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Author Topic:   Statistics 101
nator
Member (Idle past 343 days)
Posts: 12961
From: Ann Arbor
Joined: 12-09-2001


Message 1 of 199 (386463)
02-21-2007 10:31 PM


In another thread, someone posted this, which is in error:

quote:
The odds of winning the lotto can be a million to one, but if I win it on my first try, then those weren't my odds were they?

I replied:

Er, yes, those are precisely your odds.

I then went on to pose questions which, when answered correctly, would show the error in the first statement:

What are your odds of getting "heads" in a coin toss the first time you do it?

What about the second time? The 10th time? The millionth time?

I have a friend who's got a saying that goes, "The Lottery is just a tax on people who don't understand statistics."

I'd like to make it clear that I am very far away from anything close to being good at math. It has always been a struggle for me.

(but even I know that answer to the question above)

What I want to discuss is what people think the dangers are to society and individuals in not understanding basic statistics, or even basic math.


Replies to this message:
 Message 2 by jar, posted 02-21-2007 10:42 PM nator has responded
 Message 6 by PaulK, posted 02-22-2007 2:06 AM nator has not yet responded
 Message 8 by Thugpreacha, posted 02-22-2007 2:54 AM nator has not yet responded
 Message 15 by Chiroptera, posted 02-22-2007 10:29 AM nator has responded
 Message 42 by Hyroglyphx, posted 02-22-2007 5:59 PM nator has not yet responded

    
jar
Member
Posts: 30997
From: Texas!!
Joined: 04-20-2004
Member Rating: 4.2


Message 2 of 199 (386465)
02-21-2007 10:42 PM
Reply to: Message 1 by nator
02-21-2007 10:31 PM


If you win, your odds are 1.


Aslan is not a Tame Lion
This message is a reply to:
 Message 1 by nator, posted 02-21-2007 10:31 PM nator has responded

Replies to this message:
 Message 3 by nator, posted 02-21-2007 11:26 PM jar has responded
 Message 12 by crashfrog, posted 02-22-2007 10:16 AM jar has not yet responded

  
nator
Member (Idle past 343 days)
Posts: 12961
From: Ann Arbor
Joined: 12-09-2001


Message 3 of 199 (386471)
02-21-2007 11:26 PM
Reply to: Message 2 by jar
02-21-2007 10:42 PM


We are talking about the odds of winning, not the odds after one has won.
This message is a reply to:
 Message 2 by jar, posted 02-21-2007 10:42 PM jar has responded

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 Message 4 by jar, posted 02-21-2007 11:36 PM nator has not yet responded
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jar
Member
Posts: 30997
From: Texas!!
Joined: 04-20-2004
Member Rating: 4.2


Message 4 of 199 (386473)
02-21-2007 11:36 PM
Reply to: Message 3 by nator
02-21-2007 11:26 PM


Really?

The odds of winning the lotto can be a million to one, but if I win it on my first try, then those weren't my odds were they?

From what you quoted it sure looks like after the fact.

Which simply points out the idiocy of trying to apply statistics and science to miracles. All those who suggest such methods are simply being silly.

Miracles by definition are the result of an intentional act and are not, again by definition, repeatable. They are not subject to statistical analysis and any such efforts are simply a waste of time and a sure sign that the person suggesting such tests is pretty clueless about miracles.

If by some miracle someone wins the lotto on their first try, it matters not what the odds were.


Aslan is not a Tame Lion
This message is a reply to:
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Replies to this message:
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New Cat's Eye
Inactive Member


Message 5 of 199 (386474)
02-21-2007 11:40 PM
Reply to: Message 3 by nator
02-21-2007 11:26 PM


We are talking about the odds of winning, not the odds after one has won.

Are the odds the same before and after the event?

In a deterministic universe, there was only one possibility, right?


