But that should be the natural assumption, as it preserves the equal percentage (not amount) of false rape reports from each set of women. If we spread out the reports equally, what we end up with are calculations based on black women being far more likely to give a false rape claim; which isn’t what we’re trying to work out.
No, it’s not a natural assumption.
Ask yourself, if a given black woman has NOT been raped, what is the probability that she will make a false report? Perhaps it’s about 1 in 1000.
Same question for a given white woman – if she has NOT been raped, what is the probability that she will make a false report?
Why shouldn’t we assume that these two probabilities are the same (or approximately the same)? After all, we are assuming that “all other things are equal”
Put it another way: what percentage of black women who have NOT been raped make a false report?
Perhaps it’s 0.1 %?
What percentage of white women who have NOT been raped make a false report?
Isn’t it natural to assume that the two percentages are the same (or approximately the same)?
Absolutely not.
There’s a difference between the probability of a given woman making a false rape claim and the probability that a given claim is false.
If we assume that the former is equal for whites and blacks, then the latter is not equal for whites and blacks. (Under my earlier assumptions.)
I’m really not getting it - sorry, I must be having a slow day! Could you (or anyone else) dumb it down enough for me to understand?
You might try to answer the questions I posed:
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What is the likelihood that a white woman who has not been raped will make a false report?
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What is the likelihood that a black woman who has not been raped will make a false report?
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Isn’t it natural to assume that the two probabilities are the same, or close to the same?
(Obviously I’m not asking for an exact probability. Just think about it – it’s gotta be some small number like 1 in 1000.)
You’re actually asking for it to go in the wrong direction. But you are being very nice about the whole thing, so you’re a better man than I.
You are right. He is wrong.
If 25% of all rape accusations are false that means that if you have 100 claims, 25 of those claims are expected to be false. In other words, an intelligent person would see this as a rate based on total accusations.
Accordingly, a group of women who report rape twice as often as another group should make twice as many true and false accusations.
If both groups are equally honest, then the number of false accusations should be proportionate to the number of rape accusations they are making. There is no way you make it work any other way. Because if you assume that blacks and whites contribute equally to the number of false claims made, then that means that black women have more liars among than white women.
Why do I think of the Chewbacca defense when I read this?
Ladies and gentlemen, this doesn’t make sense.
Psychloan:
No. You don’t. You can’t. Whether or not a women is raped is moot for the analysis. A raped woman may still make a false accusation.
A woman who is raped can still make a false accusation.
There is no flaw. Your logic is less tight than a sieve.
You are taking as axiomatic nongiven assumptions and performing operations on them. Since you are depending on nongiven assumptions, your data does not follow from the givens.
The givens you have to work with are as follows.
- 25% of rape accusations will be false.
- 99% of rape accusations will be made by white women against white men.
- 1% of rape accusations will be made by black women against white men.
Start with a population of 100,00 rape reports (you can use any number that you want, but that will make it simple,) and proceed from there.
You are not free to make any further assumptions or add any axioms.
What do you mean?
Anyway, What **you with the face ** said. That’s what i’ve been trying to say, only i’m having a bit of trouble articulating it. I’m going to risk making people’s heads explode from illogicality and have another go.
Let’s say there’s 2000 women in our population. 200 of those women make accusations of rape. Assume there’s a false rape reporting rate of 50%. It’s likely that 50% of those women who are accusing are lying; that’s 100 women.
Ok, same population, same rate, only now 100 white women and 100 black women. Assume race makes no difference to the percentage of false claims. Again, it’s likely 50% of those women who are accusing are lying; that’s 50 white women and 50 black women. This matches the assumptions.
Last one; same population, same rate, same lack of difference. Now there are 150 white women accusing and 50 black women accusing. Again, 50% of those women are likely to be lying.
- To take this as I understand psycloan’s method, we’re assuming there is no difference due to race. Thus, we can evenly distribute the amount of false claims; that would mean 50 white women are likely to be lying, and 50 black women are likely to be lying. Yet, that’s only a third of the white women, and all the black women. What we essentially have here, then, is calculations based on the false claim rate for black women being 100%, while the same for white women is 33% - both are incorrect when compared to our initial assumption that race makes no difference. The calculations are inaccurate.
