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****Date:** Mon, 10 Jul 2006 12:36:48 +0800
**Reply-To:** Haijie Ding <haijie.ding@gmail.com>
**Sender:** "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
**From:** Haijie Ding <haijie.ding@gmail.com>
**Subject:** Question on response rate determination simulation
**Content-Type:** text/plain; charset=WINDOWS-1252; format=flowed
Dear Listers,

We have made a simulation to help us determine a minimum sample size for a
survey we'd like to distribute.

The simulation generates a series of hypothetical populations that range in
size from 100-10,000 values, drawn randomly from a normal distribution (mean
4.0, std dev 1.0)

For each population we take random samples of size 10%, 20%... 100%

For each sample we compute the Student's t-test against the parent
population and record any sample that has a significantly different mean
from the population (p < 0.05)

For each sample size we repeat the random selection/testing 1000 times and
record the ratio of sig. dif. samples to total samples (with the assumption
that if less than 5% of the samples don't approximate the population mean
then this sample size is not large enough)

We expected to find that we needed a large relative sample size when the
population size was small, but this doesn't appear to be true and has us
confused…

Even for a population of 100, taking 10 samples seems to be enough to
approximate the mean.

Since this seems to contradict experience, so there must be something wrong
with the simulation design?

Testing the populations show that they are indeed normally distributed and
have the correct mean and stddev, and the samples are random subsets of the
parent population and of the correct size. Our t_test and various other
equations (mean, stddev, variance, t_cdf (t significance test)) have all
been verified against SPSS's values and don't seem to be the problem.

Thanks for any insight!
Haijie Ding, Ph D,
Cognitive Psychologist,