How to statistically and graphically compare distributions for nine groups where group sample sizes are unequal? I conducted a study in which I collected the height, width, and weight of individuals from 9 different races (i.e I collected 10 to about 30 samples per race).


*

*How can I can display the distribution of the data for each group for a given variable (e.g., height)? I have thought of using histogram but then how do I handle the missing value ranges.

*What other statistical approaches and visualization would be suitable for examining similarity in distribution?

*How could these approaches be implemented in R?

 A: For multiple groups with 10-30 data points per group, I like "dot plots" (as I call them), which you can create with stripchart() in R.  I always use method="jitter" and pch=1.  
You might also check out the beeswarm package, which makes similar plots but with deterministic placement of points.
A: Descriptive Statistics


*

*You can produce basic tables of descriptive statistics (n, mean, sd, min, max, skew, kurtosis) for each of your dependent variables by race. describe.by in the psych package can do this. Several other options are presented in response to this question of describing data by group.


Visualisation


*

*If you want to compare distributions by group graphically, then I'd produce density plots by group. With 9 groups you are probably on the border of where I would switch from showing the densities overlayed with different colours to using a trellis style approach. You could use the densityplot() function in the lattice package to produce either an overlayed or trellis style plot. Also check out the example on quick-r of using the sm.density.compare function from the sm package.  And here's a ggplot2 example.


Statistical analysis


*

*ANOVA (or possibly MANOVA) optionally with post-hoc tests are possibilities. In R you could use the lm function because it will automatically code factors like race.


Of course your density plots, descriptive statistics, and statistical analyses would all be more accurate if you had more data for your groups, particularly for the smaller groups.