- The way I see it working is that, since the proportion of white women/black women isn’t equal, the false rape claims should be spread out in a proportion equal to that difference. So, as white women make up three quarters of the total accusing women, and black women make up one quarter, it makes sense to assign three quarters of the false claims to white women (75 women) and one quarter to black women (25). Taking these figures, we can see that 75 out of 150 white women are lying; a false claim rate of 50%. Similarily, for black women the numbers are 25 out of 50; also a false claim rate of 50%. The calculations match the assumption that race makes no difference, and that the rate is 50%
I have read almost none of this thread, but based on the GQ thread psycloan started with regards to Bayesian analysis, he is arguing that one should assume that false claims will be evenly distributed across demographics, so that if actual rapes are not evenly distributed across demographics, then some demographics are going to have higher/lower ratios of actual rapes to false claims.
If we assume this, it doesn’t affect the analysis much at all.
Suppose that 1 in 1000 women – raped or not – makes a false accusation. Then the number of false accusations from each population is exactly the same.
Again, you are changing the original question. Look at the original question. The original question assumes that 99% of ACTUAL RAPES are black on white and 1% of ACTUAL RAPES are white on black.
You are applying the 99% figure to ACCUSATIONS - true or false.
Look at the original question and redo your math.
Exactly.
So, proportionally, black women are more likely to be liars? Upon what basis would you make that assumption?
Really, I’m still reading this to be a different expression of the same error. Whether you are talking about the raw number of rapes or the raw number of rape claims, you haven’t done anything to answer a question about the credibility of two specific women making claims. When you multiple two different numbers by a constant, you haven’t changed anything about the relationship between those two numbers, you’ve just changed their size by equal amounts,
So, if you assume the probability of black and white women making false claims is the same, you have to assume that they are equally credible.
But that doesn’t make any sense if you start out with the premise that both groups are equally honest.
Plus, what Scylla said.
Absolutely no math is required to understand why psychloan’s answer is illogical.
If 99% of rapes are b-o-w and 1% of rapes are w-o-b, this is the same thing as saying that you’d expect black women to represent only 1% of the total rape victims out there. The remaining 99% will be white. (Why we’ve excluded intraracial rape from this, I dunno. But whatever.)
So why would we expect blacks to report rape at the same frequency that white women do? psychloan is expecting that if white women report 100 rapes, black women would report the same number. But it stands to reason that if white women get raped 99 times more often than black women, their number of true accusations will far outnumber the number of true accusations that black women report. Which means that there are more liars within the black woman demographic. This contradicts the assumption that both groups are equally honest.
This is beginning to seem like a question worthy of Cecil. Yay, statistics! 
Well, given that I don’t believe it, on no basis whatsoever. 
However, the idea is that what it means for black women to be equally likely to lie about rape as white women would be for black women to falsely claim rate at the same rate per capita as white women. So, say, black women and white women both falsely claim rape 7 times per 100k population. Now, if we further assume that white women are raped at a rate of 63 per 100k, and black women are raped at a rate of 3 per 100k, then we’ll have white women making 70 claims of rape per 100k, 10% of which are false, and black women making 10 claims of rape per 100k, 70% of which are false, assuming all rapes are reported.
The problem with the line of argument is that it’s assuming that false claims of rape just appear out of the aether. In actual fact, false claims arise out of specific sorts of circumstances, such as unplanned pregnancies with unacceptable fathers, or slightly inebriated consensual sexual liasons followed by regret, etc., and it seems prima facie likely that these sorts of circumstances will map onto demographics in approximately the same fashion as actual rapes do, given that they are similar to the circumstances that lead to actual rapes. If I’m right about this, there will be no statistical discrepency of the sort described in the first paragraph.
psychloan perhaps you can explain in words and not math, your conclusions?
If you say that both groups are both equally honest, then how can one group at the end of your calculation be less honest than the other? Isn’t that your conclusion? What are you adding or subtracting to make your math work?
No numbers please. Just explain it.
Perhaps honesty is something your method can’t calculate?
Nothing, it’s just an interesting consequence of imbalanced background statistics.
I will try. The basic point is that the chances that a given accusation is false depends on two things: The total number of false accusations and the total number of true accusations. If the number of false accusations is the same for two populations, but the number of true accusations is different, the resulting ratios will be different.