### Math 225 Course Notes

### Section 1.4: The Simple Random Sample

There are many ways of taking random samples,
the most theoretically important of which is the *simple random sample*.
In this book, all random samples are assumed to be simple.
Other important methods of random sampling in practice include
*stratified random sampling* and *multi-stage sampling*.

A *simple random sample* is a sample that is chosen according to
a procedure where all samples of the same size have the same chance of being
selected.
This is just like picking names from a hat.

Data from simple random samples are the easiest to analyze.
However, there are reasons for using other sampling methods.
To insure that there is sufficient representation from various groups,
a researcher could take a *stratified random sample*.
This is accomplished by taking a simple random sample
from each of several groups.

Another common sampling scheme is *multi-stage sampling*.
For example, to take a sample of households:

- Take a random sample of counties in the U.S.
- Then, take a random sample of townships within each county.
- Then, take a random sample of voting blocks within each township.
- Finally, take a random sample of households within each voting block.

It is not necessary to have a complete national list of households,
and travel between households will be easier.
We will only study data from simple random samples.

Last modified: Jan 15, 1996

Bret Larget,
larget@mathcs.duq.edu