Scratch that, I've done some tests on it, and apparently it fits an exponential curve pretty well (doing p-p or q-q plots). Also, if I natural log transform the data, it fits very well. However, as you might expect, it fits a normal distribution or t distribution terribly. My question is this, since the natural log makes it look pretty well, am I able to natural log transform it and then run the t-test on it? Because if I run non parametric tests on the data, they come back as insignificant, whereas a t-test shows it as being significant. I want it to be significant, but not at the expense of validity. I realize I lose power with non-parametric tests, so hopefully I would be falsely rejecting Ha.
Finally, I am running the t-test on a group that comes in 10's of percents - 0 (many) to 100 (few) -, and affects a certain dependent variable (lifespan). In SPSS, I select a cutoff point of 25%, that yields significant results...do I need to run a goodness of fit on the <=25% as well as the >25%, or am I able to run a goodness of fit on the whole thing?
Am I correct in assuming I don't need to run a goodness of fit on the dependent variable because it is irrelevant for the comparison of means test?
Pictured are examples of what I'm talking about.