Author Topic: Statistics update  (Read 3798 times)

anisotropy

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Re: Statistics update
« Reply #50 on: October 05, 2018, 03:44:10 PM »

For the third (or maybe fourth?) time now, do you believe there is a 5% chance or a 75% chance that a person with a single accusations is innocent?  Because you started out saying 75% innocent, then briefly started saying 5% innocent, and now you appear to be back to 75% innocent.  Keep in mind that if you say 75% innocent, you're also saying 75% of self-identified sexual assault survivors are liars.

what? No, this assertion is wrong.

There is 75% chance a person with a single accusation is innocent, precisely because we don't know which group he's in.

The false allegation rate is 5%, because allegations are most often true. These two event are NOT mutually exclusive because they describe two different events.

I quote the professor again:
"The 26% and 5% are conditional probabilities for two different events, and either one may (in general) be larger or smaller than the other. "


sol

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Re: Statistics update
« Reply #51 on: October 05, 2018, 03:44:45 PM »
Given a person is accused (and we have no idea which group he's in), what are his odds of being guilty.

One of those groups does not exist.  There is no confusion about which group he is in.  You've totally made up an entire population of innocent people who get falsely accused of rape, and you've used those made up false accusations to dilute the incidence of true accusations of rape.

But as I keep repeating, people are not randomly accused of rape the way they are randomly tested for infection.  You cannot apply this approach to the problem of sexual assault allegations.  Your math is fine, your problem setup is wrong.

anisotropy

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Re: Statistics update
« Reply #52 on: October 05, 2018, 03:46:55 PM »
Given a person is accused (and we have no idea which group he's in), what are his odds of being guilty.

One of those groups does not exist.  There is no confusion about which group he is in.  You've totally made up an entire population of innocent people who get falsely accused of rape, and you've used those made up false accusations to dilute the incidence of true accusations of rape.

But as I keep repeating, people are not randomly accused of rape the way they are randomly tested for infection.  You cannot apply this approach to the problem of sexual assault allegations.  Your math is fine, your problem setup is wrong.

which group does not exist? The innocent? Did you look at gaja's data? or Dabn's? or anyone that actually turned out to be exonerated for rape? The likelihood is very low, but this group EXISTS. Are you really this partisan and now you are just spewing wholly untrue statements now?

But since the rapist remains a minority in the population( I used 5%, you can use 10% or 15% or w/e) , what I presented is the logical account.

IF you were right and the other group (the innocent) didn't exist, there would NO FP.

Here is a way to help you think about it arithmetically:

A small % of population are rapists, their chance of being falsely accused is very low and they are 95% guilty.
A large % of population are not-rapists, their chance of being falsely accuse is extremely low and being guilty is lower still. (0.1% using dabn's number)

If we knew which group a person being accused is from, then yes, the stat appropriate for that group would be used here. The problem is we don't know. So intuitively we know the odds must be between 0.1% and 95%.

The fact that most of the population are NOT rapists means the 0.1% get much more weight in the averaging process (remember, we don't know which group the person is in). Hence the chance of guilty being 26%.
« Last Edit: October 05, 2018, 04:02:30 PM by anisotropy »

sol

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Re: Statistics update
« Reply #53 on: October 05, 2018, 04:11:27 PM »
which group does not exist? The innocent?

No, not the innocent, the large population of random innocent people who are falsely accused, the group from which you fabricate all of these hypothetical false accusations that you then use to suggest that most people who are accused are innocent.  Sexual assault allegations just don't work the same way random infection screenings do.  You don't test everyone at random, so you never create this huge group of false positives.

Quote
If we knew which group a person being accused is from,

You're still incorrectly applying the test to everyone, when you say this.  You are assuming everyone gets accused at random.  In reality, most people who are accused of rape are accused correctly because, you know, they committed a rape and gave someone a reason to accuse them.  Most people who have not committed a rape do not get accused, because nobody goes around to random people trying to decide if they should be accused of rape or not.

anisotropy

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Re: Statistics update
« Reply #54 on: October 05, 2018, 04:37:39 PM »
Sol, I did not fabricate anything. If you don't believe my numbers, let's use Dabnasty's from reply #7

Quote
In 2012 there were 87,000 reported rapes; 87,000 * .05 = 4350
The average male life expectancy is 75.5; 75.5 * 4350 = 328,425
The US population in 2012 was 312,800,000; 328,425 / 312,800,000 = ~.001

What dabnasty did was he looked at actual data from 2012, and obtained the number of reported rapes (87000), and the hypothetical false accusation cases in a given year (328425), given the 5% fp rate.

so now we have true positive / (TP + NP) (which includes all real cases) in a given year.

what is 87000 / 328425?

lo and hehold: 26.5%

This is the ULTIMATE validation in my defense.  Look, none of this is fabricated, what I did was based on bayes' statistics, calculated the likelihood of being guilty is 26% in THEORY.

Dabnasty's numbers matched almost exactly in practice 26.5%. What more do you want?

Look, none of this is fabricated. I did it right.
« Last Edit: October 05, 2018, 05:12:41 PM by anisotropy »

Caroline PF

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Re: Statistics update
« Reply #55 on: October 05, 2018, 04:58:28 PM »

Here is a way to help you think about it arithmetically:

A small % of population are rapists, their chance of being falsely accused is very low and they are 95% guilty.
So to paraphrase what you´re saying, in the group of rapists, only 95% are actually rapists.


A large % of population are not-rapists, their chance of being falsely accuse is extremely low and being guilty is lower still. (0.1% using dabn's number)
And here, in the group of non-rapists, 0.1% are actually rapists.


That makes no sense.

I´ll give you the first one. It´s possible that the guy who raped 6 women is falsely accused by a 7th women, therefore leading to the possibility that a rapist could have a false accusation.

But the second one is absolutely impossible. There´s no way for a non-rapist to be actually guilty of rape.

If your math allows for an impossibility, then there must be something wrong with the math.


And I think PathToFire is right. You have taken a positive predictive value (actually 1-ppv), and falsely called it the false positive rate.


