Bricker is a disingenous punk.

[you_with_the_face]

psychloan, please respond to this:

@ywtf

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.

[psychloan]

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.)

Yes. And I believe the point is to come up with an example that shows that background statistics matter.

So why would we expect blacks to report rape at the same frequency that white women do?

What do you mean by “frequency”? Total number of rape reports divided by total number of rapes? or total number of rape reports divided by size of population?

I am assuming that

(1) everyone who has been raped reports it.

(2) a small percentage of women who have NOT been raped make false reports. The same percentage for both races.

psychloan is expecting that if white women report 100 rapes, black women would report the same number.

No I’m not. If by “frequency,” you mean the total number of rape reports divided by the total population, then white women will have a higher frequency of reporting. Because they are victimized more often in our example.

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.

Right. The number of true accusations will be very different. But the number of false accusations will be (approximately) the same.

Which means that there are more liars within the black woman demographic. This contradicts the assumption that both groups are equally honest.

Absolutely not. There are 3 types of women in each race in the example:

(1) women who are not raped who don’t make accusations;

(2) women who are raped who make accusations; and

(3) women who are not raped who make a false accusation.

Women in groups (1) and (2) are honest. Women in group (3) are liars.

Each race has approximately the same number of honest women as the other race and approximately the same number of liars as the other race.

If you want to know the percentage of each race that are liars, it’s

(3) / (1) + (2) + (3).

Which is the same for both races.

However, if you want to know the chances that a given accusation is false, that is

(3) / (2) + (3).

Which is different for both races.

Because background statistics matter.

[you_with_the_face]

@psychloan

What do you mean by “frequency”? Total number of rape reports divided by total number of rapes? or total number of rape reports divided by size of population?

Frequency meaning, reporting false rape at the same rate.

I am assuming that

(1) everyone who has been raped reports it.

(2) a small percentage of women who have NOT been raped make false reports. The same percentage for both races.

This is a bad assumption. Your given was that 25% of all rape accusations are false. Your screw-up is in assuming that 12.5% of black women are liars and 12.5% of white women are liars. The 25% given applies to claims only, not to people.

No I’m not. If by “frequency,” you mean the total number of rape reports divided by the total population, then white women will have a higher frequency of reporting. Because they are victimized more often in our example.

You assume that the frequency of false rape reporting among the two groups are equivalent, but you have no reason to think that. Not based on a given that only tells you about the claim rate. The other monkey wrench in your logic is the assumption that women who have been raped do not ever make false claims. That’s the problem with assuming that the 25% figure applies to people instead of claims. You end up assuming that victimization precludes one from being a liar.

Right. The number of true accusations will be very different. But the number of false accusations will be (approximately) the same.

Which means that the “honest to liar” ratio in the black cohort will be a lot smaller than that ratio for white women. Which means that there are a lot more black women proportionally who are lying. This contradicts your assumption that both groups are equally honest.

Absolutely not. There are 3 types of women in each race in the example:

(1) women who are not raped who don’t make accusations;

(2) women who are raped who make accusations; and

(3) women who are not raped who make a false accusation.

Women in groups (1) and (2) are honest. Women in group (3) are liars.

What about women who are raped who make false accusations? That’s your monkey wrench.

Because background statistics matter.

Yes, you keep saying this. But understanding what is logical matters the most. You have yet to display that.

[psychloan]

@you with the face

Frequency meaning, reporting false rape at the same rate.

What is the numerator and what is the denominator?

This is a bad assumption. Your given was that 25% of all rape accusations are false. Your screw-up is in assuming that 12.5% of black women are liars and 12.5% of white women are liars.

As I’ve said many times, I think it’s reasonable to assume that a black woman who has not been raped is approximately as likely to make a false accusation as a white woman who has not been raped. Remember, I was told that “all other things are equal.”

(And I’m not assuming that the fraction of liars is 12.5 percent. False accusations are very rare in my example.)

The 25% given applies to claims only, not to people.

How are the false claims distributed? Why should it be in proportion to the number of true claims?

You assume that the frequency of false rape reporting among the two groups are equivalent, but you have no reason to think that.

I was allowed to assume that all other things are equal. Thus, I assumed that a white woman who is not raped is approximately as likely as a black woman who is not raped to make a false claim. In other words, I assumed that both populations have the same fraction of liars.

You seem to want to assume that the white women will lie with 99 times greater frequency than the black women. Why should that be?

The other monkey wrench in your logic is the assumption that women who have been raped do not ever make false claims.

If you take that assumption away, it doesn’t make a big difference in the outcome.

Do the math and you’ll see.

