I have data that closely resembles a chi squared distribution on the interval [0,1]. I want to do a t-test on two groups within this data, however, it's anything but normal because of the 0 bound. A square root transformation helps to flatten the distribution to resemble the right half of a normal distribution, which is nice. If I copy and mirror (duplicate, multiply by -1, append to df) the tranaformed data across the y axis, the new data's Shapiro-Wilk test p-value is ~0.8. That's nice, but is it "legal?" I don't think it is, but figured I'd ask. My education is mostly applied, and I'd like to show analytically whether or not this violates any assumptions of the t-test or damages the integrity of the data. TIA