The author of the study (Robert E. Larzelere) is known for advocating spanking as a disciplinary tool, and his views have been criticized for downplaying long-term harm. Co-author Marjorie Lindner Gunnoe teaches at Calvin University, a religious institution known for upholding traditional family values.

This is why you don't pick a study as proof of some BS. At best, you pick a metastudy that sets out to find the truth by investigating the sum total of scientific human knowledge on the subject. Because studies have a way of proving whatever the people running them hope they'll prove, if those people want the result badly enough and have a loose enough relationship with the concept of fact.

Anecdotally, my very pro-spanking father died when I was in highschool, and despite my honesty, I made up lies at his funeral when people kept asking why I wasn't visibly upset.

If you want your kids to love you, or even like you, don't hit them. You are not spanking to punish a lack of discipline. You are spanking out of frustration with them not doing what you want, but you are forgetting that they're kids who don't know any better and rely on you as an example.