That’s the problem with assuming that the 25% figure applies to people instead of claims. You end up assuming that victimization precludes one from being a liar.

Which means that the “honest to liar” ratio in the black cohort will be a lot smaller than that ratio for white women.

Not if you look at the total population. Only if you look at people who make accusations. Do the math.

Yes, you keep saying this. But understanding what is logical matters the most. You have yet to display that.

Honestly, I think the problem is that you don’t understand Bayesian reasoning. If you don’t understand Bayesian reasoning, you will never understand my point.

[you_with_the_face]

@psychloan

What is the numerator and what is the denominator?

of false reports/# of people

As I’ve said many times, I think it’s reasonable to assume that a black woman who has not been raped is approximately as likely to make a false accusation as a white woman who has not been raped. Remember, I was told that “all other things are equal.”

But your given was about claims not people. Think about it.

In theory, we should be able to do this word problem without knowing anything about the proportion of blacks and whites in the population. Just knowing that

99% of rape is b-o-w and 1% is w-o-b

(And I’m not assuming that the fraction of liars is 12.5 percent. False accusations are very rare in my example.)

How are the false claims distributed? Why should it be in proportion to the number of true claims?

I was allowed to assume that all other things are equal. Thus, I assumed that a white woman who is not raped is approximately as likely as a black woman who is not raped to make a false claim. In other words, I assumed that both populations have the same fraction of liars.

You seem to want to assume that the white women will lie with 99 times greater frequency than the black women. Why should that be?

If you take that assumption away, it doesn’t make a big difference in the outcome.

Do the math and you’ll see.

That’s the problem with assuming that the 25% figure applies to people instead of claims. You end up assuming that victimization precludes one from being a liar.

Not if you look at the total population. Only if you look at people who make accusations. Do the math.

Honestly, I think the problem is that you don’t understand Bayesian reasoning. If you don’t understand Bayesian reasoning, you will never understand my point.
[/QUOTE]

[you_with_the_face]

I hit return on accident. Please disregard last post.

[Scylla]

@psychloan

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.

The rate of accusations has nothing to do with the analysis. All women could make an accusation, or none. It’s not stated as a given, nor does it apply to the question.

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.

Cite that, please.

You are applying the 99% figure to ACCUSATIONS - true or false.

True. I thought it was stated. I’ll await your cite that it was not (please cite with post number.) It logically follows from the context of the question and is implied withing the question even if not overtly stated.

If this is not granted as a given (which again, I beleive is firmly implied,) than the question cannot be answered as asked without further variables such as "at what rates are actual rapes reported?)

Look at the original question and redo your math.

My math is mighty. Yours is pretty crappy.

[psychloan]

@you with the face

But your given was about claims not people. Think about it.

So what? Claims are made by people.

Anyway, we are originally told the ratio of actual rapes, not the ratio of rape accusations.

Why is it unreasonable to assume that false claims are distributed randomly through the populations of women who are not raped? Why is it unreasonable to assume that a black woman who is not raped is as likely to make a false claim as is a white woman who is not raped?

In short, why is it unreasonable to assume that both groups are equally honest?

[psychloan]

@Scylla

The rate of accusations has nothing to do with the analysis. All women could make an accusation, or none. It’s not stated as a given, nor does it apply to the question.

You need to know the rate of false accusations. If you check back, you will see I asked for it and was told 25%.

Cite that, please.

Post number 175.

My math is mighty. Yours is pretty crappy.

Sorry, but you are in the wrong here.

[Scylla]

@psychloan

You need to know the rate of false accusations. If you check back, you will see I asked for it and was told 25%.

Yes. I said “the rate of accusations.” That’s different from the “rate of false accusations.”

Post number 175.

Ok, it’s actual rapes, not accusations.

Sorry, but you are in the wrong here.

No. I’m not. You can’t answer the question without knowing what percentage of actual rapes are reported and whether it holds true between white women and black women.

Without that information you can’t answer.

[you_with_the_face]

@psychloan

What is the numerator and what is the denominator?

of false reports/# of people

As I’ve said many times, I think it’s reasonable to assume that a black woman who has not been raped is approximately as likely to make a false accusation as a white woman who has not been raped. Remember, I was told that “all other things are equal.”

But your given was about claims not people. Think about it.

In theory, we should be able to do this word problem without knowing anything about the proportion of blacks to whites in the population. Just knowing that :

1. 99% of rape is b-o-w and 1% is w-o-b
2. 25% of all rape accusations are false
3. both groups are equally honest

…should tell us that all true and false reports of w-o-b rape will be in proportion to all true and false reports of b-o-w rape. I don’t need to know anything about the number of blacks in the population relative to whites because none of the givens depend on us knowing that the population is 50:50 white and black. You assume that this information is necessary so that we can know how claims distribute, but that’s a mistake.

