Why would the number of false reports be the same?
Are the groups being raped at the same rate?
If so, why didn’t you state this as an assumption?
The number of false reports is not the same for the two groups. Nobody is saying that but you. Everybody is saying the rate of false reports is the same. Your “math” assume that rate and number are the same. They are not.
.
There’s your problem, Hawking. Where in the fuck did this number come from?
NO NO NO. A false report is made by a woman who WASN’T raped.
X/6 is the number of FALSE REPORTS made by black women. .01X is the number of TRUE REPORTS made by black women.
NO NO NO. Your figures work only if there are 100,000 ACTUAL rapes. (And note that all rapes are assumed to be interracial)
The number of rape REPORTS will NOT be in a 99 to 1 ratio.
PLEASE stop changing the assumptions.
A pool of 100,000 what? rapes or rape reports?
Ok fine. You meant 100,000 rapes.
And that’s the fatal mistake you make. You are confusing rapes with rape reports.
Please show me. Will you accuse me of assuming that X =1? LOL.
I’ve learned how to get better mileage from it. Normally, I get 20 miles to the gallon and the tank holds fifteen gallons.
I fill it up and drive 200 miles. Than I fill it with two gallons and drive 100 miles. I still have two gallons left. 300 miles divided by 2 gallons = 150 miles per gallon.
You should try it. Saves a lot of money.
I’ll go you one better - when I get to work, I just assume I had to travel 1/6 of the distance.
By “rate of false reports,” do you mean the percentage of women who are NOT RAPED who make a report?
That’s the only reasonable interpretation of the phrase.
The odds of being raped during a particular year are low enough that we can assume that the vast majority of women will NOT be raped. Thus, if the rate of false reporting is the same, you will get approximately the same number of false reports from each population.
The mistake you are making is assuming that the number of false reports should be proportional to the number of actual rapes. There is no reason to make this assumption.
I assumed that black and white women are equally likely to fabricate a rape accusation. So if the populations are equal, there should be a roughly equal number of false rape claims.
(It won’t be exactly equal, since, by hypothesis, there are more rapes of white women than of black women. So if false rape claims are distributed randomly among women who weren’t raped, the number of false claims by black women would be a little higher. Rape is rare enough that this difference can be ignored.)
Impossible. If x/6 is the number of FALSE REPORTS made by black women, and only one out of four reports is a false one, than 3(x/6) is the number of True reports.
No. It would not work that way. It would only work if it 100,000 were the number of Reported rapes, which is what I said.
That’s an incomplete statement. 99/1 to what?
I have not.
Reports
No. I meant what I said, which was “reports.”
No. You are pretending I am.
I can’t if your pretending to blind. Nobody is as stupid as you are pretending to be. Ergo, you are trolling.
They won’t be anywhere near equal if 1% of rape is w-o-b and 99% of rape is w-o-w.
That’s the fatal flaw in your thinking.
If four separate people all recognized this mistake, all independently, perhaps it’s time for you to question how much you know about this subject.
Just to make my algebra a little clearer, I will substitute numbers into the calculation.
-
Let the total number of ACTUAL RAPES be 10,000. That means 9,900 black on white rapes and 100 white on black rapes.
-
Since we know that 25% of rape reports are false, there must have been 3,333 false rape reports.
-
So the total number of rape reports is 13,333. 10,000 (75%) are true reports; 3,333 (25%) are false reports.
-
I will assume a population of 1,000,000 black women and 1,000,000 white women.
-
Thus, ignoring race, the total incidence of rape every year is 0.5% (which is 10,000 divided by 2,000,000).
-
The total number of women who AREN’T RAPED is 1,990,000. This is comprised of 999,900 black women and 990,100 white women.
-
Thus, the number of black women who AREN’T RAPED is approximately equal to the number of white women who AREN’T RAPED.
-
Since, by assumption, black women are equally likely to fabricate a claim of rape as white women, the 3,333 false reports will be (approximately) evenly distributed between blacks and whites.
-
Thus, we have approximately 1,666 false reports by black women and 1,666 false reports by white women.
