# How to analyze percent data when most of the data is 0%?

I have a set of percent data on histological abnormalities in fish gills and I need to compare the results between two sites A and B. We analyzed abnormalities in lamellae of a particular gill arch. For example for fish 1 we counted 500 lamellae and noted the number that had abnormality Y. The majority of the data is 0%. That is, in most fish, the lamellae counted had no such abnormality present. Obviously when I try different transformations the distribution does not change because of all the 0s (I have attached a graph of the distribution of the data). I do not know how to analyze this data. • It sounds like you essentially have scaled count data. It should probably be analyzed as count data, perhaps as a binomial GLM or possibly a zero-inflated binomial – Glen_b Oct 5 '14 at 4:50
• It's not correct to say that transformation has no effect on such data. What is correct is that any transformation you could try will map a spike of zeros in the distribution to a corresponding spike in the transformed distribution. That's less of a problem that you may think as other methods of analysis are available any way. I would start a comparison between sites in terms of % of fish with abnormalities and mean abnormality of the latter. – Nick Cox Oct 5 '14 at 7:54

It seems like you'd want to convert it to a binary variable (mutations vs not), then compare frequencies between sites with Logistic Regression or similar.

Fish are measurement units. Each fish has own total. Proportions may be modeled by the beta distribution. In particular this data may be modeled with the beta[0,1) distribution; where 0 is included and 1 is not. Analysis can proceed in to steps:

1) Estimate the proportions of 0s and >0 by a finite mixture. See SAS manual for the FMM procedure. For a similar case I used this code:

proc fmm data=ddd componentinfo technique=trureg; class case; model percent = case / noint dist=beta k=1; model + / dist=constant k=2; probmodel ; run;

Instead of k=2, you might need to use k=1.

2) Using DOI: 10.1037/1082-989X.11.1.54 and these 2 references you would be able to ascertain differences among sites: http://support.sas.com/resources/papers/proceedings11/335-2011.pdf http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.470.7064&rep=rep1&type=pdf

Also (not tested) could use module 'metamix' for STATA or Package ‘zoib’ in R