Empirical logit transformation on percentage data I have already used the logit transform on my outcome variables (which are displayed in percentages). However, this obviously gives me -INF values and since my data includes a lot of zeros in some instances, this makes it hard to analyse. 
I have now tried an empirical logit transform, adding the smallest non-zero promotion to the numerator and denominator of my variables to remove the -INF values (as suggested in http://www.esajournals.org/doi/abs/10.1890/10-0340.1). 
However, now my data are very non-normal again. I have tried experimenting with error terms to add to the logit transform but since have had no luck. 
Is there any way I can find a value to add to my transformation to ensure normality?
 A: I've had luck with setting epsilon to half of the smallest non-zero value and replacing all 0 values with epsilon and all 1 values with 1-epsilon. Then apply the logit transformation. 
This method keeps the original form of the logit transformation, but allows 1 and 0 to be transformed to values that match the overall shape of the intended transformation (note the black dots in the figure at raw=0 and 1).  In particular, it preserves the quality that 0.5 is transformed to 0, and the rest of the values are symmetric.  
On the other hand, adding the smallest non-zero value as described in the paper changes the shape of the curve and destroys the symmetry. 

A: One approach, which would solve the problem you are having, is to use a robust regression method on the raw, untransformed values. For example, in R, you could do the following:
example = data.frame(outcome = c(0,0,0.3,0.7,1), 
                     predictor = c('left','left','left','right','right'))
m = glm(outcome ~ predictor,example,family=quasibinomial())
summary(m)