How are the false claims distributed? Why should it be in proportion to the number of true claims?

Because the given is that 25% of all rape accusations are false. In other words, you expect that out of 100 claims, 25 will be false. The given doesn’t allow us to assume that half of these claims will be made by blacks. That’s a reach.

I was allowed to assume that all other things are equal. Thus, I assumed that a white woman who is not raped is approximately as likely as a black woman who is not raped to make a false claim. In other words, I assumed that both populations have the same fraction of liars.

Bad assumption to make.

You seem to want to assume that the white women will lie with 99 times greater frequency than the black women. Why should that be?

No, I only expect white women to report rape 99 times more than black women. These reports will be both true and false, but it will be in proportion to what black women do.

Not if you look at the total population. Only if you look at people who make accusations.

But that’s thing: upfront you know nothing about the people making the false accusations. Upfront, you do know that white women report true rape 99 times more than black women. But you don’t know anything about who is reporting false ones. Based only on the givens supplied, it’s wrong to assume that equal numbers of false claims will come from black women.

The only reason you make that assumption is because you think the proportion of blacks to whites in the population matter. But it doesn’t. That’s information you’re throwing in there for no good reason.

And for all we know the 99% b-o-w rape statistic could be the same damn white woman getting raped over and over again. We have no idea how these claims distribute over populations. Again, you are assuming stuff that is not in evidence.

Honestly, I think the problem is that you don’t understand Bayesian reasoning. If you don’t understand Bayesian reasoning, you will never understand my point.

I understand it well. I just don’t think it applies in the way that you think it does.

[psychloan]

@you with the face

I understand it well. I just don’t think it applies in the way that you think it does.

No you don’t understand it at all. Here’s the proof:

Quote:

Yes. I’m assuming that “all other things are equal.” i.e. that an unraped black woman is approximately as likely to make a false rape claim as an unraped white woman.

And yet this is your conclusion.

Even so, the probability that any given black woman’s claim is false is much much higher.

I think thinks counts as bona fide proof that you are idiot

Sorry, but anyone who thinks that the two statements I made are contradictory and constitute proof that I’m an idiot has absolutely no grasp of Bayesian reasoning.

I’m not going to respond to your other points, as I’ve made my argument reasonably clearly and you are simply repeating the same fallacious arguments you made earlier. The problem is that you don’t understand Bayesian reasoning.

[psychloan]

@Scylla

No. I’m not. You can’t answer the question without knowing what percentage of actual rapes are reported and whether it holds true between white women and black women.

Without that information you can’t answer.

To make things simpler, I assumed that all actual rapes are reported. If you assume that some rapes are not reported, it won’t make a huge difference in the result.

Anyway, if you still think my math is bad, you might check out the general questions thread I started.

Or you might want to re-do your own math.

[you_with_the_face]

@psychloan

Even so, the probability that any given black woman’s claim is false is much much higher.

You don’t understand that this is the same thing as saying this:

If a black woman reports that she was raped, there’s a greater chance that she’s a [SIZE=4]lying whore [/SIZE] than a white woman who reports being raped.

But at the same time, black women are just as honest as white women.

Yes, you’re right. This makes perfect sense. How silly we are.

[holmes]

psychloanThe only conclusion I can come to using your math is that the minority is always less credible than the majority. I don’t see any other conclusion. People with blue eyes will be less credible than people with brown eyes. Left handed people too, so will Redheads and Jews and whomever is represented the least…and I confess that makes no sense to me.

I don’t see how external features or lack of them can be used to determine credibility. I just don’t see it.

[Gorsnak]

@you with the face

You don’t understand that this is the same thing as saying this:

If a black woman reports that she was raped, there’s a greater chance that she’s a [SIZE=4]lying whore [/SIZE] than a white woman who reports being raped.

But at the same time, black women are just as honest as white women.

Yes, you’re right. This makes perfect sense. How silly we are.

Allow me to restate things slightly in a way that might make them clearer. What psychloan means when he says that black women are just as honest as white women is that if we asked all women whether they were raped, we would get truthful answers at the same rate from both groups. If we look only at those who claim to have been raped, then yes, amongst that group, a greater percentage of the black women claiming to be raped are lying. That’s because there are proportionately more un-raped black women in the honest group. Here, maybe a bar graph will help.

