Statistics puzzle - answers by Friday

[RJT]

He has made assumptions about the mindset of the responders by relying on bad data and refuses to acknowledge that a properly-formed puzzle would be every bit as useful in demonstrating the difficulties of using statistics in the courtroom (or everyday life for that matter).

vQ

Well if it's "every bit as useful", then it's no more useful than the example that was provided. Why would i feel the need to change it?

RJT.

 

[vonQuux]

Yup, i can see that - yet it still doesn't in anyway invalidate the task. Just because i didn't state right at the start that "the real task is to realise that the qustion has no clear answer without further information", or "what else do you need to know to answer this?" doesn't change a thing.

You can keep trying to change my question but that won't fly.

My difficulty with your puzzle precludes any complaint about insufficient data. If the question was only missing data, I'd have no quarrel.

My difficulty with your puzzle is that there were multiple interpretations about what was being asked in the first place.

These are two entirely different things. The former is a statistics puzzle. The latter is not.

The exercise was actually to test whether or not you would question the validity of drawing any conclusion from the statistic.

Again, a reader can be 100% ignorant of statistical methods and still see a problem with your question as phrased.

Perhaps a different example will help.

When I was in grade school, a teacher asked the class a question along the lines of "Bobby puts $20 into the bank at 5% interest per year. How much money will you have after three years?"

One might logically ask "is this interest compound?" The query does not invalidate the original question as a math problem since I realized I needed more math data to provide an accurate answer.

On the other hand, one might ask what the teacher means by "you." People might begin saying, "Who's this 'you?' I thought it was Bobby's money. Does the teacher want to know how much money Bobby has or how much money I have?"

One need not have any knowledge of math or the concept of interest to have a problem with understanding what, exactly, the teacher was asking. One can reasonably criticize the teacher for asking an imprecise question. One can also reasonably state that if the word "you" was replaced with "Bobby" then the math lesson would be every bit as useful as without the imprecision of language (indeed, moreso).

And here is the crux of my point: One may reasonably complain that this imprecision renders the question no longer one of math but instead a question of syntax and that one cannot address the math without first addressing the syntax. Sure, the teacher may indeed have been testing to see if the students would realize that the critical question of compounding was omitted but the students have abandoned the problem since they don't even know whose money we're talking about.

You're no longer demonstrating a flaw in the application of statistical methods. Is this a bit clearer?

VO can huff and puff all he likes, but if you pick up a new paper right now there's a safe bet that you could find % being used in a similar way.

Well, there goes your excuse about not wanting to waste any more time on this thread.

Well if it's "every bit as useful", then it's no more useful than the example that was provided. Why would i feel the need to change it?

What I said is "...a properly-formed puzzle would be every bit as useful in demonstrating the difficulties of using statistics in the courtroom...."

"Every bit as useful" does not mean "exactly equal to," it means "at least equal to." In other words, the imprecision of the language could have been omitted while making just as useful a point as intended.

My entire argument here is that the imprecise language made your point harder to understand and appreciate.

Good lord, man, you really don't want to engage in a discussion about the merits of my argument, do you? Your contortions to avoid the simple problem are remarkable!

I won't go back and count but for the nth time, what specific line of my logic is flawed? It's no longer possible for you to credibly claim you don't read my posts or that you won't spend any more time on this thread so...

vQ

 

[RJT]

I'm sorry i'm just missing your entire argument - what do you want to hear?
I've stated the purpose of the question, everyone else seems to have quite enjoyed it and appreciated it for what it was. A simple exercise that demonstrates how little it takes to draw incorrect conclusions. Such as a title is as little as it needs.
If there's such a major issue with the question, why are you the only one that sees it?
Are you honestly trying to say you've never seen stats being used in such an ambiguous manner in a valid setting? Or being placed on such a deliberately misleading background?
This is actually my last post on this topic - you've got your argument. We all get it, you want the question to be more specific and to avoid the ambiguity that was deliberately instilled into it. Not every question in life is and regularly stats are used in a misleading fashion. The question was fashioned to be misleading in both its wording and the information it provided. It deliberately attempted to cause the reader to draw the wrong conclusion. It served very well in the lecture given and it seems to have served the same purpose equally well here with everyone barring you got a reasonable sense of amusement out of it.
If you feel that another question would have served the purpose as well i award you a round of applause. I see no need nor reason to change it. You are right, it has absolutely nothing to do with statistics however - which is what you really want here - and everything to do with the assumptions that people can be drawn to. I posted the title to be deliberately misleading, that is undeniable and I am completely unapologetic for the heinous crime.


RJT.

