Presentation of statistics and probabilities...

PantsOnFire · #1 06-06-2007, 12:11 PM

Let's say an event Y has a one times in a million chance of happening. Now let's say some new factor X is discovered and in the cases where factor X is true, it is now determinied that this same event Y has a more likely chance of occurring and is now 1.4 times in a million.

Can we say that this new factor X (when true) has increased the chance of the event by 40%? Can we say that this new factor X (when true) has increased the chance of the event by .4 times in one million? Do these two statement say the same thing?

And what are the ethics of simply stating something like "Factor X causes a 40% increase in event Y" Is this sort of statement misleading since in reality the actual chance of event Y happening is statitically still very, very low?

SamIAm · #2 06-06-2007, 02:07 PM

You state your first paragraph as fact (and not observation), so I assume you trust your .4 number perfectly. If that's the case, I don't think you have to worry about discussing "stastically very, very low" events. That's the nature of any discussion about your Y.

PantsOnFire · #3 06-06-2007, 04:21 PM

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You state your first paragraph as fact (and not observation), so I assume you trust your .4 number perfectly. If that's the case, I don't think you have to worry about discussing "stastically very, very low" events. That's the nature of any discussion about your Y.

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I had hoped not to bring this up but if it causes a move in this thread so be it.

Let's say that indeed event Y was a very low probability event but the event had severe social and indeed life or death conotations like this example: Event Y = getting lung cancer from tobacco smoke.

ncray · #4 06-06-2007, 05:00 PM

Take your sample space to be whatever. Then P(Y) = .000001 P(Y|X) = 7.142857142857143*^-7

So P(Y|X) / P(Y) = 1.4

This is the same as saying given that X occurred, Y is 40% more likely to occur than if we had no information about X.

I'm fairly certain that you cannot infer any causation from this, but I cannot come up with a good example off the top of my head.

PantsOnFire · #5 06-06-2007, 07:27 PM

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I'm fairly certain that you cannot infer any causation from this, but I cannot come up with a good example off the top of my head.

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I am not so much concerned with the theory or probability or causation, rather I am concerned with the presentation or representation of statisical numbers.

I will go back to my example although in my last post I blew what event Y meant. Event Y is the chance of getting lung cancer with no other factors (like you don't smoke or work in a coal mine). Factor X is the the addition to this norm for getting lung cancer as the fact of living with a smoker (i.e. in a house or apartment for many years).

Let's say for a moment that actually living with a smoker and inhaling second hand smoke increases your chance of getting lung cancer from 1 to 1.4 in one million.

My question was about the presentation of this fact (let's assume it is a fact). Is there any difference between saying your chance of getting lung cancer increases by 40% when you live with a smoker or stating like in the previous paragraph.

My contention is that both statements are true, but you can make more of an impression with one statement than then other. And if you are trying to make an impression with statistics or probability, is it ethical to try to do this?

ncray · #6 06-06-2007, 07:55 PM

You're correct in that both statements are true. I also agree with you that you can make a stronger impression with the 40% statement. I wouldn't say it's unethical to include that statement when trying to make an impression, but it gives less information than the "one in a million vs...". I realize that one in a million is a big underestimate of the incidence of lung cancer, but people might interpret that statistic as meaning that because one in a million is so small, it's not worth worrying about lung cancer, despite the fact that with ~ 6 bil people, we would have 6,000 with lung cancer. It's just an argument about absolute vs relative statistics and when each is useful for what purpose.

UtzChips · #7 06-07-2007, 02:21 AM

I'm not qualified to answer your question, as it pertains to the scientific community, however, if it served the purpose of a politician or the news media, he/she/they would not give it a second thought.

CT11 · #8 06-07-2007, 04:34 AM

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Take your sample space to be whatever. Then P(Y) = .000001 P(Y|X) = 7.142857142857143*^-7

So P(Y|X) / P(Y) = 1.4

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Didn't he state P(Y|X) = 1.4/1000000?

I personally don't see anything ethically wrong with saying event X increases the odds of event Y by 40%. Its true and its not really misleading IMO. I suppose it all depends on context though. As long as you aren't intending to be misleading I think it will come across as not misleading.

Besides their are better ways to lie with statistics [img]/images/graemlins/wink.gif[/img]

peterchi · #9 06-08-2007, 09:04 PM

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And what are the ethics of simply stating something like "Factor X causes a 40% increase in event Y" Is this sort of statement misleading since in reality the actual chance of event Y happening is statitically still very, very low?

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standard.

p.s. unfortunately.

peterchi · #10 06-08-2007, 09:08 PM

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I'm fairly certain that you cannot infer any causation from this, but I cannot come up with a good example off the top of my head.

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Correct. You basically can say nothing about causation without doing a randomized study. Which in many cases is clearly unethical (i.e. randomize to smoke vs. not smoke) or otherwise unfeasible (i.e. randomize to SES).