quote:
You're asserting that for large enough numbers of schools, half will fall below average. You are basing this on the central limit theorem which applies to random samples - however, the samples are not random, meaning you are wrong. (Not surprising from a guy who thinks ice has no mass.)

Actually your use of a sample is flawed since we are actually talking about the population as a whole. Regardless you seem to be arguing that if a sample doesn't meet each assumption of the CLM that the scores won't be normally distributed; however, the underlying distribution is normal because the variables are theoretically normal and raw test scores are "transformed" into a scale that is normal (e.g., t-scores, standard scores, normal curve equivalents, etc).

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Posted by SpidermanTUba

my house

Member since May 2004

36128 posts

Posted on 10/1/14 at 11:11 pm to buckeye_vol

quote:
. Regardless you seem to be arguing that if a sample doesn't meet each assumption of the CLM that the scores won't be normally distributed;

No. That is not what I am arguing. I am arguing that "Half the schools are below average" is not a tautology, even for large numbers of schools. That is it.

quote:
however, the underlying distribution is normal because the variables are theoretically normal and raw test scores are "transformed" into a scale that is normal (e.g., t-scores, standard scores, normal curve equivalents, etc).

Yes - IF the raw scores are transformed to conform to a normal distribution, the distribution will be normal - I certainly agree with that. Its not a presumption I was making.

It still doesn't guarantee a normal distribution of school performance as measured by average test scores, as the individuals' test scores that a school has aren't independent of one another.

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