to data visualized on the map. – Nathanus Aug 1 '11 at 21:06
@Nathanus. Maybe. But the question is meaningful, with no changes whatsoever, to a situation where the margin of error refers to position, even though that's a different problem. Whence the advisability of clarification. – whuber Aug 1 '11 at 22:03
up vote 9 down vote accepted

A rencent journal article I came across discusses exactly what @Aksel in another answer (Sun and Wong, 2010) (It is available here for free online, but that link is void of pictures of the maps as far as I can tell). Essentially they suggest they prefer the overlay approach as opposed to the small multiple approach (i.e. making two maps, one showing the estimate and another showing uncertainty).

Value by alpha maps as have been mentioned on this forum are an alternative way to representing uncertainty than the overlay of the dash lines (which I find more intuitive).

Other works that I have read that may be of interest (although they don't directly answer the question) are;

  • Mapping the Results of Geographically Weighted Regression (Mennis, 2006) PDF here
  • All maps of parameter estimates are misleading (Gelman, 1999) PDF here
  • The original article I cited is Incorporating Data Quality Information in Mapping American Community Survey Data (Sun and Wong, 2010)
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I have seen it done on a choropleth with the coloring showing the estimate, and a dotted/hashed overlay representing coefficients of variation. But I have not seen a standard for this.

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As pointed out by Andy whiteness blurring is an option. A different option is using some kind of presentation filter: you only show those results which are more certain than a certain threshold. You could provide different maps with different thresholds.

The lowest threshold could be the standard deviation of the whole population (or some very simple model, depending on your data). If a complex map procedure is used with a high uncertainty, large areas may have uncertainties higher than this standard deviation. (depends of course on your variable: for Organic carbon in a soil that statement is true, for visualising eg the error on an elevation map that threshold doesn't make sense at all). Some shameless self promotion: a paper that uses such a technique is: this paper

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For point level data, Jay Fowler's thesis 'Cartographic communication of point level uncertainty' (link to citation, full text, poster; found via CartoNews) provides excellent overview of methods:

enter image description here

Some more visual examples.

As @ako suggested, dotted overlay might be used to represent significance. Example from Nagy, C., et al. (2014). Hierarchical spatio-temporal mapping of premature mortality due to alcoholic liver disease in Hungary, 2005-2010. European Journal of Public Health, 24(5), 827–33 (link, paywall):

enter image description here

Somehow opposite method, that blurs away areas of lower significance can be found in Cancer Atlas of Northern Europe:

enter image description here

Later maps of NORDCAN atlas seem to switch to more aggressive shading:

enter image description here

Apologizing for my shameless plug, here is a map from publication I was involved in presenting results from Bayesian spatial model. Uncertainty of area (postcode) level odds ratios estimated by the model (which are presented by hues of the squares) was incorporated as a background choropleth map.

enter image description here

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Many good references on the topic can be found on Kristi Potter's website – radek Oct 21 '15 at 11:48
CGV: Large: Collaborative Research: Modeling, Display, and Understanding Uncertainty in Simulations for Policy Decision Making is another place providing few resources on ongoing projects exploring the topic. – radek Jan 6 at 13:55

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