I think DH is too harsh with our DDs (13 months and 4 years). He thinks I'm too soft.
DD1 has started being rude to me and DH thinks I need to take a firmer hand. Whereas I think she's copying his sometimes aggressive approach. If DD1 is being naughty I give her a few warnings, explain why she shouldn't be doing whatever it is and then I make her do a naughty step if she does it again. She's a bright girl and generally understands the implications of things but most toddlers/preschoolers do like to test the boundaries. If she's obviously upset about something though I'll give her hugs and try to get to the bottom of the problem rather than launching into discipline. I think that's a sensible approach, rather than being too soft. Whereas DH will give a few warnings and then shout at her regardless of what the underlying cause is. I think I'm showing her a good example. He thinks she's walking all over me.
After he's shouted at them I'll tell him that I don't like it but he won't accept that as a reason to stop. His reaction is that they need discipline, it's better than smacking them and that we shouldn't 'wrap them up in cotton wool' but prepare them for the real world. I think they've got plenty of time for that during their school years.
He also says that it's the only thing that gets a result. e.g. If DD1 is distracted by something else and won't listen he'll give a couple of warnings (fair enough) and then shout at her to get her attention. The other day she was sitting on my lap when he did this and I felt her physically start - I think that's going too far. We asked her recently if she was frightened of DH. She said she wasn't, which is reassuring, but that still doesn't make it right. Or am I being too sensitive?
I suppose I'm more worried about DD2 who's still so young. Although DH is firmer with DD1 as she's older, he DOES shout at DD2 too. She's not sleeping well at the moment, and a few times when I've worked nights he's told me that he eventually snapped and shouted "shut up" at her. She went quiet so he thought it worked. Whereas I think he's teaching her to not ask for what she needs and that she might become insecure. He did this to her the other day whilst I was trying, unsuccessfully, to settle her in the middle of the night; half an hour later it turned out that all she wanted was a bottle of milk and she settled quite happily after that. I felt so bad for her. 
I think it could emotionally damage them in the long run, particularly DD2 who's still so young. DH however says that there's no such thing as maternal instinct and that my gut feeling doesn't mean a thing. He values logic and common sense over emotion. He also says I'm telling him we should bring up the children the way I think is right with no regard to what he might think is best. It's difficult to know what to say to that. I feel like we should be a team deciding together what's best for the whole family but I do worry when he shouts.
Am I misinformed about child development? I don't want my children to grow up spoilt but I do want them to be confident and happy.
So, after a long-winded explanation,
He needs scientific evidence that shouting is wrong. He won't accept my opinion or something that I might have read on-line or in a book, he needs verifiable proof!
Does anyone have any links to a scientific study proving that children are happier, more confident, well-adapted, etc with positive reinforcement rather than shouting? I'm struggling to find any studies that prove this beyond reasonable doubt.