Here´s another:
Sol, I did not fabricate anything. If you don't believe my numbers, let's use Dabnasty's from reply #7

Quote
In 2012 there were 87,000 reported rapes; 87,000 * .05 = 4350
The average male life expectancy is 75.5; 75.5 * 4350 = 328,425
The US population in 2012 was 312,800,000; 328,425 / 312,800,000 = ~.001

What dabnasty did was he looked at actual data from 2012, and obtained the number of reported rapes (87000), and the hypothetical false accusation cases in a given year (328425), given the 5% fp rate.

so now we have real / hypo false (which includes all real cases)

what is 87000 / 328425?

lo and hehold: 26.5%

This is the ULTIMATE validation in my defense.  Look, none of this is fabricated, what I did was based on bayes' statistics, calculated the likelihood of being guilty is 26% in THEORY.

Dabnasty's numbers matched almost exactly in practice 26.5%. What more do you want?

Look, none of this is fabricated. I did it right.

Using actual numbers, you are saying that there were 328425 false accusations in a year. But only 87000 reported rapes.

How can you have more false accusations than total accusations?

anisotropy

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Re: Statistics update
« Reply #56 on: October 05, 2018, 05:07:57 PM »

So to paraphrase what you´re saying, in the group of rapists, only 95% are actually rapists.

And here, in the group of non-rapists, 0.1% are actually rapists.

That makes no sense.


Right I screwed up, this is what happens when you spend all day arguing with people who has no clue how Bayes work (not you Caroline PF). Let me try it again.

5% of false allegation means 5 % of allegations are false. Says nothing about the groups.

the 0.1% means if one is from the innocent group, there is a 0.1% chance he would be wrongly accused.

Again, sorry for the mix up. Clearly I've spent too much time on this today and I am no longer thinking clearly.

I labeled those as hypo false cases in a year given the 5% false allegation rate. Not false accusations.

Here is the way to look at it, we KNOW there were 87000 cases reported, but based on the 5% false allegation rate, we calculate there COULD be 328425 cases in a year.

If we knew the case from the 87000 pile, then it ends there. Problem is we don't know. so we must consider the possibility it came from the pile outside of the 87000 too. Hence the 26%.
« Last Edit: October 05, 2018, 05:16:01 PM by anisotropy »

Caroline PF

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Re: Statistics update
« Reply #57 on: October 05, 2018, 05:15:58 PM »
I labeled those as hypo false cases in a year given the 5% false allegation rate. Not false accusations.

What do you mean by this? I don´t understand what you are saying here.

Caroline PF

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Re: Statistics update
« Reply #58 on: October 05, 2018, 05:33:00 PM »
I labeled those as hypo false cases in a year given the 5% false allegation rate. Not false accusations.

Here is the way to look at it, we KNOW there were 87000 cases reported, but based on the 5% false allegation rate, we calculate there COULD be 328425 cases in a year.

If we knew the case from the 87000 pile, then it ends there. Problem is we don't know. so we must consider the possibility it came from the pile outside of the 87000 too. Hence the 26%.

I´m sorry, I´m just not following you here. Could you explain the groups that these numbers are representing in plain english to me?

For instance, my understanding is that the number 87000 represents the total number of allegations (both true and false) in that year.

What group does the number 328425 represent?

sol

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Re: Statistics update
« Reply #59 on: October 05, 2018, 05:38:10 PM »
Quote
The average male life expectancy is 75.5; 75.5 * 4350 = 328,425

What dabnasty did was he looked at actual data from 2012, and obtained the number of reported rapes (87000), and the hypothetical false accusation cases in a given year (328425), given the 5% fp rate.

so now we have true positive / (TP + NP) (which includes all real cases) in a given year.

what is 87000 / 328425?

lo and hehold: 26.5%

This is the ULTIMATE validation in my defense.

Lol, I find this hilarious.  Now you're explicitly explaining why what you did is wrong, and still claiming vindication.

Here's a quick reminder since you haven't gotten the message yet:  the entire male US population is not equivalently subject to rape accusations.  As a general rule, rapists get accused of rape and nonrapists don't.

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Re: Statistics update
« Reply #60 on: October 05, 2018, 05:39:22 PM »
Here is the way to look at it, we KNOW there were 87000 cases reported, but based on the 5% false allegation rate, we calculate there COULD be 328425 cases in a year.

If we knew the case from the 87000 pile, then it ends there. Problem is we don't know. so we must consider the possibility it came from the pile outside of the 87000 too. Hence the 26%.

This is the fundamental flaw in your analysis. You assume that the false positive rate applies at the same value to the accused population from which the false positive rate is derived and to the entire population. That is not correct. As you said, if an allegation comes from the 87,000 pile (the number actually accused) then it ends there. There is a strong bias in the accused data set. Of course if you accuse a person from the general population you will get a bigger likelihood of being innocent. But that is an inane question to ask within the given context. Kavanaugh is clearly in the "87,000" group for the purposes of this discussion and, as you said above, that is where the analysis should stop.

sol

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Re: Statistics update
« Reply #61 on: October 05, 2018, 05:47:38 PM »
Of course if you accuse a person from the general population you will get a bigger likelihood of being innocent. But that is an inane question to ask within the given context.

That's the whole shtick, here.  Anisotropy's math is predicated on the underlying assumption, as part of the way that the problem is phrased, that millions of Americans are falsely accused of rape.  He thinks that the false accusation rate applied to the population size gives you the number of false accusations, and doesn't recognize that this would only be true if everyone in the population were accused.

Stats is definitely counterintuitive sometimes.  This is not one of those cases.  This is just a poorly formed problem.

Caroline PF

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Re: Statistics update
« Reply #62 on: October 05, 2018, 05:55:40 PM »
I labeled those as hypo false cases in a year given the 5% false allegation rate. Not false accusations.

Here is the way to look at it, we KNOW there were 87000 cases reported, but based on the 5% false allegation rate, we calculate there COULD be 328425 cases in a year.

If we knew the case from the 87000 pile, then it ends there. Problem is we don't know. so we must consider the possibility it came from the pile outside of the 87000 too. Hence the 26%.

I´m sorry, I´m just not following you here. Could you explain the groups that these numbers are representing in plain english to me?

