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bob.appleyard
Joined: 15 Oct 2005
Posts: 7718
Location: Manchestar, innit
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| Posted: Wed Oct 11, 2006 7:48 pm Post subject: Central Limit Theorem |
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| I know roughly what the conclusion means -- that a large enough population is (approximately) normally distributed -- but why? I looked at some seriously nasty proofs, so I'm hoping someone would be kind enough to break it down for me... |
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Josh
Joined: 01 Feb 2004
Posts: 6604
Location: Across America
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| Posted: Wed Oct 11, 2006 8:44 pm Post subject: |
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It's kinda tricky and can be misleading if you don't realize that this all is dependent upon the original population but, the population distribution doesn't matter... according to the law of large numbers.
You've got a population.
1. People (and lots of em)
You take a sample.
2. Some people (usually more than 30) within the People.
You've got a mean value.
3. The height of 5.9 ft. (that's just a guess)
Your sample grows.
4. The first 10 people were all giants, but as you increase your sample you begin to have other heights and the limit of the standard deviation approaches zero (like in calculus kinda) (note: zero is the center, thus the "central limit")
Basically, your taking a population and applying it to a new scale that measures based on Z-scores and standard deviations from the mean.
The law of large numbers says that the difference between a sample mean and a population mean approach zero as your sample grows. (usually around 30, don't ask me why, it's just 30... it just happens to always start to become normally distributed around this number.)
I'm guessing that this doesn't help. I'm sure someone else can explain it better. I just give it another try later when I can sit down to review my old statistic books. |
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bob.appleyard
Joined: 15 Oct 2005
Posts: 7718
Location: Manchestar, innit
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| Posted: Thu Oct 12, 2006 9:08 am Post subject: |
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| Sorry, when I said "population" I meant "sample size". |
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GTTofAK
Joined: 09 Jan 2005
Posts: 5968
Location: Alaska
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| Posted: Fri Oct 13, 2006 5:16 pm Post subject: |
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Not true at all. There has to be steps taken to make sure that the sampling is representative. In 1936 a major magazine concluded that Alfred Landon would win the presidency from Roosevelt in a land slide. They believed their poll to be fool proof because of how large the sample was. If memory serves me correctly the number of respondents was in the hundreds of thousands.
But there was one slight problem. The respondents were picked from the automobile registries and the few rich people owned cares in 1936 were not feeling the same effects of the depression as everyone else. |
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Josh
Joined: 01 Feb 2004
Posts: 6604
Location: Across America
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| Posted: Sat Oct 14, 2006 4:49 pm Post subject: |
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Quote: But there was one slight problem. The respondents were picked from the automobile registries and the few rich people owned cares in 1936 were not feeling the same effects of the depression as everyone else.
Sorry I forgot to include the words, "RANDOMLY SELECTED".
Otherwise your example doesn't apply here and you just stated why. |
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