I'm trying to integrate effect size measures into bio-assay studies (Cohen's d and others) but am reluctant to use the thresholds identified by Cohen and would much rather a scheme centred on the data I actually produced.
Cohen's scale is a common and simple one. You can use three other methods which are more complicated and precise. They are p-value, Beta value (type II error) and power function (1-beta). All of these three statistics are related. The most common one is p-value which shows the probability of seeing a value in a population (it's different from alpha level=type I error). After p-value, the power function is more informative than beta, but still the choice is yours.
By the data you already produced, do you mean the effects are on a metric that makes sense natively? In other words, are the numbers (mean differences, regression coefficients, etc.) intuitively meaningful to readers in your field?
If so, I would not convert to effect sizes at all. Why throw away the raw information? Instead, I would report your point estimates and confidence intervals for those estimates and interpret them directly -- you and your readers would know what constitutes a "meaningful" effect without reference to standards that were not developed for your field.
Check out a key search with Dr. Jeff Kromrey. He is a specialist in effect sizes and power. There are eight other commonly used effect sizes that are not Cohen's d. We did a study on them and there are three others that perform pretty well in comparison to Cohen's d. there are macros that use these effect sizes and simulations which will show you the effect size information. Check out our paper Dicotomized d: Patrice Rasmussen et al. with Dr Kromrey.
There are box plots which show you all eight effect size formulas and results. There were three that had acceptable . If I remember only d-b is had result which produced extreme variance differences. The paper is on my page it will at least teach you all about effect sizes and the other eight types that are widely used yet not as proficient as Cohen. However, there are three choices that were acceptable. Please check the paper. I am studying for quals and I cannot recall all the details.
If you have any more questions after reading our paper then look up Jeff Kromrey and you will find a lot of information.
I very much agree with Patrick. If you have a metric that makes sense, and on which the results can be interpreted use it. If you don't, then how are you going tobe able to make sense of your results anyway?