For instance, my understanding is that the number 87000 represents the total number of allegations (both true and false) in that year.

What group does the number 328425 represent?

To clarify my question further, my understanding of the number 328425, based on Dabnasty´s numbers is the number of false accusations (4350) in one year multiplied by 75.5 years. So it is the total number of false allegations in 75 years; or the number of false allegations in the US over an average male´s lifespan, in order to calculate his odds of ever being falsely accused in his lifetime.

But you seem to be applying that number to a single year.
we calculate there COULD be 328425 cases in a year.

So I´m confused.
number of accusations in one year / number of false accusations in 75 years
doesn´t seem to give a useful number.

sol

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Re: Statistics update
« Reply #63 on: October 05, 2018, 06:41:16 PM »
So I´m confused.
number of accusations in one year / number of false accusations in 75 years
doesn´t seem to give a useful number.

It's not just you.  I'm not sure anisotropy understands what's going on here either, no matter how many times he says "I did it right".

anisotropy

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Re: Statistics update
« Reply #64 on: October 05, 2018, 06:46:51 PM »
The age/year is moot. As long as there is a non-zero rate that the "innocent specific" population could be falsely accused of, in this case 0.1%. Which incidentally tied back to laserlady's post in the original thread to produce a 5% overall fp rate, which I might write separately about on why and how they are related, because they are two sides of the same coin.

you can work backwards to find the number of hypothetical false positives in a given year IF you know the innocent specific fp rate and the population base.

once you have that, then true positive / (fp + tp) will give you the likelihood of a person (without knowing which group he belongs) being guilty when accused.

In short:
If you know the fp for criminal group, population breakdown, and fn, you can do bayes to get the answer

If you know the fp for innocent group, population base, and true positives, you can do it this way too. As long as a fp for innocent group exists, you are implicitly agreeing with the notion one could be accused by chance.

If your assumptions are valid for a given year, they will agree with each other. I have said all there is to say, I don't know what else to add.
« Last Edit: October 05, 2018, 07:10:00 PM by anisotropy »

Caroline PF

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Re: Statistics update
« Reply #65 on: October 05, 2018, 08:42:29 PM »
In short:
If you know the fp for criminal group, population breakdown, and fn, you can do bayes to get the answer

If you know the fp for innocent group, population base, and true positives, you can do it this way too. As long as a fp for innocent group exists, you are implicitly agreeing with the notion one could be accused by chance.

This is where I disagree with you. I don´t think we know the false positive rate.


You are saying that the 5% false allegation rate is equivalent to the false positive rate.

The rest of us are saying that the 5% false allegation rate is equivalent to 1-ppv.

We´re not disagreeing with your bayesian math. We´re disagreeing with your initial assumption of what the 5% is defining.


But, hey, let´s go back to the original numbers, and figure out how the original 5% that we´re fighting over was calculated.

Using google, I found the following publication which explains where they got the false accusation rate of 2-8%.
https://www.nsvrc.org/sites/default/files/Publications_NSVRC_Overview_False-Reporting.pdf
Diving into the studies they based this publication on, I found some of the real life data that they used:
Quote
For example, in a multi-site study of 8 U.S. communities involved in the “Making
a Difference” (or “MAD”) Project, data were collected by law enforcement
agencies for all sexual assault reports received in an 18-24 month period. Of the
2,059 cases that were included in the study, 140 (7%) were classified as false.

For example, Clark and Lewis (1977) examined case files for all 116 rapes
investigated by the Toronto Metropolitan Police Department in 1970. As a result,
they concluded that seven cases involved (6%) false reports made by victims.

Grace, Lloyd, and Smith (1992) conducted a similar analysis of the evidence in all
348 rape cases reported to police in England and Wales during the first three
months of 1985. After reviewing the case files, reports from forensic examiners,
and the statements of victims and suspects, 8.3% were determined to constitute
false allegations.

A similar study was then again sponsored by the Home Office in 1996 (Harris &
Grace, 1999). This time, the case files of 483 rape cases were examined, and
supplemented with information from a limited number of interviews with sexual
assault victims and criminal justice personnel. However, the determination that a
report was false was made solely by the police. It is therefore not surprising that
the estimate for false allegations (10.9%) was higher than those in other studies
with a methodology designed to systematically evaluate these classifications.

The largest and most rigorous study that is currently available in this area is the
third one commissioned by the British Home Office (Kelly, Lovett, & Regan,
2005). The analysis was based on the 2,643 sexual assault cases (where the
outcome was known) that were reported to British police over a 15-year period of
time. Of these, 8% were classified by the police department as false reports. Yet
the researchers noted that some of these classifications were based simply on the
personal judgments of the police investigators, based on the victim’s mental
illness, inconsistent statements, drinking or drug use. These classifications were
thus made in violation of the explicit policies of their own police agencies. The
researchers therefore supplemented the information contained in the police files
by collecting many different types of additional data, including: reports from
forensic examiners, questionnaires completed by police investigators, interviews
with victims and victim service providers, and content analyses of the statements
made by victims and witnesses. They then proceeded to evaluate each case using
the official criteria for establishing a false allegation, which was that there must
be either “a clear and credible admission by the complainant” or “strong
evidential grounds” (Kelly, Lovett, & Regan, 2005). On the basis of this analysis,
the percentage of false reports dropped to 2.5%.

Finally, another large-scale study was conducted in Australia, with the 850 rapes
reported to the Victoria police between 2000 and 2003 (Heenan & Murray, 2006).
Using both quantitative and qualitative methods, the researchers examined 812
cases with sufficient information to make an appropriate determination, and found
that only 2.1% of these were classified as false reports.

All of the studies used a total number of accusations, and the number that were false. All rates were calculated by dividing false accusations by total accusations.

So, if accusations are positive tests, you now know the false positives and the true positives. You know nothing about the negative tests (those who were not accused)


You have been saying that the 5% is referencing the false positive rate. The definition of false positive rate is FP/(FP + TN).

In none of these studies did they have a true negative number, therefore they could not calculate a false positive rate. In real world terms, in order to calculate the false positive rate, we would need the number of innocent men accused divided by all the innocent men in that population. No study attempted to calculate this number.