-
At the same time, we have 100 TRUE REPORTS by black women and 9,900 TRUE REPORTS by white women.
-
Thus, the total number of reports (true or false) by black women is 1,766. 1,666 of these reports are false.
-
Thus, if a black woman reports a rape, the probability that it is false report is 1,666 / 1,766 which is approximately 94%.
-
The total number of reports (true or false) by white women is 11,233. 1,666 of these reports are false.
-
Thus, if a white woman reports a rape, the probability that it is a false report is 15%.
And that, friends, is the magic of Bayesian reasoning.
Background statistics matter.
If you disagree, please point to the step you disagree with.
Of course they will be roughly equal. The vast majority of women are not raped in any given year. False reports are made by women are NOT raped.
But in figuring the number of false reports by women of each race, you have to look at the number of women who are NOT raped. Not at the number of women who ARE raped.
Because false reports are made by women who are NOT raped.
That’s the fatal flaw in your reasoning.
I redid the calculation with actual numbers. Look at it with an open mind. You will see.
That should be “false reports are made by women who are not raped.”
By the way, I re-did my calculation with actual numbers to make it a little easier to follow.
Out of curiousity, I did the calculation a second time, getting rid of the approximation you complain of. Instead of 1666 false reports by black women, I got 1672 false reports. This makes the probability of a black woman’s report being false slightly higher.
I may be wrong, but surely what you want is to to distribute the false reports proportionally, and not evenly? If there’s less people altogether, then there’s going to be proportionally less false claims of rape.
Yes! But . . . proportionally to WHAT?
Proportionally to the number of women who AREN’T raped!
That’s the key insight here.
In my example, proportionally and evenly are close enough not to make a significant difference. If you do it proportionally, you get a 1661/1672 split, as opposed to 1666/1666.
Ok, i’m still not getting this.
Say there’s 200 white women. The false rape claim rate is 50%. That’s 100 false claims, and as there’s only one group in this assumption, we assign them all to those women; 100 are likely to be lying.
Now let’s say 100 white women and 100 black women. Same false rape claim rate. That’s still 100 false claims, and as the two groups are even in number, we can spread them evenly; 50 white women are likely to be lying, and 50 black women are likely to be lying.
Ok, so this time it’s 150 white women and 50 black women. Same false rape claim rate. That’s still 100 false claims. Spreading them evenly, 50 (a third) of the white women are likely to be lying, whilst 50 (all) of the black women are likely to be lying. See the problem? What we should be doing is assigning them proportionally; since there are three times the number of white women, they are assigned three quarters of the false rape claim number; 75, leaving us 25 to assign to the black women. Each group has half their number likely to be lying; a 50% false rape claim rate.
Or am I barking up entirely the wrong tree?
In my example, I assumed 1,000,000 white women and 1,000,000 black women. So the false claims will be distributed roughly evenly.
(I have one little nit with your analysis: When you say that the false claim rate is 50%, it’s not entirely clear what you mean. Does it mean that 50% of women who are not raped will make rape accusations? Does it mean that 50% of accusations are false? It’s important to be precise about what you mean.)
Apologies. I mean 50% of women of rape claims will be false; the amount of people total are the amount of people accusing (i.e. in my first example, that’s 200 accusations from white women).
I think I see the problem. You’re saying that the number should be taken proportionally to the total number of black/white women, and i’m saying the number should be taken proportionally to the number of accusations. Is that right?
Basically, yes.
More specifically, the numbers of false accusations should be taken proportionally to the total numbers of black/white women who are NOT raped. This is approximately equal to a proportion of the total numbers of black/white women.
Remember, the original problem I was given asks me to assume that 99% of rapes are black on white and 1% are white on black. (Actual rapes, not rape reports.)
The next assumption is that 25% of rape reports are false.
Nowhere are we told that false rape reports have the the same 99/1 breakdown.
So if you are given a total number of rape reports and want to break it down, two steps are required:
First, figure out how many ACTUAL rapes took place, and then break it down.
Second, figure out how many false reports took place, and break that number down.