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I didn't read this article, so idk how they spun things, but given the title and the information you shared from the actual study, they sensationalized, not exaggerated. 5.31 is an 87% increase from 2.31, which is a rounding error off 2x. Honestly, in medical/psychological/anthropological/sociological studies the sigmas are never high enough for my comfort as a probabilist anyway.
Usually rates that involve small raw numbers get swayed pretty significantly by relatively small changes. For example, Malta had a 3 murders last year, if that number doubled to 6, the homicide rate would increase by 100%. That's a very significant increase, but does it imply that Malta has turned into a dangerous country? Not really, no. The increase would make it's rate go from 0.561 per 100k to 1.122 per 100k, that's around the same as New Zealand which is another very safe country. It should still be noted and discussed because there's value in that, but my point is that these trends and swings in statistics can be pretty misleading if not put into proper context.
Oh, I get that. I actually have a BS in Applied Mathematics and specialize in Statistics, Probability Theory, and Data Science professionally. I am well aware of how unstable thses numbers are, which is why I made the jab at the "soft sciences" and their acceptable sigma analysis points.
What I was more noting was the linguistic tic of OP saying that they 'exaggerated'. I freely admit that I did not actually read the article and do not know what the author did in it, but the click-bait title was accurate given the data shared. So what was done is to 'sensationalize' the results. If we are ever going to get better and teach society how to understand when statistics are being used to manipulate, we need to be sure to describe it in a way that people can recognize one manipulation from another.
I would see an example of manipulation through exaggeration being "cops kill more white people per year than black people". Yes, this is true, but it is inflating one piece of the statistics that ignores a lot of relevant factors, like the per capita rate, the proportion of stops and actions by police which result in violence, etc.
Sensationalizing is what we have here. Intentionally choosing words that fell the full picture of the statistic in a way which causes knee jerk reactions. There isn't anything left out per se, the time frame is described, the change in the statistic is mentioned, and a potential causal relationship is proffered. Would "The overturning of Roe has caused a statistically significant increase in the number of voluntary sterilizations among young US Citizens' haave been more genuine, yes. Is it catchy or emotional, no.