All studies calculated the number of false positives divided by the number of total positives. Which is the definition of 1-ppv.


anisotropy

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Re: Statistics update
« Reply #66 on: October 05, 2018, 09:33:25 PM »
I have to think about what you said Caroline PF. But even if you are right, and 5% is indeed 1-PPV like you said, I think we can still do the calculation.

1 we know the population composition and 2. we know (assumed really) the false negative rate being crimes not reported. And this reverts back to what laserlady proposed some days ago.
           
                          positive                      negative
50                           17                              33                   this part doesn't change
950                           1                              949                 this changes and 1-PPV = 1/18 ~5%
                               18                             982

But when you do the problem like this, you can derive the fp for the innocent group. 1/950, and when we apply it to the general population with known 87000 reported (assumed to be true positive). We still get the probabilities of being guilty to be 20ish% given accused.


Caroline PF

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Re: Statistics update
« Reply #67 on: October 05, 2018, 10:01:04 PM »
I have to think about what you said Caroline PF. But even if you are right, and 5% is indeed 1-PPV like you said, I think we can still do the calculation.

1 we know the population composition and 2. we know (assumed really) the false negative rate being crimes not reported. And this reverts back to what laserlady proposed some days ago.
           
                          positive                      negative
50                           17                              33                   this part doesn't change
950                           1                              949                 this changes and 1-PPV = 1/18 ~5%
                               18                             982

But when you do the problem like this, you can derive the fp for the innocent group. 1/950, and when we apply it to the general population with known 87000 reported (assumed to be true positive). We still get the probabilities of being guilty to be 20ish% given accused.

Quick note: 87000 reported is total number accused in 2012. It is the total positive (equivalent to the 18 in your box), not just the true positive.

I agree with your derived false positive rate based on these numbers of 1/950.
But how do you get 20% probability being guilty given those numbers that you wrote? Can you show me the math you used?

The way I see it, if you are accused, you are by definition in the positive test group, and either a false positive (innocent) or a true positive (guilty). You cannot be a true negative or a false negative, because the negative group is the group that wasn´t accused of anything. 
« Last Edit: October 05, 2018, 10:11:18 PM by Caroline PF »

anisotropy

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Re: Statistics update
« Reply #68 on: October 06, 2018, 12:22:28 AM »
Sorry I was out.

If like you say, 87000 is the total positive, then true positive for the year would be 87000/18*17 = 82166
With a false positive rate of 1/950, meaning, out of every 950 person 1 would be accused falsely.
If we apply that to the population 312M, of which 95% is not rapist. We would expect to get 312000 false accusations. 312M *0.95 /950.

The issue is that even with a low false accusation rate of 1/950, given the population base and relatively small amount of criminal ratio, the true positives will become only a small portion.

Your view is that if accused, you are automatically from either the rapist group or the non-rapist group. I agree with you here. We just don't know exactly which one.

Rapist group: We know these cases account for ~95% of the 87000. If we KNEW one is from the rapist group, he would be guilty.
Not-rapist group: We know these cases account for ~5% of the 87000. If we KNEW one is from the nonrapist group, he would be innocent.

So far I think we are in agreement. But now we need to deal with the ~0.1% of the false accusation rate.

I understand you may find it nonsensical to account for 312000 accusations which were not reported, but they are not fabricated. Because we are not dealing with cases any longer. If our knowledge were perfect or that we had 100% fpr / 0 false accusation, there would be no need to do this calculation, but we are not omniscient.

Each of the 82116 case is also an true positive accusation. Given one is accused (without knowing where it comes from, as we have no way of knowing which group the case came from), the odds of the case coming from the rapist group (hence guilty) is true positive accu/ (false positives accu + TP accu).

The odds of being from the accusation rapist group (therefore guilty) is 82166 / (312000 false accusations + 82166 true accu.) =21%. Note how 82166/87000 = ~95%. They are describing two different events.

One 95% of reported cases are guilty (rapist cases). Another is when accused (not a case), there is a 21% chance of being guilty. They are both true.

I think if we do the problem by treating the 5% as fpr instead of fp, we are making the distinction that we will be working with rates and would need to be tied back to the actual population and need to work with actual case#. With fp, we can work on it as long as the population composition is known.


« Last Edit: October 06, 2018, 01:32:55 AM by anisotropy »

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Re: Statistics update
« Reply #69 on: October 06, 2018, 01:41:54 AM »

I understand you may find it nonsensical to account for 312000 accusations which were not reported, but they are not fabricated.

Well, yes.  If an accusation is not reported, it has not been made.  It is not an accusation.  (Is it a dead parrot?  Or is that just this thread?)

Do you ever stop to think logically about what you are writing?

You seem to be trying to treat these so-called 312000 false accusations as a double negative in order to bring them into the calculation.  Which is nonsense.  You can say "this would be a false accusation if it had been made".  You can't then say it has been made when it hasn't, which is what you are doing.


Jesus wept.

anisotropy

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Re: Statistics update
« Reply #70 on: October 06, 2018, 01:47:30 AM »
No, each case is an accusation, but the reverse is not true.

An accusation does not need to be a case. With 0.1% false accusation rate assumption that was built in, we need to apply that to the population. Otherwise, what does that number even mean?

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Re: Statistics update
« Reply #71 on: October 06, 2018, 02:05:58 AM »
No, each case is an accusation, but the reverse is not true.

An accusation does not need to be a case. With 0.1% false accusation rate assumption that was built in, we need to apply that to the population. Otherwise, what does that number even mean?


Quite.  It doesn't mean anything because if an accusation has not been made it does not exist.

https://www.youtube.com/watch?v=DkQhK8O9Jik

Caroline PF

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Re: Statistics update
« Reply #72 on: October 06, 2018, 08:32:18 AM »

I understand you may find it nonsensical to account for 312000 accusations which were not reported, but they are not fabricated.

Well, yes.  If an accusation is not reported, it has not been made.  It is not an accusation. 

Former Player is right. This is nonsensical and impossible. The number of accusations are by definition the number of accusations reported to authorities. And the number of false allegations are the subset of that number that are shown to be false.

