there's a threshold that's 0.67 SDs (10 points) above the higher-performing of two groups with equal variances who are separated by 0.97 d.
With simulated group sizes of one million persons each, the mean differences decline, and the SDs do too. The new gap is 0.412 d.
But we know that the 0.97 d gap is an underestimate due to range restriction.
Using MBE scores, it looks like the unrestricted gap should be more like 1.22 d. That leaves us with a 0.537 d gap above the threshold.
Do we have subsequent performance measures?
Yes! We have three:
- Complaints made against attorneys
- Probations
- Disbarments
For men, the gaps, in order, are 0.576, 0.513, and 0.564 d. For women, the gaps are 0.576, 0.286, and 0.286 d.
Men fit expectations and women apparently needed less discipline.
These gaps probably replicate nationally.
For example, here are Texas pass rates from 2004 - a 0.961 d Black-White first-pass gap. The 2006 update to these figures raised the gap to 0.969 d.
Those figures are basically in line with LSAC's national study of Bar exam pass rates.
And those are basically in line with New York's gaps.
And this should probably be expected, since tests measure the same things.
Since all of the people included in these statistics went to ABA-accredited schools, they all had the opportunity to learn what was required to perform well on these tests.
But just like the Step examinations for medical doctors, the gaps on the tests and in real life remain.
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The idea is to put large, powerful animals like bulls or lions in the ring with several dogs, and the winner lives.
The sport has existed for thousands of years. One of our first records is of Indians showing it to Alexander the Great.
The first record in England comes from 1610 and features King James I requesting the Master of the Beargarden—a bear training facility—to provide him with three dogs to fight a lion.
Two of the dogs died and the last escaped because the lion did not wish to fight and retreated.
For one, there's no supportive pattern of sanctions. For two, you can develop in near-autarky, and before post-WW2, that was comparatively what the most developed countries were dealing with.
I'm not talking fatalities, but bites, because bites are still a bad outcome and any dog who bites should be put down.
If we take the annual risk a dog bites its owner, scale it for pit bulls and Golden Retrievers, and extrapolate 30 years...
How do you calculate this?
Simple.
First, we need estimates of the portion of the U.S. population bitten by dogs per year. Next, to adjust that, we need the portion of those bites that are to owners. So, for overall dogs, we get about 1.5% and roughly ~25% of that.
Then, to obtain lifetime risk figures, we need to pick a length for a 'lifetime'. I picked thirty years because that's what I picked. Sue me. It's about three dog lifetimes.
P(>=1 bite) = 1-(1-p)^t
It's pure probability math. To rescale for the breed, we need estimates of the relative risk of different dog being the perpetrators of bites. We'll use the NYC DOHMH's 2015-22 figures to get the risk for a Golden Retriever (breed = "Retriever" in the dataset) relative to all other dogs, and Lee et al. 2021's figures to get the risk for a pit bull. The results don't change much just using the NYC figures, they just became significantly higher risk for the pit bulls.
To rescale 'p' for b reed, it's just p_{breed} = p_{baseline} \times RR_{breed}.
Then you plug it back into the probability of a bite within thirty years. If you think, say, pit bulls are undercounted for the denominator for their RR, OK! Then let's take that to the limit and say that every 'Black' neighborhood in New York has one, halve the risk noticed for them, and bam, you still get 1-in-5 to 1-in-2.5 owners getting bit in the time they own pit bulls (30 years).
And mind you, bites are not nips. As Ira Glass had to be informed when he was talking about his notorious pit bull, it did not just "nip" two children, it drew blood, and that makes it a bite.
Final method note: the lower-bound for Golden Retriever risk was calculated out as 0.00131%, but that rounded down to 0. Over a typical pet dog lifespan of 10-13 years, an individual Golden Retriever will almost-certainly not bite its owner even once, whereas a given pit that lives 11.5 years will have an 18-33% chance of biting, and if we use the DOHMH RRs, it's much higher. If we use the DOHMH RR and double their population, that still holds.
The very high risk of a bite associated with a pit bull is highly robust and defies the notion that '99.XXXX% won't ever hurt anyone.' The idea that almost no pit bulls are bad is based on total fatality risk and it is a farcical argument on par with claiming that Great White Sharks shouldn't be avoided because they kill so few people.
Frankly, if we throw in non-owner risk, the typical pit bull *will* hurt some human or some animal over a typical pet dog's lifespan. And because pit bulls live a little bit shorter, you can adjust that down, but the result will still directionally hold because they are just that god-awful of a breed.
Final note:
Any dog that attacks a human or another dog that wasn't actively attacking them first should be put down. That is a big part of why this matters. These attacks indicate that the dogs in question must die.