 

[sagefr0g]

Yup, i can see that - yet it still doesn't in anyway invalidate the task. Just because i didn't state right at the start that "the real task is to realise that the qustion has no clear answer without further information", or "what else do you need to know to answer this?" doesn't change a thing.
You are confronted with statistics just as vague and ambiguous every day of your life. In the media, your place of work and your social life and every day you will take for granted what conclusions can be drawn from them - generally the conclusion that the author wishes you to draw.
In the case mentioned above, the jury and the court both accepted the testimony of an "expert" witness who had drawn completely erroneous conclusions simply because an equally ill-founded statistic seemed logical. Nobody questioned this because it seemed intuitive.
The exercise was actually to test whether or not you would question the validity of drawing any conclusion from the statistic. VO can huff and puff all he likes, but if you pick up a new paper right now there's a safe bet that you could find % being used in a similar way.

RJT.

lol you may not believe this but i was going to respond to Von that i don't even believe totaly the answers even when i to the best of my ability know that they are correct. lol . this is the thing that i'm sure so many forum members and guests alike see from my posts. i know and understand a lot of what is being bandied about here. i believe most of the orthodox stuff. yet i still question and seek other 'directions' if you will. this may not be fair to interject into some problem put forth or some set of ideas like those we discuss on this forum but i'll say it anyway. yes maybe the math is correct, yes the theory is sound. but no that doesn't necessarily preclude other possibilities for better results or equal results, accurancy or things working out well when all your best efforts are put forth as directed. other things can happen that are outside of the scope of the math, the theory and the practical circumstances you live under. something is usually left unsaid or maybe said and then not fully addressed what ever i don't know. just shooting the breeze here lol. maybe my teachers inflicted me to hard and heavy with that critical thinking thing lol. ever get the sense your like a deer froze in the headlights when facing so much information overload lol. do they even have deer in England?

 

[vonQuux]

You are right, it has absolutely nothing to do with statistics however - which is what you really want here - and everything to do with the assumptions that people can be drawn to.

Precisely!

Now you just need to recognize that there were two camps of people who read your post. There were some who felt that the question was incomplete and for them, the lecture went "as planned." There were also those who weren't even sure that what question was being asked and that specific ambiguity was not necessary to demonstrate your point on statistics.

In other words, some people gave up on your puzzle due to elements of the puzzle which were not necessary to make the point.

In other-other words, some people were inadvertently excluded from the lesson due to language that did not make that lesson any better.

To make an apropos comparison, the vagueness in syntax was a bit like betting against a slightly incorrect TC. It didn't wreck your game but it was suboptimal.

This is what you get for replying to a linguistics geek.

And no offense intended. I was just seeking to help you make that story more useful to your audience the next time you told it.

In fact, I'm not even concerned that you agree with my criticism so much as grasp what I'm driving at. That didn't seem to occur until now.

So if you think I have a point, great, roll with it. If you think my advice is garbage, or that the language used is necessary to demonstrate the point, disregard it.

You know what they say about advice/opinions...

vQ

 

[Bigdiggie]

Here's an interesting little puzzle for everyone to have a hard think about.
I will post a solution to this on Friday, until then if you genuinely already know the answer, please keep it to yourself and let others have a go -

Suppose we have a diagnostic test for a particular disease which is 99% accurate.
A person is picked at random and tested for the disease.
The test gives a positive result. What is the chance that the person actually has the disease?

RJT.

I "think" i disagree with most of what has been posted here. I believe answer is 99%, only because the fact that the statement was made "the test is 99% accurate" already takes into account that the test has been right and wrong at particular samples of populations. Thus, doing additional caculations based on population samples is redundant and would account for a slight inaccuracy in the answer (98%). To be able to say that the test is 99% accurate, one would have already had to have done population sampling tests to indicate that statistic. I would very much argue the point that one does not need to know the occurance of the disease in the general population in order that the question need to be answered.

 

[la_dee_daa]

I "think" i disagree with most of what has been posted here. I believe answer is 99%, only because the fact that the statement was made "the test is 99% accurate" already takes into account that the test has been right and wrong at particular samples of populations. Thus, doing additional caculations based on population samples is redundant and would account for a slight inaccuracy in the answer (98%). To be able to say that the test is 99% accurate, one would have already had to have done population sampling tests to indicate that statistic. I would very much argue the point that one does not need to know the occurance of the disease in the general population in order that the question need to be answered.

the idea is that every individal test is 99% accurate so for every individual person that is tested there is a 99% chance of the test being accurate.
That is generally what they mean when the test is 99% accurate.

:cow:

 

[InPlay]

This is the answer !

 

[vonQuux]

This is the answer !

The answer is Ted Nugent?

vQ