So the number of false allegations made in 2012 can be assumed to be around 4350, applying the 5% historical rate to the 87000.

Or the number could be a total of 312000 false accusations based on a 0.1% false positive rate that we calculated earlier, applied to the population. I agree with this math. If the FP rate is correct, this is the number of false allegations we should see.

But both of these numbers can´t be right. Which means we screwed up our math somewhere, and the false positive rate of 0.1% is wrong.


I was mulling it over last night, and I believe I know where we went wrong. The numbers for false positive rate that we calculated earlier are nonsensical because we changed units mid calculation. Let me explain.

         
                          positive                      negative
50                           17                              33                   this part doesn't change
950                           1                              949                 this changes and 1-PPV = 1/18 ~5%
                               18                             982

But when you do the problem like this, you can derive the fp for the innocent group. 1/950,

To start, we took a population of 1000 men, and applied an assumed statistic of 5% have assaulted in their lifetime to come up with 50 men who have assaulted sometime in the past, and 950 who have never assaulted.

So far, so good.

But then we took that 50 and changed it to 50 assaults, in order to apply the assumed statistic that 2/3 assaults are not reported. And came up with 17 reported assaults and 33 non-reported assaults.

But the number of men who have ever assaulted, and the number of assaults in a year are not the same number. This is where we screwed up.

So the 949, the true negative number we calculated, is nonsensical because it was derived from nonsense inputs.


So, I´m going to try to find the false positive rate again, without making the same logical error.

Inputs: false allegations (1-ppv) of 5% and 2/3 of cases not reported.

                         positive                      negative
285                         95                             190                   
???                           5                              ???             
???                         100                            ???

I don´t think we have enough information to finish the derivation. If there are 285 assaults, how many non-assaults do we have in the same time frame? How would we even define non-assaults? Number of consensual sexual encounters? Number of attempted sexual encounters that failed? Number of days that an assault didn´t happen, multiplied by the at-risk population?

Okay, try again with the 2012 population numbers.
Inputs: total reported cases 87000, false allegation rate of 5%, and male population of 156M (312M / 2), 95% of whom are non-rapists.

                         positive                      negative
7.8M                    82650                           ???                   
148.2M                  4350                           ???             
156M                   87000                           ???

If the first column is total population of men, the second column would be total men accused in a year. The third column should thus be total men not accused this year, and can be calculated with simple subtraction.

                         positive                      negative
7.8M                    82650                           7.7M                   
148.2M                  4350                        148.2M             
156M                   87000                        155.9M

So the false positive rate in this example is 4350 / 148.2M = 0.003%
« Last Edit: October 06, 2018, 08:52:22 AM by Caroline PF »

anisotropy

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Re: Statistics update
« Reply #73 on: October 06, 2018, 09:33:05 AM »
So.... based on your reasoning, given a person is accused, what are the odds they are guilty? just 95%? That doesnt seem very Bayesian to me, I am not saying you are wrong btw.

Ya i was thinking about it last night too. I think I will actually go to the local college next week and see if I could talk to a prof, not necessarily the same prof. I will present to them the following, just like i had done the first time. In addition to the questions below, I want to find out specifically which treatment of "5% as the false allegation rate" is appropriate, ie, as fp or fpr. And of course, the "Fabricated" false accusation in the population thing from the previous post. Oh the things I would do for knowledge. Stay tuned, thanks.

Now, I am going to apply the same method for "actually being a criminal". In this hypothetical case, the numbers are just an estimate with assumptions built in (let's assume they are appropriate), but that is not the main issue I am concerned about.
I am assuming 5% of the population are criminals. 5% as the false allegation rate. Assuming only about 1/3 of the crimes are reported, so I am using 2/3 as false negative rate.

The 2x2 table would look like this

                                  5%                             accused                          not accused
Criminals                    50                                  17                                   33
Not Criminals             950                                48                                  902
                                 1000                                65                                  935

so, 65 people are accused but only 17 people are actual criminals; that's 26% chance of a person being actual criminal when accused of a crime, despite the false allegation rate being only 5%.

Now my questions are (if you find this interesting enough to answer): Was my framing/formulation of the problem appropriate? What logic trap did I fall in which yielded this puzzling result? Under what circumstances can I or can't I set up the table like this?
« Last Edit: October 06, 2018, 09:38:02 AM by anisotropy »

Caroline PF

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Re: Statistics update
« Reply #74 on: October 06, 2018, 10:20:51 AM »
So.... based on your reasoning, given a person is accused, what are the odds they are guilty? just 95%? That doesnt seem very Bayesian to me, I am not saying you are wrong btw.

Yeah, it doesn´t seem very Bayesian, because it doesn´t require Bayesian calculations.


You are asking for the following: given someone is accused of a crime, what are the chances he is actually guilty? So what part of the Bayesian square are you looking to find? The false positive rate? The sensitivity? The specificity?

You are taking a positive test (accused of crime) and wanting to know what percentage are true positives (actually guilty). That is the Positive Predictive Value that you are looking for.

Quote
Positive predictive value is the probability that subjects with a positive screening test truly have the disease.
Negative predictive value is the probability that subjects with a negative screening test truly don't have the disease.

I already showed you that the real world data is calculating the 1-ppv, and calling it the ¨false accusation rate¨.

So you are asking the following:
Given a 1-PPV of 5%, what is the PPV?

Simple calculation, which doesn´t require Bayesian calculations, despite being based on Bayesian numbers.


So if you do go talk to another professor, don´t focus on your calcuations, because you have been doing them right. Focus instead on asking about where the real world numbers fit in the grid, and which output that you are looking for. The example that you created for the professor, had correct math, but I believe that the assumptions were faulty. The professor responded that your math was correct, and that FPR and PPV were different numbers because they are different concepts. That is all correct. But he never addressed your assumptions, and that´s the real question that we have been discussing in this thread.

maizeman

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Re: Statistics update
« Reply #75 on: October 06, 2018, 10:41:03 AM »
So.... based on your reasoning, given a person is accused, what are the odds they are guilty? just 95%? That doesnt seem very Bayesian to me, I am not saying you are wrong btw.

