I would like to unify multiple sample data (of different sizes) into some "unified sample" to evaluate its collective variance. Is this something statisticians do? I thought of unifying multiple samples in the following way :
1.From each data value, reduce the average of the sample it belongs to
2.Then, collect all these modified values from all samples, into a unified sample
I have a good reason to believe that the unified-sample generated this way will distribute normally. Than, I could evaluate the variance of the unified sample and compare it to variances of other unified samples (with F-test). The problem I see with this approach is that the values in the unified sample are not independent, since each of them was created by reducing the sample average from the original value…. I'll be happy to hear your thoughts, suggestions about this.