"Parents of lower income and with less formal education spank more often".
I suspect those factors should have more weight in their hypotheses than the idea that
"Corporeal punishment correlates to higher levels of acting out in school and trouble in academic performance".
Lots of issues exist in many families with low incomes and lower education levels. Those would be better factors to be studied to find correlations for why children act out and/or are not as successful in life.
My sibs and I were spanked (wooden spoon and dad's belt). We are all college grads and have good jobs. Yes, I suffer with depression, but I view that more as a genetic issue.
"The American Academy of Pediatrics and The American Psychological Association oppose striking a child or adolescent for any reason". Fine to say - but none of them were there helping me raise my children. I did my best not to spank - but sometimes a little pain in the butt was the wake-up call my children needed.
Just my 2 cents.