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re: "Half the schools are below average" - not always true

Posted on 9/30/14 at 10:24 am to
Posted by SpidermanTUba
my house
Member since May 2004
36128 posts
Posted on 9/30/14 at 10:24 am to
quote:


However, it has been shown that in large enough sample sizes, and when averaging the scores of the students (i.e., the mean of means) that we come to be able to use something called the Central Limit Theorem.

Dont worry, your 7005 class will cover this in November.



Your understanding of the central limit theorem is flawed.

The central limit theorem means that if we take a large enough population of Presidential polls - the results of those polls will be normally distributed.

It doesn't mean if we sample a large enough population, the result of the poll will always tend towards 50/50.


So in this context - it would mean if we created samples of schools by random selection - the distribution of scores among those samples is normally distributed - it doesn't mean the scores themselves are normally distributed. If that's the case - it means there can be no skewed distributions in nature - which is kinda absurd as they are observed all the time.
This post was edited on 9/30/14 at 10:29 am
Posted by CptBengal
BR Baby
Member since Dec 2007
71661 posts
Posted on 9/30/14 at 10:31 am to
quote:

It doesn't mean if we sample a large enough population, the result of the poll will always tend towards 50/50.


Go reread what I said, clown.

When we are getting testing values for schools, we are averaging the testing of the students in that school.

Then by computing the mean value to determine central tendency, we are also computing a mean.

By computing the mean of the means for a large number of students nested within schools and then calculating the central tendency of that higher population we are doing exactly what you suggest by

taking the average of a population of polls. Each school is a population.

good god man.
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