Math 225 Course Notes

Section 1.4: The Simple Random Sample

Key Concepts

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.

Types of Random Samples

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:

  1. Take a random sample of counties in the U.S.
  2. Then, take a random sample of townships within each county.
  3. Then, take a random sample of voting blocks within each township.
  4. 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,