# Choosing intervals for a map of race in the United States

I'm creating an open map layer of race in the United States using Census Data. This layer will be publicly available in the near future as "Justice Map". The goal is to help others create maps using this data layer. I'm generating tiles with TileMill. I will be creating tiles for Google Maps zoom levels 0-13 -- all the way down to the block level.

How should I choose my intervals for coloring the map?

The problem is that all the non-white racial groups are heavily concentrated in medium or small sized areas (notably Asians and Native Americans). I don't want to distort the geography to make the size of a state proportional to its population, as that would make it hard for other people to use this open map layer.

The maps below are an example of percent black for each census tract. However, I will be doing this for other races including Black, Asian, Native American, Hispanic, White Non-Hispanic, Multi-Racial, other race, and Hawaiian or Pacific Islander.

So far I'm planning on using a sequential color scheme from colorbrewer2.org and nine categories.

I'm going to create maps for counties, census tracts, block groups and blocks.

Categorization Methods

Equal Breaks: it makes the map look too empty for most racial groups.

Jenks Natural Breaks: also makes the map too empty.

Percentile: map looks nice, but emphasizes very small differences. For percent Black and census tracts it has breaks at 0.4%, 0.8%, and 1.6% (so 33% of the census tracts have 1.6% or less blacks).

I want to give more emphasis to the tail distribution than the Jenks algorithm does, and less emphasis than percentile.

I made up my own distribution without using an algorithm. Then I tried to fit an algorithm to it. I get an approximate fit using a 10% weight for equal breaks, and a 90% weight for percentile. This makes the first break (percent black) be 0.4*0.9 + 10*0.1 = 1.36. Next break is 2.8%. This example uses the algorithm (and a new color scheme):

Yet another idea is to use a Sliding Percentile method. For instance, instead of using deciles (putting 10% of the data in each category) - you could use percentages like 18, 16, 14, 12, 10, 8, 6, 4, and 2. Or you could use a geometric series with a ratio of 1.1 or 1.2 between the percentile in each category. This method would balance the goals of having the data falls into different categories, and that the difference between the categories is significant.

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Have you tried posting this question on cartotalk.com? It's a cartography forum and has a very good mix of academic and professional users relating to this type of work. You would definitely get some good feedback there if you're question isn't answered to your liking here. – clhenrick Sep 24 '13 at 0:03
It is difficult to tell what you need because (a) the maps are wholly unexplained, having no legends or descriptions, and (b) understanding the purpose and audience of a map is crucial to its design. Could you edit your question to clarify these points? – whuber Oct 1 '13 at 14:01
From a cartographic perspective I would be wary of using 9 classes for qualitative data. Once you get over 5 it gets harder to distinguish the data types on the same map. – clhenrick Mar 8 '14 at 14:24
True, but less true for data types with patterns that the observers already understand. For instance, race in most US cities. I'm balancing the goals of being able to quickly read the map with being able to use it for data analysis. – Aaron Kreider Mar 12 '14 at 20:12

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Interesting. Unfortunately, it looks like it could have even less polygons in the "high" categories than Jenks. I'm trying to get a balance between the look of Jenks (and its lack of color) and percentile (which has too much color as it gives too much emphasis to small differences). I want to give more weight to differences in the tail of the distribution than Jenks, but less than percentile. – Aaron Kreider Oct 1 '13 at 21:06

I could use a sliding percentile system.

Say there are nine categories. One approach is to decide how much of the data tail should fit in the lowest category to ensure that it has an adequately large percent range. For instance, I might want to have 22% of the data be in first category. Then the percentile in the remaining categories could be calculated using a ratio.

In this case: 22 + ratio*22 + ratio^2*22 + ... ratio^8 *22 = 100

I think the ratio can be calculated using ln.

Alternatively the percentile ranges could be an arithmetic sequence (18, 15, 12, ... 0).

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How do you solve for this using ln? I'm doing something wrong. I subtract 22 from both sides, take ln, but I end up with 36 ln(x)= 4 (or really a number near 4). And this gives me an x of 1.039 (or so) when I really it should be around 0.85. – Aaron Kreider Oct 4 '13 at 22:19
Since you have no upvoted Answers to your Question after 8 months, I think you should edit it to revise it with the information you have made above (in a Comment on your own Answer to it). – PolyGeo Jun 22 '14 at 22:04
You mean this comment where I use a mathematical calculation that gives the wrong result? I only get the 0.85 by plugging in numbers - which is not ideal. – Aaron Kreider Jun 23 '14 at 1:56
More or less - it is odd to Answer your own Question and then not to Accept it (or at least to reward another Answer that helped you get there by Accept-ing that). I'm assuming you still don't have a solution but I do not have the domain expertise to be certain. So basically, if you still need a solution I think the best approach will be to revise your Question to try and elicit an Answer that is Accept-able to you. – PolyGeo Jun 23 '14 at 2:02
OK, I understand that. I took your advice and accepted my solution as I ended up using it. I still haven't heard from anyone with a background in this area as to whether my solution is logical. There are a lot of people who make mistakes when they do data visualization and I don't want to be one of them. – Aaron Kreider Jun 23 '14 at 2:07