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Date:         Mon, 10 Jul 2006 08:05:27 -0400
Reply-To:     Joseph Teitelman temp2 <cmtemp2@pgahq.com>
Sender:       "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From:         Joseph Teitelman temp2 <cmtemp2@pgahq.com>
Subject:      Re: Question on response rate determination simulation
Comments: To: Haijie Ding <haijie.ding@gmail.com>
Content-Type: text/plain; charset=ISO-8859-1

You should be able to derive the sample size mathematically given your prespecified type I and type II error requirements.

>>> Haijie Ding <haijie.ding@gmail.com> 7/10/2006 12:36 AM >>> 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,


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