It is, of course, possible to prove pretty much anything using statistics, but I doubt this is one of those cases. Here's the basic A/B comparison:
Smacking/spanking/etc allowed: crime rates/etc value at year XXXX is "X"
Smacking/spanking/etc banned: crime rates/etc value at year YYYY is "Y"
The years and their respective values are not numbers in any way controlled by the lawmakers. They are yearly statistics. They are also numbers that can be obtained in similar manner from other countries, as reported by the other country.
Now, if Y<X, I'm sure you agree that in principle it means the new legislation works. Note that since they avoid the issue of defining "smacking" as opposed to "hitting" by making them equal for the purposes of the new law, any smacking/spanking/etc is a crime and thus means every reported instance after the legislation was passed affects Y.
Of course, there is any number of other reasons for crime rates fluctuating so getting relevant numbers is hard. What causes what? Does one change correlate to the new figure or not?
So the easiest solution is to interpret the numbers using the same methods for both X and Y. With everything else being equal, the easiest explanation (attributing the smallest change) is likely (or at least possible) to be true.
It's not perfect but it's what we have.
What's the alternative? Well, you could say that "no, I don't believe 'smacking' is harmful to my child" and be right, but in a situation where the laws also are permissive enough to allow the person who *hits* his child or smacks it with intent to harm to go unpunished, the statistics will be skewed, but for you it will be in the wrong direction for what you were trying to prove.
So your burden of proof is actually much harder than mine. For my study, I have been able to say "ban it all" and watch what happens, but you have to a) define "smacking" as opposed to "hitting", b) provide the statistics that support you definitions, and c) interpret them in such a way that a comparison between them and my study is possible and relevant.
See the difference? If I choose to ban every form of smacking, regardless of definition, my work is easier, with everything else being equal, and I actually don't have to work the numbers as hard.
If we assume that both parties might work the numbers in their favour but the basic data is freely available, it should be easy to make a feasibility study.
What does this mean? Well, only that I do have the numbers and an accompanying study, but you don't. If you mean to prove me wrong, you'll be busy for quite some time.
Further than that, I think Odeon.
If I was to say that one child was beaten by both parents daily and over nothing, with randomness and ferocity. When they were "smacked" It was with extension cords and until they bled. Then I was to say that child number two was smacked on the bottom by an open hand not hard enough to mark them and only when they were naughty, and was stopped when they reached an age that they could be reasoned with. I think in this instance you are not talking about two children who were parented the same. I think that you could possibly see one becoming badly adjusted and dysfunctional whereas the other possibly would not be at the same risk.
But here is the kicker. If someone defines smacking to make both child one and two part of the same study group then any statistic reliant on the results will tar child two's upbringing with the upbringing of child one and likewise child two's behaviour will be tarred with that of child one. Sure I have no doubt that some of the kids like child two will be tearaways. But I would say that some kids who were not smacked will be affected.
But we can go further, I would assume that if the laws were passed preventing smacking that the culture around this had changed too. I still remember when breathalisers were introduced in Western Australia. It changed the drinking culture. People suddenly were aware that drinking a six pack at a friends and whilst watching the footy was needing to change. The really excessive drink drivers stopped risking it, because their time was up (mostly - exclusions to the general rule and all that not withstanding) . It did ask people to be mindful of what they drank before driving. Where they were excessive they got punished. A glass or two was no bother.
This may be similar to the change of culture just prior to the no spanking laws. When the culture or community was suddenly mindful of a problem. The types of parents who were like child number one's started becoming a rarity because they felt a lot more eyes on them. So the ones who remained where the ones not prepared to change.
Further still, if the community driving these changes (not making moral judgements to merits) were wanting to make the best cases then are they likely to water down the study groups by removing the parents like those of child number two away from the parents of child one or make them equally culpable? Are they going to consider child one and two's upbringing and criminal records the same? Sure it is easier.
Not fair. but easier.
Yes were I to I could, given time and research and enough drive find ways to qualify and quantify this to change results I think do not give decent figures as their definitions are too broad and their results too willing therefore to be interpreted too generally.
I could even perhaps suggest forms of non-smacking parenting approaches that are flawed and make a case for what they may prove. Being clever and with creative definitions, I am sure I could run down most non-smacking parenting available to parents. Would be completely unhelpful aside from a way to give parents an unfair needling.
But I am not so inclined. I can agree to disagree. I do not think that parents who are bad parents should be rewarded or let off from punishment. Do not know any adult who was bought up in abusive households living with fear, angst, pain and dread, that would be well disposed to their parents. I do know a lot of adults who say things like "I got an occasional smack on the bottom for being a little shit. but Mum and Dad were pretty cool" but I have yet to hear anyone say "When I was a little kid, I used to be bone tired when Dad finally pull up in the drive way. Late. He would make a racket coming in. He knew he was in trouble with Mum. I would shake because it was the moments of reprieve before the fights. I could not cry because I was about to go out and face him and stop him getting angry with Mum, because she was little, almost as short as me. When he was out I was the man of the home and protect her from noises outside. I had to protect her now because she was upset and scared. I was frightened. I came to love them both." Will not hear it from me, either
I think it is a little off collating them all together and I could define them differently 10 ways but it will not matter if they are included together for the definitions stipulated in the studies.