          Black     White
           _         _
          | |       | |
          | |       | |
          | |       | |
          | |       | |
          | |       | |
          | |       | |
          | |       | |
          | |       |T|
          | |       |T|
          | |       |T|
          | |       |T|
          | |       |T|
          |T|       |T|
          |F|       |F|
__________|F|_______|F|____

The bars indicate the total population. T’s are truthful reports of rape. F’s are false reports of rape. As you can see, F’s appear in each bar in equal proportion. T’s do not. Hence, blacks and whites are equally likely to make a false report. However, if we now look only at those making reports, we’ll see that 2 out of 3 or 66% of blacks making reports are making false reports, while 2 out of 8 or 25% of whites making reports are making false reports.

As I said in my earlier post, I think the structure of the hypothetical is unlikely to map onto reality, because it assumes that false reports of rape arise out of nowhere, rather than out of specific sets of circumstances that likely correlate with actual instances of rape across demographics. But that’s neither here nor there. Given the facts laid out in the hypothetical, psychloan’s analysis is correct.

[you_with_the_face]

psychloan, magellan, and anyone else: can you read my post 193?

How are your beliefs any different from the Creationists who believe that there must be a God because of all the uncanny coincidences that occurred to create a planet perfectly suited for carbon-based life?

Is this a position that you hold? Or do you think your opinions on credibility are nothing like the Creationist’s infamous puddle-of-water logic?

Because to me, your opinions look just like theirs. You’re applying probability in reverse and using whatever number you come up with as a basis for establishing whether or not something is plausible, either in the absolute sense or relative sense.

[holmes]

@Gorsnak

As I said in my earlier post, I think the structure of the hypothetical is unlikely to map onto reality, because it assumes that false reports of rape arise out of nowhere, rather than out of specific sets of circumstances that likely correlate with actual instances of rape across demographics. But that’s neither here nor there. Given the facts laid out in the hypothetical, psychloan’s analysis is correct.

The problem is Gorsnak in at least one of his posts psychloan, alludes that due to statistics, early warning flags should’ve popped up in that case and so I’m not so sure this is a hypothetical experiment for him.

Perhaps he’ll clarify.

[Scylla]

@psychloan

To make things simpler, I assumed that all actual rapes are reported.

That assumption is not acxiomatic. You can’t make it.

If you assume that some rapes are not reported, it won’t make a huge difference in the result.

That’s another bad assumption implied. What makes you think that black and white women will report actual rapes at the same rate?

Anyway, if you still think my math is bad, you might check out the general questions thread I started.

I don’t think it’s bad. I know.

[you_with_the_face]

@Gorsnak

As I said in my earlier post, I think the structure of the hypothetical is unlikely to map onto reality, because it assumes that false reports of rape arise out of nowhere, rather than out of specific sets of circumstances that likely correlate with actual instances of rape across demographics. But that’s neither here nor there. Given the facts laid out in the hypothetical, psychloan’s analysis is correct.

But as I said above, in order to make his math “add” up, he has to assume additional stuff. In other words, he has to make the problem a lot more convoluted than is necessary in order to reach his answer.

Like I said above, we have no idea how these claims distribute in either population. We dont know if the 99% b-o-w statistic represents one woman making the same claim over and over again, or if it comes from a different one every time. The same goes for the 1% statistic. That’s why it doesn’t matter what the proportion of black to white is in the total pop. That’s unimportant information if all we’re given are stats for claim percentage and not people percentages.

Why does this matter? Well, if we don’t even know how the true accusations distribute within the subpopulations making them, then we sure as hell don’t know how the false ones distribute across subpopulations. Especially if we are only told that 25% of claims are false. This is a rate based on claims, not number of people making claims.

To come to this conclusion:

Even so, the probability that any given black woman’s claim is false is much much higher.

What he’s really saying is there will be fewer true w-o-b claims proportional to true b-o-w claims. But again, that’s only if you assume that you know how false claims distribute across subpopulations. But we don’t know that.

I think it’ll be easier to see what I’m saying if I reframe the problem like this:

There are the two women in a town full of horny men. One is named White Woman (WW) and the other is named Black Woman (BW). The sheriff told the women to call him every time they got raped.

1. 99% of all rape reports come from WW; 1% comes from BW

2. For every 3 true reports they each make, the women agree to lie about one. (which is equal to the 25% false accusation rate given initially)

3. both women are equally honest.

Now using psychloanian logic, we are to assume that BW is reporting the same number of false claims that WW is, which goes against our second given. In order to reach his conclusion the given needs to read thusly:

2. Both women agreed to lie about being raped every Friday

Do you see what I mean, now? That still doesn’t address the most egregious flaw in his conclusion, which Hentor has been getting at. But it at least explains why his answer doesn’t follow from the information given in the word problem.