ANOVA and Count/Percent Data

Question

I'm just starting to work with some count data and I'm still trying to understand some of the complexities of it, so any help would be greatly appreciated. First the simple version, and then the potentially more complex version.

I have a dataset that looks something like this:

Group   Count
L         4
R         5
C         9
L         16
L         3
R         8
C         5

Etc.

A central part of my research question is within/between group variation; my hypothesis suggests that observations in L, for instance, will be more like each other than they will observations in C and R. There are some 0 observations, but not a great amount of them. (Edit: The data describes the number of articles over a time period by a news outlet on a given topic. Group is a characteristic of the news outlet.)

Because it's count data, I understand I can't really use a straightforward one way ANOVA, so what should I do?

Now the more complex version: I also have those observations in Count as a percentage of each individual across 20 different test cases. So this data looks more like:

Group   Perc1     Perc2   ...  PercN
L         .3         .04         .2
R         .15        .6          .02
C         .9         .04         .2
L         .21        .08         .34
L         .13        .75         .02

Etc. (Edit: Each row represents the proportion of that outlet's coverage on each topic measured. Perc1 = Count1 / (Sum(Count1..CountN) .)

What would be the best approach? I'm comfortable using R or Stata, whichever is best/easiest. This is somewhat similar to this post, but I'm not sure it fully applies.

Thank you in advance.

Answer 1

I assume that were your data normally distributed with nearly equal variances, you would like to try something like an omnibus test/pairwise multiple comparisons tests. And I assume that you would want to adjust your p-values (or, alternatively, your rejection criterion) for multiple comparisons.

Your first example (with count data) could be approached using the Kruskal-Wallis test as a nonparametric analog of the one-way ANOVA, followed by Dunn's test which is akin to performing rank sum tests based on the same rankings from the Kruskal-Wallis test, and using a pooled variance term based on rank sum distributions. The accuracy of the Kruskal-Wallis test and the Dunn's test statistics will be somewhat compromised by ties (technically these tests are of continuous data), but the adjustments for ties typically implemented in software packages performing these tests will help compensate—the larger a range of count values you have, the better. Multiple comparisons adjustments here for the win!

Your second example looks like a repeated measures/blocked design, so you might consider Cochran's Q test as a nonparametric analog of the one-way repeated measures ANOVA specifically for binary outcomes (which your percentages/proportions are one representation of), followed either by Cochran's Q tests between pairs or by McNemar's test between pairs (these are equivalent). Multiple comparisons adjustments here also for the win!

References
Cochran, W. G. (1950). The comparison of percentages. Biometrika, 37(3/4):256–266.

Dunn, O. J. (1964). Multiple comparisons using rank sums. Technometrics, 6(3):241–252.

Kruskal, W. H. and Wallis, A. (1952). Use of ranks in one-criterion variance analysis. Journal of the American Statistical Association, 47(260):583–621.