This message is a reply to:
 Message 3 by nator, posted 02-21-2007 11:26 PM nator has not yet responded

  
PaulK
Member
Posts: 15085
Joined: 01-10-2003
Member Rating: 3.3


Message 6 of 199 (386489)
02-22-2007 2:06 AM
Reply to: Message 1 by nator
02-21-2007 10:31 PM


I'm really not sure of the reasoning behind the statement. The a priori odds do not change based on the outcome. So the only sensible argument I can see is that if you win first time then the game must be rigged somehow. But even that is wrong. It's not AS wrong - but a single win is very unlikely to be sufficient evidence for such a conclusion.
This message is a reply to:
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Modulous
Member (Idle past 277 days)
Posts: 7789
From: Manchester, UK
Joined: 05-01-2005


Message 7 of 199 (386490)
02-22-2007 2:20 AM
Reply to: Message 4 by jar
02-21-2007 11:36 PM


The odds of winning the lotto can be a million to one, but if I win it on my first try, then those weren't my odds were they?

Yes they were. After the fact, the odds of you having won are 1 (almost).


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Replies to this message:
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Thugpreacha
Member
Posts: 12445
From: Denver,Colorado USA
Joined: 12-30-2003
Member Rating: 1.3


Message 8 of 199 (386492)
02-22-2007 2:54 AM
Reply to: Message 1 by nator
02-21-2007 10:31 PM


statistics will not cure a gambler
nator writes:

What I want to discuss is what people think the dangers are to society and individuals in not understanding basic statistics, or even basic math.

As a compulsive gambler, you would think that I was clueless about statistics. I was, but only because I believed in divine intervention on behalf of my statistics. I figured that even if the odds were a million to one, I would be favored somehow and some way.

Pathological gambling is a brain disease that seems to be similar to disorders such as alcoholism and drug addiction. These disorders likely involve problems with the part of the brain associated with behaviors such as eating and sex. This part of the brain is sometimes called the "pleasure center" or dopamine reward pathway.

Treatment for people with pathological gambling begins with the recognition of the problem. Since pathological gambling is often associated with denial, people with the illness often refuse to accept that they are ill or need treatment. Most people with pathological gambling enter treatment under pressure from others, rather than voluntarily accepting the need for treatment.

I am also aware of the gamblers fallacy and can logically understand it. Gambling is not done because one does not comprehend statistics. To cure a compulsive gambler, you don't teach them statistics.


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Replies to this message:
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riVeRraT
Member (Idle past 93 days)
Posts: 5746
From: NY USA
Joined: 05-09-2004


Message 9 of 199 (386522)
02-22-2007 9:29 AM
Reply to: Message 4 by jar
02-21-2007 11:36 PM


Well put jar
Maybe now nator will understand it.

Let me add that the odds of a particular number coming up is just a representation of the number of possibilities.

The odds of getting the number for a particular person cannot be figured, because we don't know what number they will pick, and what number will actually come out.

How can you explain the course of events that led that person to pick that number on the same day that the winning number came out?

There is your objective result, or you data, so now tell us nator, how did that person win? Keep in mind, that luck is not a scientific term.


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 Message 4 by jar, posted 02-21-2007 11:36 PM jar has responded

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PaulK
Member
Posts: 15085
Joined: 01-10-2003
Member Rating: 3.3


Message 10 of 199 (386526)
02-22-2007 9:51 AM
Reply to: Message 9 by riVeRraT
02-22-2007 9:29 AM


Re: Well put jar
Well Jar says you're being silly, so it's good that you agree.

And he's right - your argument is silly. YOu've given no reason to believe that that person won for any different reason than other people win. Some number comes up, and one of the many people who play happens to have chosen it. It happens all the time.


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jar
Member
Posts: 30997
From: Texas!!
Joined: 04-20-2004
Member Rating: 4.2


Message 11 of 199 (386527)
02-22-2007 9:54 AM
Reply to: Message 9 by riVeRraT
02-22-2007 9:29 AM


Re: Well put jar
How can you explain the course of events that led that person to pick that number on the same day that the winning number came out?

There is your objective result, or you data, so now tell us nator, how did that person win? Keep in mind, that luck is not a scientific term.

When we are dealing strictly with the Lottery though, I agree with Schraf. There the answer is simply luck. Frankly, IMHO your position is even sillier than her's.


Aslan is not a Tame Lion
This message is a reply to:
 Message 9 by riVeRraT, posted 02-22-2007 9:29 AM riVeRraT has responded

Replies to this message:
 Message 54 by riVeRraT, posted 02-22-2007 8:28 PM jar has responded

  
crashfrog
Inactive Member


Message 12 of 199 (386534)
02-22-2007 10:16 AM
Reply to: Message 2 by jar
02-21-2007 10:42 PM


If you win, your odds are 1.

