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re: "Half the schools are below average" - not always true
Posted on 10/1/14 at 5:26 pm to buckeye_vol
Posted on 10/1/14 at 5:26 pm to buckeye_vol
quote:never read it
Look I think The Black Swan is a great book
quote:
Test scores would fall in the latter groups for a number of reasons that I explained in an earlier post.
Not of the reasons you explained in an earlier post are correct reasons.
The central limit theorem only applies when the sample is randomly selected. In this case the sample is chosen by school.
Ignoring the political impossibility of it - are you seriously telling me its mathematically impossible for a state to allocate 100% of its education resources to 10% of the schools and 0% to 90% of the schools, thus creating a system with 90% of the schools below average - regardless of the number of schools involved?
This post was edited on 10/1/14 at 5:32 pm
3
Posted on 10/1/14 at 5:44 pm to SpidermanTUba
quote:
Not of the reasons you explained in an earlier post are correct reasons.
The central limit theorem only applies when the sample is randomly selected. In this case the sample is chosen by school.
Tests are designed to have an underlying normal distribution. Furthermore, test scores are then converted from raw scores to another scale so that the scores are truly normal.
quote:
Ignoring the political impossibility of it - are you seriously telling me its mathematically impossible for a state to allocate 100% of its education resources to 10% of the schools and 0% to 90% of the schools, thus creating a system with 90% of the schools below average - regardless of the number of schools involved?
Then maybe the score that represents the average will be different but since these are norm-referenced tests, they usually adjust accordingly when converted (e.g., Flynn Effect for IQ stores). Although the distribution may be slightly impacted, it should still be relatively normal because there will be ceiling and floor effects (i.e., usually can't go lower than a 200 on SAT composite or higher than an 800. Not to mention, there are so many other variables at play in your hypothetical that aren't accounted for (e.g., demographics, developmental limitations, cognitive limitations).
Posted on 10/1/14 at 6:01 pm to SpidermanTUba
quote:
The central limit theorem only applies when the sample is randomly selected. In this case the sample is chosen by school
If we are using the entire population then we aren't worrying about randomization of a sample because it's not a sample. Furthermore, it is often difficult to get a truly random sample of an entire population and instead use convenience sampling. Guess what? Most of the time the distribution is approximately normal. The generalization of results may be impacted though. Besides the variables themselves are still random and there are statistical methods that are used to account for the non-independence of participants (HLM) if that is necessary.
Posted on 10/1/14 at 6:08 pm to SpidermanTUba
quote:
are you seriously telling me its mathematically impossible for a state to allocate 100% of its education resources to 10% of the schools and 0% to 90% of the schools, thus creating a system with 90% of the schools below average - regardless of the number of schools involved?
Where is this being done?
If you can't point a link to a state where this policy is implemented, then why would it be wrong to assume a normal distribution?
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