Data Visualization: Alternatives to Choropleth maps for spatial data and statistical graphics This question is about data visualization and statistical graphics. I have been trying to present statistical data in map. The data is at county level in the US and also at time state level. My data looks some what similar to the one below (sourced from here).
There are two issues with Choropleth maps, small counties tend to be lost and in addition small states (Like Rhode Island, Delaware) cannot be shown. My second problem is it has been hard to engage the audience in the choropleth maps. The heat map such as the one shown below does discriminate the high low values well enough.
I have read few books on data visualization, and none of them seem to have alternative presentation to choropleth maps. So my question is are there any alternative to Choropleth maps to present statistical data?

 A: Choropleths have a number of flaws, as you note. Most infamous is the way a shape size is usually unrelated to it's measure yet the size is very prominent visually (electoral maps are a classic example).
Cartograms strive to solve the sizing issue but distort the geography, which looks odd and can be a problem if you're looking for geographic patterns.
A few common alternatives more applicable to US counties:
Geographic Scatterplot
Draw a dot for each shape. That way every shape gets the same amount of color, though overstriking is still an issue for very tiny shapes.

Micromaps
Works with choropleths or geographic scatterplots. Partition the graphs by geographic sector or some measure, not necessarily the same as the coloring variable.

Custom Coloring
You mentioned needing to focus on a particular range of values. One way to help with that is to use a coloring scheme that highlights that range at the expense of others.

Smooth Contours
It sounds like you want to see individual shapes, but if you're looking for broad patterns, plotting a smoothed contour like in a weather map can be useful (no picture).
No Map
Finally, if the data values are more important than the geographic patterns, consider another kind of graph altogether, such as a ranked bar chart of the top and bottom counties. The general weakness of maps is that they use the two most prominent dimensions (X and Y) for geography and leave lesser dimensions of the data measures, so the geography must be relevant to justify using a map.
A: Here is a slew of examples (hopefully that's OK) which try to show variations on the map theme while providing a range of flexibility that is lacking in the standard choropleth.  This may overlap other answers, but I am trying to be as exhaustive as possible.
Favorite: Interactive density with multiple levels of scale
Before going through them, I will say that the "racial dot plot" of US census data is one of the most compelling visualizations that solves this problem.  It is highly interactive, handles scale, and allows for an incredible density of information.  Creating it may be difficult, but it sure is beautiful.  Check it out first: http://demographics.coopercenter.org/DotMap/index.html

After that, here is a more systematic take on the examples.
Option 1: plot the data based on the size of an object instead of coloring an area.  This can be with a bubble, density, or weather map style.

*

*This is called out on the same site that you linked to: http://indiemapper.com/app/learnmore.php?l=dot_density

*This is done with a bubble plot in this example: http://bost.ocks.org/mike/bubble-map/


*The racial dot map above is another example.

*The "stop and frisk" viz is also a great example of using density to encode info. http://www.nytimes.com/interactive/2014/09/19/nyregion/stop-and-frisk-is-all-but-gone-from-new-york.html


*Here is a weather map example showing how drought affects the US over time.  It is good for an overall spatial representation that is independent of man made boundaries. http://www.nytimes.com/interactive/2014/upshot/mapping-the-spread-of-drought-across-the-us.html?abt=0002&abg=1

Option 2: extract the shapes of the counties/states and plot them small multiple fashion with the same scaling

*

*The same site you linked to talks about "non-contiguous cartograms".  You can extend this idea to scale the states all the same and show them in a grid or other orderly arrangement.  This allows small states to be shown at the same level of detail as large ones. http://indiemapper.com/app/learnmore.php?l=cartogram

*Along that same vein, here is an example of the small multiples comparing different bike sharing options across the world.  It removes boundaries and scale and encodes info as density. http://qz.com/89019/29-of-the-worlds-largest-bike-sharing-programs-in-one-map/

Option 3: allow for a degree of interactivity so that the scale can be changed at will by the user

*

*The racial dot map is the best example of this above.

*There is another stop and frisk example which allows for zooming in and out on the neighborhoods for emphasis. http://www.nytimes.com/interactive/2010/07/11/nyregion/20100711-stop-and-frisk.html?_r=0

Option 4: have multiple visualizations that highlight areas of interest at the small scale

*

*Some of the NYTimes examples do this.  Here is one showing baseball fans over the US with small scale maps of the intersections.  It does a great job of splitting scale. http://www.nytimes.com/interactive/2014/04/23/upshot/24-upshot-baseball.html?abt=0002&abg=1


