Is it possible to compare different frequency distributions with ANOVA and how would you go about it?

Question

For example if I have three different samples of red blood cells, and I created a frequency distribution of the red blood cell size for each sample how would I run ANOVA to compare the differences between each frequency distribution?

Answer 1

It's best to start with the actual sizes for each red cell rather than to pre-categorize the values into histograms.

Look at the data first, with density plots (which you can think of as a type of smoothed histogram) of the sizes for each of your samples. That's provided by standard statistical software packages, with reasonable default choices of the smoothing function. Visual inspection will probably be the most useful comparison both for you and for your audience, as it will show the entire distribution rather than summarizing it with just a few numbers.

As you have individual values taken from underlying continuous distributions of cell sizes, you could do all 3 pairwise comparisons among the 3 samples with the Kolmogorov-Smirnov test. You probably have a large number of red cells analyzed, however, so you are very likely to get some "statistically significant" differences that aren't of practical significance. That's where you apply a combination of the density plots and your understanding of the subject matter to evaluate practical significance.