Then you're not testing the impact of divorce. You're testing the impact of parents who like each other vs parents who don't like each other.
Not if you only include kids of parents who got divorced.
Imagine the following question: For all kids or a sample of kids whose parents got divorced at age 10, did the rate of math proficiency increase or decrease at age 11?
I appreciate that people may not like that question or think it's a good question, but it's not a particularly difficult question.
The problem is that this is the
only question that has been tested. That's where all these "divorce is bad for kids" studies come from: they compare things like standardized test scores from kids from divorced or single-parent families against kids from two-parent households, see the scores are lower, and then conclude "therefore, divorce is bad for kids."
The problem with the conclusion is that it ignored all of the confounding factors. For example, do they group kids by SES? We all know that SES is highly correlated with academic performance, so if you're ignoring SES variations, you're not testing the harm of the divorce itself. And of course what we've all be talking about here: the parental relationship. It's safe to assume that the parents who divorced don't like each other very much and couldn't find a way to get along. But what about the baseline group of non-divorced parents? Some of them may not like each other very much, but have found some way to get along. Some don't like each other but are staying together for some external reason (can't afford to live separately, don't believe in divorce, etc.). Some of them do like each other and get along fine. So you are comparing apples and oranges.
Your data shows that kids from divorced families do worse at math than the broad group of kids who do not come from divorced families. But it cannot show that that those kids do worse at math than kids from unhappy marriages where the parents are staying together from some other reason. And unless you do that apples-to-apples comparison, you cannot conclude that it is the divorce itself that leads to the worse math performance vs. the poor relationship between the parents.
The best analogy I can think of is the college admissions/success data. For years, many many people (including me) have seen admission to a great college as the path to subsequent career success. And if you look at the overall population data, you'd reach the same conclusion, because certainly, overall, Harvard graduates are going to be much more successful in their careers than kids who don't go to college at all, or go to East Directional State U. The problem is that you are comparing a very specific, limited universe of kids -- kids who are smart/hardworking/privileged enough to go to Harvard -- with a much broader universe of kids. Sure, some of those kids will be just as smart/hardworking/privileged as the kids who go to Harvard, but many, many of them will be missing one or more of those traits. So how do you know it's the Harvard education that makes the difference, instead of the IQ, or work ethic, or SES, or lack of connections, or any of a thousand other things?
Well, a few years ago, some scientists had a pretty brilliant idea: they'd compare the career success of kids who attended schools like Harvard with kids who applied and met the standards for admission but were rejected and went to another school instead. Because with those top schools having admissions rates on the order of 5%, there will always be many, many more kids who are just as smart/hardworking/privileged than the schools can admit. And you know what that study showed? No significant difference between the kids who went to a school like Harvard than similar kids who went elsewhere. Which suggests that long-term success is driven more by the characteristics that make you eligible for admission to a top-notch school than the actual school you attend.
The problem with these divorce studies, including the proposed math one, is that you're still comparing a very specialized cohort (kids from divorced/single-parent families) against a much broader universe of kids. And many of the kids within that broader universe will have other traits that will lead them to perform better in math, including happy families, psychologically healthy parents, higher SES, etc. etc. etc. Which is why people keep saying you need a comparable control group. You cannot conclude that A causes B unless your study involves similar universes of study participants, so you take those confounding variables out of play. Or to put it another way: the proposed math study will show, overall, that kids from divorced families will do worse in math than kids from families that are not divorced. But the study cannot show that the kids from divorced families will do worse in math than
the same kids would do if their parents had stayed together. You can mock the anecdotes here about how we're all statistical outliers who benefited from their parents' divorce. Or you can look at it another way: we have the advantage of having witnessed our parents' behavior, and having felt the impacts of that behavior, both before the divorce and after it. So if we are saying that we are better off because we divorced, it's because we actually have something to compare it to -- we've seen, with our own eyes, what the relationship was like pre-divorce, and how that tension made us feel as kids.
Now, I'm not going to blow smoke up your ass and say everything was hunky-dory and we were surrounded by unicorns farting rainbows for the rest of our lives. As I mentioned above, it was fucking hard at times, particularly being made fun of because I was both poor and the daughter of an apparent Jezabel (because in 1970 in SE TX, that was how the word "divorcee" was interpreted). OTOH, I can tell you from personal experience that if my mom and dad stayed together "for the kids," that better SES would have been more than offset by the insecure, angry household I'd have lived in. My very first memory, c. 2 1/2 yrs old, is being in my crib and hearing my parents yelling at each other in the living room and being terrified to utter a single sound. And even though the marriage ended only a few years after that, I still have trouble voicing fears/negative emotions to other people -- when I'm really upset, I just shut down and curl up in that same little psychological ball. I cannot imagine how fucked I'd be if I'd lived with that terrible fear and insecurity for another decade or more.
IOW, all these anecdotes here are individual data points that
can directly attest to the effect of divorce as compared to the effect of an unhappy marriage. Obviously, the plural of anecdote is not data. At the same time, the various studies that we do have have not been able to figure out how to find a comparably-situated control group for comparison. So in the abscence of any actual study, our individual data points at least provide some insight.