You can certainly take a bayesian approach, but if you did you'd want to feed into it the assumptions of a population of about 250,000 rapists, each with a 1/3 chance of being accused, and about 159,750,000 innocent men, each with an approximately 1 in 40,000 chance of being accused.

This is based on the following assertions:

-160M men living in the USA
-87,000 accusations of rape
-5% of accusations of rape are later shown to be false
-1/3 of rapes are reported/result in accusations.

From those four assertions we can calculate:

1. The number of true positives (total accusations of rape * (1 - the proportion of accusations of rape which are false)).
2.  The number of false positives (total accusations of rape * the proportion of accusations of rape which are false)
3. The number of false negatives (number of true positives * 2) <-- since if 2/3rds of rapes are unreported then the number of false negatives must be 2x the number of true positives.
4. The number of true negatives (total men in the USA - the sum of the first three categories).

This gives a confusion matrix that looks like this.

Code: [Select]
                    Rapists             Non-rapists
Accused              82,650 (TP)              4,350 (FP)
Not Accused         165,300 (FN)       159,747,700 (TN)

So for non-rapists the chance that they are accused is 0.0000027* (or ~1 in 40,000) and for rapists the chance that they are accused of rape is .33 (or 1 in 3). If you plug this numbers into the Bayesian formula you're already using, you should get an answer which is correct (or at least as correct as the accuracy of the four assertions listed above).

This also simplifies by assuming a rapist will only attack one person per year. In reality, studies suggest that even among rapists and those who commit sexual assault, a small number of perpetrators are responsible for a large proportion of total assaults.

*This doesn't quite match Caroline PF's number just because we started with slightly different numbers of assumed total men.
« Last Edit: October 06, 2018, 10:53:37 AM by maizeman »

Caroline PF

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Re: Statistics update
« Reply #76 on: October 06, 2018, 10:47:53 AM »
Here is how I would word the question to the statistics professor:


Assume there is a type of crime. When retrospective studies were done on accusations of this crime, they concluded that 5% of accusations turned out to be false accusations.

Let's also assume that 5% of the population will commit this crime in their lifetimes.

Further, let's assume that only 1/3 criminals will ever be accused of this crime in their lifetime.*

I am interested to know what the likelihood is of an innocent man being accused of this crime (false positive rate?), and what the likelihood is that the accused is guilty (positive predictive value?).

How would I fill in the following square?

                                   accused              not accused
criminal         50               ???                       ???
non-criminal 950               ???                       ???
                 1000               ???                       ???

In other words, let the professor fill the table in and see if it matches the numbers that you filled in.


* I made this number up. I have no idea what the real world number is. 2/3 rapes not reported is not the same as 2/3 rapists never reported. So the numbers derived here would not necessarily apply to the real world.

shenlong55

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Re: Statistics update
« Reply #77 on: October 06, 2018, 11:23:53 AM »
So.... based on your reasoning, given a person is accused, what are the odds they are guilty? just 95%? That doesnt seem very Bayesian to me, I am not saying you are wrong btw.

Yeah, it doesn´t seem very Bayesian, because it doesn´t require Bayesian calculations.


You are asking for the following: given someone is accused of a crime, what are the chances he is actually guilty? So what part of the Bayesian square are you looking to find? The false positive rate? The sensitivity? The specificity?

You are taking a positive test (accused of crime) and wanting to know what percentage are true positives (actually guilty). That is the Positive Predictive Value that you are looking for.

Quote
Positive predictive value is the probability that subjects with a positive screening test truly have the disease.
Negative predictive value is the probability that subjects with a negative screening test truly don't have the disease.

I already showed you that the real world data is calculating the 1-ppv, and calling it the ¨false accusation rate¨.

So you are asking the following:
Given a 1-PPV of 5%, what is the PPV?

Simple calculation, which doesn´t require Bayesian calculations, despite being based on Bayesian numbers.


So if you do go talk to another professor, don´t focus on your calcuations, because you have been doing them right. Focus instead on asking about where the real world numbers fit in the grid, and which output that you are looking for. The example that you created for the professor, had correct math, but I believe that the assumptions were faulty. The professor responded that your math was correct, and that FPR and PPV were different numbers because they are different concepts. That is all correct. But he never addressed your assumptions, and that´s the real question that we have been discussing in this thread.

Thank you!

anisotropy

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Re: Statistics update
« Reply #78 on: October 06, 2018, 12:52:22 PM »
The professor said my "framing was correct", which I understood to be my assumptions were valid. But I will check again as you suggested.


In other words, let the professor fill the table in and see if it matches the numbers that you filled in.


That's a fair suggestion, thanks.
« Last Edit: October 06, 2018, 01:33:07 PM by anisotropy »

anisotropy

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Re: Statistics update
« Reply #79 on: October 06, 2018, 02:38:29 PM »
UPDATE

I am now 99% sure I have been wrong this whole time. I sincerely apologize to all. It was not my intention to be malicious or gross, I had genuinely believed what I said was true. The odds of being guilty off a single accusation is not 26%, it's much higher. I am sorry.

I want to thank Caroline PF and Maize especially as their step-by-step guidance made my error glaringly clear (even to a halfwit such as myself).

Regards,

Caroline PF

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Re: Statistics update
« Reply #80 on: October 06, 2018, 03:19:06 PM »
Anisotropy,

Thank you for being willing to engage in discussion with me. I am not a statistics expert by any means, and I found that I learned a lot about statistics through my exchanges with you.

Maybe I'll even improve my scores on my re-certification exams, as they usually include questions on bayesian statistics. :)

former player

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Re: Statistics update
« Reply #81 on: October 06, 2018, 03:36:44 PM »
Thank you for the apology. Many would not have had the guts to make one, even anonymously on the internet, and I appreciate that you have done it.

shenlong55

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Re: Statistics update
« Reply #82 on: October 06, 2018, 04:40:01 PM »
Thank you for the apology. Many would not have had the guts to make one, even anonymously on the internet, and I appreciate that you have done it.