On what planet?

If you win, the odds are the number of combinations of numbers that result in your winning - 1 - to the number of possible combinations of numbers in total.

You're just being glib, I guess, but you're also being completely inaccurate. Even if you were the only one who played the lottery that time, unless you bought every single number combination, the odds of you winning were not 1 - even if you did win.

This is a thread about understanding statistics. Let's not undercut that aim with glib misrepresentations of mathematics, ok?


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crashfrog
Inactive Member


Message 13 of 199 (386535)
02-22-2007 10:21 AM
Reply to: Message 7 by Modulous
02-22-2007 2:20 AM


After the fact, the odds of you having won are 1 (almost).

The odds don't change after you win.

You still figure the odds by looking at the outcome sample space - the total number of different combinations of lotto numbers - compared to the subset of those outcomes that results in your victory.

In the case of the Powerball, that's 1 in 146 million. Before, after, it doesn't matter. The actual outcome doesn't change the probabilities of any of the outcomes. That something happened or didn't happen doesn't change the probability of it happening.


This message is a reply to:
 Message 7 by Modulous, posted 02-22-2007 2:20 AM Modulous has responded

Replies to this message:
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crashfrog
Inactive Member


Message 14 of 199 (386537)
02-22-2007 10:28 AM
Reply to: Message 9 by riVeRraT
02-22-2007 9:29 AM


Re: Well put jar
The odds of getting the number for a particular person cannot be figured, because we don't know what number they will pick, and what number will actually come out.

Irrelevant.

We know how lotto numbers are generated, so we can develop a sample space of outcomes. We know exactly how many different combinations (not permutations, the lottery doesn't work like that) of numbers are possible.

And it doesn't matter what number any particular individual picks; they all have the same probability of being the winning numbers (because the game isn't fixed.)

There is your objective result, or you data, so now tell us nator, how did that person win?

They won because they picked the winning numbers. Given the average size of the population who buys tickets (and assuming they all play different numbers) we can tell you, on average, how long it will be before somebody wins.

That they picked the winning numbers is not significant. Imagine that you have two machines running - one generates one random lotto number every night, and the other machine generates a hundred thousand random lotto numbers every day. It shouldn't surprise anyone that, every few days or so, there's a match between the number generated by the first machine and one of the numbers generated by the second.


This message is a reply to:
 Message 9 by riVeRraT, posted 02-22-2007 9:29 AM riVeRraT has responded

Replies to this message:
 Message 55 by riVeRraT, posted 02-22-2007 8:35 PM crashfrog has responded

  
Chiroptera
Member
Posts: 6649
From: Oklahoma
Joined: 09-28-2003
Member Rating: 5.1


Message 15 of 199 (386539)
02-22-2007 10:29 AM
Reply to: Message 1 by nator
02-21-2007 10:31 PM


Hi, scraf.

First, I have to point out that your situation is about probability, not statistics, which are different, although they are related and even overlap a bit.

I'm teaching the Introduction to Probability course this term. I've never taken nor taught a probability course before myself (although I have taken and taught statistics courses) so it's been jolly fun.

Taking a cue from the text, the first day I told the class that if I toss a fair coin, the probability that it will land heads is 1/2. Then I asked what did that sentence mean? Some (including myself) would say that it means that if I toss the coin a whole bunch of times, then about half the time the coin should land heads. But what does "about half the time" mean? In fact, it is entirely possible that if I toss a coin 100 times in a row, even if it is fair, I can get heads every time.

I also asked what it would mean if I only intended to toss the coin once. Or what does it mean that the probability of rain tomorrow will be 20%, given that tomorrow will only come once.

So I told them (being an honest sort) that we will develop the mathematical formalism for probability and then learn how to take real situatlions like coin tosses and dealing cards and translate them into the mathematics to calculate the probabilities, and I hoped they wouldn't notice that I never actually answer the original question.


Actually, if their god makes better pancakes, I'm totally switching sides. -- Charley the Australopithecine
This message is a reply to:
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Replies to this message:
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