Does anyone know of good reference material on exploratory analysis and diagnostic plots for count data?
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Even given your extended description of your project in the comments it is, IMO, still too broad a question to give much useful advice. Specifically for analysis of categorical data (of which your count data would seem to fall within given the description), I would perhaps suggest Michael Friendly's book, Visualizing Categorical Data. It is specific to analysis in SAS, but there is also an R pacakge, vcd, which implements many of the same graphs. Potentially 20 values though will be a stretch for some (many?) of the suggested categorical displays.
For diagnostic plots, I would suggest John Fox's Regression Diagnostics green book. It is in the context of linear regression models, but the majority of same diagnostics (or very similar ones) can be utilized for generalized linear models as well.
I suspect most advice given in general for EDA for continous data types could be fairly easily extended to low count data. So I wouldn't be fixated on looking for resources specific to count data. It matters more for models, but the way to graphically explore/present/diagnose those models should be fairly similar.
Have a look at this book (and associated R package) M Friendly: Visualizing Categorical data http://www.amazon.com/Visualizing-Categorical-Data-Michael-Friendly/dp/1580256600
(Given that the author has been working for SAS, there must be some code for that system as well ...)