In inferential statistics, one makes a guess about the value of a parameter in the population--the null hypothesis--and compares the value to measured statistics, finally reaching a conclusion about whether or not the null hypothesis is likely to be true.
In a legal proceeding or informal discussion about someone's culpability, the notion of ''innocent until proven guilty'' is often used as a sort of null hyopthesis; the person is assumed innocent and that assumption is tested against evidence. However, in inferential statistics, situations can arise in which different nullhypotheses are preferable to others. Is it possible that assumptions other than ''innocent until proven guilty'' might better suit certain situations? Is the analogy a bad one?
I have a suggestion for a null hypothesis: Guilty until proven Innocent.
What, you might ask, are the benefits of this experimental model?
There are several, if you are the accusor.
1. The party bringing the indictment has no burden. The burden lies with the accused
to defend himself.
2. If the accusor and the trior are the same party, the trior can set the rules of
the trial to make the accused's burden difficult or impossible to overcome. One way
to do this would be to not allow the accused to present any evidence or argument
in his own defense. To go further, the defendent could be prohibited from even
entering the courtroom at all during the proceeding.
Coupling 1 and 2 above yields a perfect method for an accusor to have a perfect record,
and thus a flawless and impeccable reputation.
This sounds like a great system to me. I never understood why the U.S.
bothers with that other model at all. What are the benefits of that, anyway?
Originally posted by royalchickenIn all the inferential statistics I've studied, the null hypothesis is actually the opposite of what you guessing about the parameter. So for instance, if you want to test that the effect of having blond hair on wages, h, is greater than zero at some significance level, then your null hypothesis would be h = 0. The alternative hypothesis would be h not equal to 0. Running the appropriate test statistic and checking it against a table, you would decide whether to reject or not to reject (different than accepting) the null hypothesis. If you reject it, then you would accept your initial guess about the parameter. If you do not reject, then you cannot tell at that significance level. In this case, you might want to increase your significance level.
In inferential statistics, one makes a guess about the value of a parameter in the population--the null hypothesis--and compares the value to measured statistics, finally reaching a conclusion about whether or not the null hypothesis is likely to be true.
In a legal proceeding or informal discussion about someone's culpability, the notion of ''inn ...[text shortened]... ocent until proven guilty'' might better suit certain situations? Is the analogy a bad one?
Originally posted by royalchicken
Is it possible that assumptions other than ''innocent until proven guilty'' might better suit certain situations? Is the analogy a bad one?
Like what other framework would you suggest? Maybe degrees of deviation from innocence (shades of guilt if you will)? I guess I just need some examples of what alternatives you have in mind.
As far as maybe using "guilty until proven innocent," it just depends on what you want to make more difficult to do: convict an innocent man or acquit a guilty man. In statistics you try to make the test rather difficult for your guess. You want to make sure that you have statistically ruled out the null before accepting your guess. So in the American (and other) legal systems as you say "accused=innocent" is the null. But if you wanted to, you could make "accused=guilty" your null.
Originally posted by royalchickenAh here's an example. Uh . . . ok so you want to make it more difficult to "acquit a guilty man" than to "convict an innocent one."
I have a suggestion for a null hypothesis: Guilty until proven Innocent.
What, you might ask, are the benefits of this experimental model?
There are several, if you are the accusor.
1. The party bringing the indictment has no ...[text shortened]... th that other model at all. What are the benefits of that, anyway?
Why?
Originally posted by telerion''In all the inferential statistics I've studied, the null hypothesis is actually the opposite of what you guessing about the parameter.''
Originally posted by royalchicken
Is it possible that assumptions other than ''innocent until proven guilty'' might better suit certain situations? Is the analogy a bad one?
Well, not really. The type of test you use is affected by your expcetations, but your null hypothesis isn't. Let's use your example. Since you're testing the idea that the effect is different (greater) than 0, your null hypothesis is, as you say, h=0 but since you suspect that being blond makes h > 0, you use a right-tailed test. If you simply suspect that some effect exists, your null hypothesis does not change, but you use a two-tailed test. In other words, you're not supposed to guess about the parameter, but you are supposed to understand the situation to know what to expect. Your post is completely correct--I just had a minor quibble.
''So in the American (and other) legal systems as you say "accused=innocent" is the null. But if you wanted to, you could make "accused=guilty" your null.''
That's what I said. I'm wondering about how different circumstances should affect which null hyppothesis to use.
Originally posted by royalchickenI don't necessarily agree with this post.
I have a suggestion for a null hypothesis: Guilty until proven Innocent.
What, you might ask, are the benefits of this experimental model?
There are several, if you are the accusor.
1. The party bringing the indictment has no burden. The burden lies with the accused
to defend himself.
2. If the accusor and the trior are the same party, t ...[text shortened]... tood why the U.S.
bothers with that other model at all. What are the benefits of that, anyway?
Correct. I had meant to write that the effect was different than zero not greater. Thanks for catching that.
Well, like I say, I think the effect would be that many more innocent people would be wrongly convicted. Actually, I have a strong hunch that this is the kind of standard in place in Guantanamo right now.
So I suppose in cases where the perceived cost (financial, social, political, whatever) of acquiting a guilty person is very high compared to wrongly convicting him/her than go with the "guilty until proven innocent." In most cases though, this sort of standard makes me shiver.
