The problem is that if there is a custody dispute, then probably at least one, and usually both, sides will be pleading circumstances which pull one way or the other. And any court is likely to issue fact findings that lean the same direction as the custody order. So, if you are going to find what bias exists in the court system you can't look at just custody orders and legally determined facts, you've got to separately readjudicate the fact disputes with an unbiased process. Which is...problematic.
That said, instead of changing individual decisions you can punish the state for outcomes whether they be intended or unintended. Disparate impact (https://en.wikipedia.org/wiki/Disparate_impact) is one such tool the courts are already familiar with. There's more nuance to that which can't be ignored - a person can sue an entity for disparate impact but disparate impact is also calculated regularly with respect to lending. The same could be done for custody.
No, I mean the study would have to readjudicate the cases (not change the legal outcome, but redivining the actual facts from the trial record) to identify differing treatment in different factual circumstances between states.
I didn't notice that bit, so good find. I was bummed to see that most studies don't actually try to ascertain who usually wins when both parents want custody and there are no extenuating circumstances. That seems like an obvious metric to track the health of custody laws.
This is the only government data I found: https://www.census.gov/content/dam/Census/library/publicatio...