+1

shuffler

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Re: Statistics update
« Reply #83 on: October 06, 2018, 05:08:06 PM »
Thank you for the apology. Many would not have had the guts to make one, even anonymously on the internet, and I appreciate that you have done it.

+1
+1

... though perhaps you should also voice it, briefly, on the BK thread.
Your "vindicated by the professor" post over there was ... rather over the top.

anisotropy

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Re: Statistics update
« Reply #84 on: October 06, 2018, 05:36:10 PM »
Thank you for the apology. Many would not have had the guts to make one, even anonymously on the internet, and I appreciate that you have done it.

+1
+1

... though perhaps you should also voice it, briefly, on the BK thread.
Your "vindicated by the professor" post over there was ... rather over the top.

Done

shuffler

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Re: Statistics update
« Reply #85 on: October 06, 2018, 05:54:51 PM »
Thank you for the apology. Many would not have had the guts to make one, even anonymously on the internet, and I appreciate that you have done it.

+1
+1

... though perhaps you should also voice it, briefly, on the BK thread.
Your "vindicated by the professor" post over there was ... rather over the top.

Done
Forthright.  Well done.  Thanks.

golden1

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Re: Statistics update
« Reply #86 on: October 06, 2018, 06:58:35 PM »
Heh, I have been reading along with fascination.

Anisotropy has done this before in arguments before, when we were talking about racism and he refused to deal with any history prior to some arbitrary date that he specified.  He has a need to control the discussion and to be correct, and can only do that by irrationally defining his argument to some arbitrary standard.

It’s honestly not worth arguing here.  I would not trust this person to be able to frame the question to the professor correctly or without bias.

What an odd person.

anisotropy

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Re: Statistics update
« Reply #87 on: October 06, 2018, 07:36:43 PM »
Heh, I have been reading along with fascination.

Anisotropy has done this before in arguments before, when we were talking about racism and he refused to deal with any history prior to some arbitrary date that he specified.  He has a need to control the discussion and to be correct, and can only do that by irrationally defining his argument to some arbitrary standard.

It’s honestly not worth arguing here.  I would not trust this person to be able to frame the question to the professor correctly or without bias.

What an odd person.

We did not discuss "racism" per se, rather, more about how progressive helped Trump win. I did not want to conflate that issue with race related topics because those should be discussed on their own.

I have been reading a slew of books from your list, including Stamped. I have not changed my views expressed in the progressive helped Trump win thread.

Like everyone else, I won't know I am wrong until I do.

This one was a serious mea culpa. I mistook P(A|B) for P(B|A), which was not correct.

Gin1984

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Re: Statistics update
« Reply #88 on: October 06, 2018, 08:52:42 PM »
Here is how I would word the question to the statistics professor:


Assume there is a type of crime. When retrospective studies were done on accusations of this crime, they concluded that 5% of accusations turned out to be false accusations.

Let's also assume that 5% of the population will commit this crime in their lifetimes.

Further, let's assume that only 1/3 criminals will ever be accused of this crime in their lifetime.*

I am interested to know what the likelihood is of an innocent man being accused of this crime (false positive rate?), and what the likelihood is that the accused is guilty (positive predictive value?).

How would I fill in the following square?

                                   accused              not accused
criminal         50               ???                       ???
non-criminal 950               ???                       ???
                 1000               ???                       ???

In other words, let the professor fill the table in and see if it matches the numbers that you filled in.


* I made this number up. I have no idea what the real world number is. 2/3 rapes not reported is not the same as 2/3 rapists never reported. So the numbers derived here would not necessarily apply to the real world.
Just a side note here, when psychology researchers discribes rape, 30% of the undergraduate male students in the studies (on average) admit to raping.  So maybe using number 5% may not be good idea.

golden1

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Re: Statistics update
« Reply #89 on: October 07, 2018, 07:05:16 AM »
Right, and you refused to incorporate any facts into your world view prior to 1964.

I have no proof that you actually are reading anything, just as we have no proof that you are talking to professors. This could all be trolling or just virtue signalling on your part.

The thing that really gets me about you is the fucking arrogance.  Anyone who doesn't agree with you is less intelligent or "doesn't get it".  Maybe you have high IQ, but you seem to struggle with EQ quite a bit.  If you are trying to sway people to your arguments, you seem to be failing, pretty dramatically.  You might want to do some introspection on why that is. 

radram

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Re: Statistics update
« Reply #90 on: October 07, 2018, 09:37:42 AM »
UPDATE
I want to thank Caroline PF and Maize especially as their step-by-step guidance made my error glaringly clear (even to a halfwit such as myself).

Anyone else wonder why Sol got absolutely nothing. He tried 3 ways from Sunday to explain what you were doing, and how to do it correctly. When you finally took his advice and posed another question to your expert, they "showed you the way".

Even if you hate Sol for other reasons, I found it a little rude to ignore his efforts.

And thank you for publicly apologizing here AND the original thread. That just does not happen anymore, and should.

I must admit, I enjoy very much playing with numbers, but this discussion was creeping me out. I am glad it was moved to another thread.


anisotropy

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Re: Statistics update
« Reply #91 on: October 07, 2018, 10:10:40 AM »
Right, and you refused to incorporate any facts into your world view prior to 1964.

I have no proof that you actually are reading anything, just as we have no proof that you are talking to professors. This could all be trolling or just virtue signalling on your part.

The thing that really gets me about you is the fucking arrogance.  Anyone who doesn't agree with you is less intelligent or "doesn't get it".  Maybe you have high IQ, but you seem to struggle with EQ quite a bit.  If you are trying to sway people to your arguments, you seem to be failing, pretty dramatically.  You might want to do some introspection on why that is.

lol ok

anisotropy

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Re: Statistics update
« Reply #92 on: October 07, 2018, 10:13:21 AM »
UPDATE
I want to thank Caroline PF and Maize especially as their step-by-step guidance made my error glaringly clear (even to a halfwit such as myself).

Anyone else wonder why Sol got absolutely nothing. He tried 3 ways from Sunday to explain what you were doing, and how to do it correctly. When you finally took his advice and posed another question to your expert, they "showed you the way".

Even if you hate Sol for other reasons, I found it a little rude to ignore his efforts.

