*Sampling Distributions*

*David C. Howell*

There are several things that can be done to demonstrate sampling
distributions. The ones that I can think of easily mostly involve computer programs, but I
do have a few other ideas.

- Use a simple computer program written for SAS to draw samples
from one population to illustrate the sampling distribution of the mean. A. This program
draws from different population distributions, and illustrates some features of the
central limit theorem. It is very simple to rewrite it for other software packages.
- Draw multiple samples from a population with a known mean and run a simple
*t* test of the sample mean against the population mean.
This has the advantage of giving them some idea about the sampling distribution of *t*,
and illustrates that even when the null is true, *t* varies from sample to sample,
and rejects the null for some samples, but not for others. (This assumes that students
already understand the idea behind the *t* test. However, they should be able to
understand the basic idea even if they have no idea how to calculate *t*.)
- Use a SAS or an SPSS program to examine the sampling
distribution of
*F* both when the null hypothesis is true and when it is false.
Both programs are included in this link.
- Go to the three door problem and discuss the varying
results of repeated applications of that experiment.
- How can we apply the concept of a sampling distribution, as discussed here, to the
"three door" problem?

- Ask each student to collect data from three acquaintances on their subjective
probability that some specific event will occur (e.g., the chances that Ross Pirot will
run for President again).
- Have students obtain the price of a family sized tube of Colgate toothpaste at each of a
dozen different stores, and then ask them to calculate the mean price of all toothpastes
(Regular size) sold at those stores. This will provoke a discussion of standardizing on
sizes, the variability of the number of brands sold (they'll need to pick a fixed sample
size), and other issues in sampling.

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Last revised: 7/11/98