I measured count data across different sites for multiple dependent variables. I encountered a problem with zero inflation, so I added a count of '1' to all my data points, converted all count data to relative proportions (densities), and arcsine transformed my entire data set.
Graphically, it appeared that my data follows a poisson distribution. Consequently, I measured the mean and the standard deviation (not variance), and found that they are approximately equal for some dependent variables, but not all of them. To get an idea about how different the mean is from the standard deviation, I measured the ratio of mean: standard deviation, and the results ranged from 0.29 to 1.34, with an average of 0.81.
My question is: How important is the assumption of mean = variance for analyses of data based on poisson-distribution generating transformations?