And thank you for publicly apologizing here AND the original thread. That just does not happen anymore, and should.

I must admit, I enjoy very much playing with numbers, but this discussion was creeping me out. I am glad it was moved to another thread.

I do not hate Sol or anything like that. I thanked CPF and Maize because it was specifically through their replies I realized the mistake I had made. I did not receive the same "benefits" from reading Sol's posts, unfortunately.

Regardless, Sol was right, what I originally said was indeed counterfactual. I am sorry Sol.


sol

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Re: Statistics update
« Reply #93 on: October 07, 2018, 10:30:56 AM »
I am sorry Sol.

No worries.  I'm glad you came around.  If my explanations weren't clear enough to convince you, I have no hard feelings about someone else doing a better job than I did. 

Despite having this math questions resolved, I think it's important to take a moment to reflect on this discussion and the way it went down, because you made a lot of people very uncomfortable with your absolute insistence that sexual assault survivors are mostly liars.  It's possible to be mathematically correct and still a huge asshole, and admitting your math mistake in this instance doesn't change that.

anisotropy

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Re: Statistics update
« Reply #94 on: October 07, 2018, 12:05:20 PM »
I was a huge asshole.

I was a huge asshole precisely because I insisted what was counterfactual to be "objectively true". I inadvertently spread lies and created unjustified doubt and confusion. I became someone I despise the most.

There was a huge problem with my treatment of false allegation rate, as many had pointed out. But I did not understand at the time.

As golden1 pointed out, hubris played a big role, I have no excuse for that.

Watchmaker

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Re: Statistics update
« Reply #95 on: October 08, 2018, 02:49:55 PM »
Wow, that was quite a thread.

I'm glad several of you stuck it out with anisotropy to help him understand his mistake. Kudos to Caroline PF and Maize for finally getting through, but also for Sol and the others for continuing to try. (I also appreciate how this conversation was moved to a new thread when people objected to it in the BK one).

Anisotropy -  Admitting your error was a good move (and I imagine a hard one). It doesn't cancel out the fact that your were 1) very incredibly wrong 2) arrogant 3) and a jerk (these last two would have been true even if your math wasn't wrong). I truly hope you learn from this and use it as an opportunity to grow.

Jeez, you people actual have me feeling (a tiny, tiny bit) optimistic.

anisotropy

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Re: Statistics update
« Reply #96 on: October 08, 2018, 03:47:47 PM »

Anisotropy -  Admitting your error was a good move (and I imagine a hard one). It doesn't cancel out the fact that your were 1) very incredibly wrong 2) arrogant 3) and a jerk (these last two would have been true even if your math wasn't wrong). I truly hope you learn from this and use it as an opportunity to grow.


Nothing cancels past actions out to those affected.

I always admit my errors freely when proven wrong, it is easy for me to do. I have no baggage and no identity in an argument. The only thing that matters is if the situation/argument is factual.

Therefore, being arrogant and a jerk is often a inexorable outcome from where I stand, for truth must be defended no matter what.

In the case that I am wrong (like this one), I simply switch side with the same (if not higher) level of conviction. I do what I think is right, people's perception (of me) mean little to me. That being said, I do need to keep my hubris in check, I succumb to it from time to time.

sol

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Re: Statistics update
« Reply #97 on: October 08, 2018, 03:56:28 PM »
Jeez, you people actual have me feeling (a tiny, tiny bit) optimistic.

I got the exact opposite impression.  Anisotropy continued to argue that sexual assault victims are mostly liars right through the nationally televised testimony of a sexual assault victim, up until the moment the perpetrator was confirmed to the supreme court and the whole thing became moot, then changed his mind. 

Maybe that was a genuine change of heart, but it sure does look like awfully convenient timing.

Watchmaker

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Re: Statistics update
« Reply #98 on: October 08, 2018, 03:59:09 PM »

Anisotropy -  Admitting your error was a good move (and I imagine a hard one). It doesn't cancel out the fact that your were 1) very incredibly wrong 2) arrogant 3) and a jerk (these last two would have been true even if your math wasn't wrong). I truly hope you learn from this and use it as an opportunity to grow.


Nothing cancels past actions out to those affected.

I always admit my errors freely when proven wrong, it is easy for me to do. I have no baggage and no identity in an argument. The only thing that matters is if the situation/argument is factual.

Therefore, being arrogant and a jerk is often a inexorable outcome from where I stand, for truth must be defended no matter what.

In the case that I am wrong (like this one), I simply switch side with the same (if not higher) level of conviction. I do what I think is right, people's perception (of me) mean little to me. That being said, I do need to keep my hubris in check, I succumb to it from time to time.


I think you're missing a couple lessons here. Namely:

Perhaps the fact that you can be so astonishing wrong about such a simple thing that you claimed to understand well means that you should approach your future opinions more humbly.

And there's the issue that, even if you had been correct, you brought your "facts" to the wrong audience, in the wrong way, at the wrong time. You hurt people needlessly. You can serve truth and be kind at the same time. This time, you managed neither. Next time, try for both.

...

And there goes my optimism.  That was short lived.

anisotropy

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Re: Statistics update
« Reply #99 on: October 08, 2018, 04:03:10 PM »

Maybe that was a genuine change of heart, but it sure does look like awfully convenient timing.

lol ok. It was right here

Quote
Simple calculation, which doesn´t require Bayesian calculations, despite being based on Bayesian numbers.

and

Quote
This gives a confusion matrix that looks like this.

Code: [Select]

                    Rapists             Non-rapists
Accused              82,650 (TP)              4,350 (FP)
Not Accused         165,300 (FN)       159,747,700 (TN)


So for non-rapists the chance that they are accused is 0.0000027* (or ~1 in 40,000) and for rapists the chance that they are accused of rape is .33 (or 1 in 3).

I started to see where I went wrong. I wish I had known better and understood sooner. But that's the nature of arguing on the internet via posts. If we had been face to face, someone would have pointed out my error ie, I took P(A|B) to be P(B|A), very quickly in a convincing manner.
« Last Edit: October 08, 2018, 04:07:41 PM by anisotropy »