How to make a good color intensity scale? I am by no means good in statistics, but I think I have come to the right place.
My question is simple:
My problem consists of comparing the population of several states in a small country, but some states have a population of 3000,000 and some a population of 2,000.
I am painting it on a map, and the "intensity" of the color depends on how the population of every state compares to the population of the whole country.
The problem is that the states with a lot of population are shown with really intense colors and the small states barely have any color.
Is there an easy way to "normalize" or make the data comparable?
I dont know if I am explaining myself properly but I hope some one can help me.
Please comment if my question is not clear and I will clarify.
Thank you for your help!
 A: I'm sorry, but to me it sounds like you are trying to fix what isn't broken.  In fact, you might even be trying to break what isn't broken.  When you have a quantitative variable (here, population) that spans a wide range, then whatever metric you use to represent it should also span a wide range.
But for all things related to color (and esp. maps), the key source is, I think ColorBrewer
A: Good question, One solution is to rescale the colors to have them more uniformly distributed, or to a distribution with lower tails... but then your legend has to be clear enough because deforming the scale, somehow, is unfair... 
For example, in R, rescaling a normal to a uniform . (what you have maybe goes more the other way since you have large tails and you want them smaller, but the principle is the same) 
X=array(rnorm(10000),c(100,100))
ramp=colorRamp(c("blue","cyan","white","yellow","red"),space ="rgb")
kleur <- rgb( ramp(seq(0,1,length=200)),max = 255)
par(mfrow=c(1,2))
image(X,col=kleur)### image without rescaling
Fn=ecdf(X)
ScaledX=array(Fn(X),c(100,100))
image(ScaledX,col=kleur)

A: You could divide by the total population. This would ensure that everything lies between 0 and 1. If the scales are still too disparate, consider a log scale.
A: I feel awkward asking it, but are you really committed to using colour to portray a quantitative amount? Is there no way to put a bar in each state, whose height represents the quantity?
Another way might be to show the map with areas representing the geographic areas, together with a map where each state's area is proportional to the population size - similar to how the sensory homunculus does. But that would be a painful amount of drawing - I don't know of any way to automate that (though it may exist)
A: Your stated objective: 

Compare the population of several
  states in a small country.

Your stated problem: 

Since some states have a population of
  3000,000 and some a population of
  2,000. Is there an easy way to
  "normalise" or make the data
  comparable?

Aim of normalising your data before mapping
This answer will be lacking since I am not sure of the context of why you are making the map.
Nevertheless, here are some thoughts to explore: Normalise your data so that the map provides interesting meaning to the map's potential readers, so they can link what they see on your map to some concept they normally think about. Basically, I think your new normalised numbers should be linked to some qualitative concept that the map readers find interesting to understand (random tidbit: Measure = Quantity x Quality, Hegel). 
Two proposed ways to normalise your data
1. In order to give a sense of how much open space is in each state. 
Create a new state variable for population density by calculating the population divided by total state area.
2. In order to make the coloring of the states contrast with one another.
Create a new state variable by calculating the deviation from the mean of each state. For example, say you have 3 states with populations as follows:


*

*State A is 100.

*State B is  50.

*State C is 1.


The mean will be be about 50.
The new variable's values for each state will be as follows:


*

*State A is +50 (color intense green).

*State B is  0 (color grey).

*State C is -49 (color intense red).


You can use any color scheme where positive numbers contrast with negative numbers (google 'colorbrewer' for lots of examples of color schemes for maps). 
