A very practical way to "test" if your profit factor of 1.5 can be attributed to skill, would be to run a confidence interval on the trades. Excel has it all built in, so you don't even need to know the statistical calculations.
I fully understand that confidence interval calculations work based on assumptions that are somewhat suspect for the distributions in trading, but if I see that I get a confidence for profits being positive of 90% or better, I would consider that much more significant than most other objective measurements.
If anything, the fat-tail distributions seen for profit distributions, tend to make confidence calculations appear less favorable than they actually are (my opinion based on my trades).