Originally posted by telerionYeah, Guantanamo is a good example, although I wonder if they even use something analogous to a statistical test 😕.
Correct. I had meant to write that the effect was different than zero not greater. Thanks for catching that.
Well, like I say, I think the effect would be that many more innocent people would be wrongly convicted. Actually, I have a strong hunch that this is the kind of standard in place in Guantanamo right now.
So I suppose in cases where the perce ...[text shortened]... "guilty until proven innocent." In most cases though, this sort of standard makes me shiver.
I had an interesting discussion with Cribs about this--he has some ideas regarding no-contest pleas, and I some about how quality of evidence (akin, sort of, to differing levels of significance) affects how we should change our policy in practice. I think he'll post on this in the near future.
First, let me say that I don't have the first clue about null hypotheses or whatchacallit statistics. I just recently (and just barely) understood the Monty Hall Problem, so I doubt even if I really really tried, I would come to even the dimmest understanding of what all this means.
But, as it pertains to what you were asking, about guilty until proven innocent, I have a few thoughts.
The reason that this exists is because the creators of the American judicial system (and whether it was modeled after something, I don't know) believed that the moral consequences of letting a guilty person go free were smaller than convicting a innocent one. It is a matter of creating a moral payoff matrix, as it were.
The logistical ramications would be crippling. For example, the whole concept of due process would have to be totally revised. On a more local level, when a person is accused of a crime, there is a sort of fact finding hearing which the accused can wave and go straight to trial or, if advised can take. The prosecution has to present evidence that could potentially point to this particular accused. The evidence has to only suggest a reasonable possibility of guilt, but without it the case is tabled until new evidence is found (in which case they have another such hearing). If the accused were assumed guilty, this whole process of weeding out completely spurious cases would be perfunctory; the person would be assumed guilty and go straight to trial. The reverse couldn't be applied because a person would have to do more than "suggest innocence" in order to win the hearing. It would clog up a system that is already overwhelmed.
Similarly, the rules for trial itself would have to be completely altered. Take the following example. Let's say Person X and Person Y were seen arguing vehemently at 11:00 by many witnesses. Y leaves at 11:15, and X at 11:20. At 12:00 Y is found dead, murdered by stabbing. X doesn't have an alibi until 12:30 (he lives 15 minutes from Y). There are no witnesses and no forensic evidence linking anyone to the crime (knife wiped clean). Police investigate and charge X.
He's guilty and has to prove innocence, remember. No one finds any evidence that he ever owned this kind of knife, but how can he PROVE that he didn't have it? No finds any blood on his hands or clothes, but how does he PROVE he never had blood on his clothes. No witness sees him anywhere near the crime, but how does he PROVE he wasn't there? &c, &c, &c.
There is no reason to conclude X did this crime; he is no more likely a candidate than you or I am, except that he had an argument with Y. Why not charge me or RoyalChicken? We might not be able to PROVE we weren't there; maybe each of us was alone all evening.
Do you see how this can get complicated, even with a simple case? The payoff for having greater ease in convicting criminals is making it very easy to convict the innocent. This is too great a liability for me, and I would guess for most people. Yes, it means people like OJ Simpson go free, but person X and many other people who can't prove their innocence would be free, too.
Maybe I'm missing the point because I don't understand the statistics, so I apologize if this post states the obvious.
Nemesio
Originally posted by nemesioNo, that's pretty much exactly right. My second post was, I think, facetious. I'll post more tomorrow about some other alternatives.
First, let me say that I don't have the first clue about null hypotheses or whatchacallit statistics. I just recently (and just barely) understood the Monty Hall Problem, so I doubt even if I really really tried, I would come to even the dimmest understanding of what all this means.
But, as it pertains to what you were asking, about guilty until proven ...[text shortened]... e I don't understand the statistics, so I apologize if this post states the obvious.
Nemesio
Originally posted by royalchickenI'm afraid I must strongly disagree with this approach.
I have a suggestion for a null hypothesis: Guilty until proven Innocent.
What, you might ask, are the benefits of this experimental model?
There are several, if you are the accusor.
1. The party bringing the indictment has no ...[text shortened]... th that other model at all. What are the benefits of that, anyway?
While you have outlined some key benefits to the accusor,
there are also some severe drawbacks for the accused.
I know from first-hand experience, because I am familiar
with one community in particular that enforces law using
your proposed method.
In that community, the public at large is required to put
a great degree of faith in the integrity of the law enforcement.
Often times, accused people suddenly disappear from society,
without any explanation given by the authorities. Further,
in this society, the public at large does not have the right
to inquire about the investigation or to question the legal
procedure. They must simply trust that the accused was
justly dealt with. In this community, there is an undercurrent
of unrest, as one never knows exactly what goes on behind
the scenes, and one can never be sure that he will not one day
be accused.
Although the community I describe is in fact quite a real
establishment today, to learn more about this phenomenon,
I have two readings to suggest. One is a factual, historical
account of the Russian Gulag system of several decades past,
entitled The Gulag Archipelago. The other is a work of fiction
by Franz Kafka, entitled, The Trial.
Hopefully, after one reads either or both of these, one would be
left with the feeling that all such systems should be eradicated.
But unfortunately, life does not always work out as we would expect,
and there do in fact exist real systems like this today. If anybody
has any personal accounts of their dealings with such a system,
they might make for an interesting continuation of this thread.
Dr. Cribs