1. ## Graduate Research (how much variation can I have?)

I am currently working on a graduate research paper and statistics is not something I'm good at.

In my proposal I need to compare the STAAR test scores of two schools. The demographics of the schools need to be representative of the average Texas school. African American 14%, Caucasian 35%, Hispanic 48%. The remaining 3% fall into the other group.

How much variation can I have in the percents of the students so that there is a minimum statistical difference? How do I determine that?

On other important number is the Economically Disadvantaged Students, Texas data says its in between 52-55 percent.
Because of the variation can I assume an acceptable variation is built in?

2. ## Re: Graduate Research (how much variation can I have?)

Hey Ranger SVO.

What kind of parameter, measure are you looking at? (For example, the mean? Median?)

If you are doing surveys with stratification then the best linear stratification measure with uniform cost constraints (a cost function is used to introduce how much it costs to actually do a survey/experiment/whatever) will be based on this:

http://eprints.soton.ac.uk/7796/1/7796-01.pdf

This gives the best stratification policy (i.e. the number of samples required for each strata) to get the smallest variance with a uniform cost function (think of it as it costs the same amount resource wise to do one survey at any school).

In terms of difference between the two means, you will need to solve for t-distribution where t_a/2*SE(x_bar-y_bar) < v where t_a/2 is the information for the quantile with alpha/2 in each tail and SE(x_bar - y_bar) is the standard error x_bar - y_bar (given in the formula for t-distribution) and this is just a function of your variance above.

You then solve for a particular (n1,n2) combination and choose any value that satisfies the inequality.

3. ## Re: Graduate Research (how much variation can I have?)

Thank you for your response, let me reword the question a little bit.

If school 1 has a 50% Hispanic, 31% White, 18% African American and 1% other
and school 2 has 47% Hispanic 29% White 21% African American and 3% other

Would these two schools be statistically similar? Could I use something as simple as an F-Test?

If the schools are statistically similar then 30 from each school could be randomly selected, and tested.