# Section 1.4: Other Effective Sampling Methods

## Objectives

By the end of this lesson, you will be able to...

- describe the difference between the stratified, systematic, and cluster sampling techniques
- identify which sampling technique was used
- determine an appropriate sampling technique given a situation
- obtain a stratified, systematic, or cluster sample

For a quick overview of this section, feel free to watch this short video summary:

## Review: Simple Random Sampling

Do you remember how simple random sampling works? Visually, it's just numbering each individual and randomly selecting a certain number of them. Here's the image we used in the previous section:

## Stratified Sampling

Stratified sampling is different. With this technique, we separate the population using some characteristic, and then take a proportional random sample from each.

A **stratified sample** is obtained by separating
the population into non-overlapping groups called *strata* and then
obtaining a proportional simple random sample from each group. The individuals
within each group should be similar in some way.

Visually, it might look something like the image below. With our population, we can easily separate the individuals by color.

Once we have the strata determined, we need to decide how many individuals
to select from each stratum. (Man, that's a weird word!) The key here is that
the number selected should be *proportional*. In our case, 1/4 of the
individuals in the population are blue, so 1/4 of the sample should be blue
as well. Working things out, we can see that a stratified (by color) random
sample of 4 should have 1 blue, 1 green, and 2 reds.

For another take, watch this YouTube video:

Example 1

One easy example using a stratified technique would be a sampling of people
at ECC. To make sure that a sufficient number of students, faculty, and
staff are selected, we would stratify all individuals by their status -
students, faculty, or staff. (These are the *strata*.) Then, a proportional
number of individuals would be selected from each group.

## Systematic Sampling

A **systematic sample** is obtained by selecting every *k*th
individual from the population. The first individual selected corresponds to a random number between
1 and *k*.

So to use systematic sampling, we need to first order our individuals, then select every *k*th.
(More on how to select *k* in a bit.)

In our example, we want to use 3 for *k*? Can you see why? Think what would happen if we
used 2 or 4.

For our starting point, we pick a random number between 1 and *k*. For our visual, let's
suppose that we pick 2. The individuals sampled would then be 2, 5, 8, and 11.

In general we find *k* by taking *N*/*n* and rounding
down to the nearest integer.

For another take, watch this YouTube video:

Example 2

Systematic sampling works well when the individuals are already lined up in order. In the past, students have often used this method when asked to survey a random sample of ECC students. Since we don't have access to the complete list, just stand at a corner and pick every 10th* person walking by.

* Of course, choosing 10 here is just an example. It would depend on the number of students typically passing by that spot and what sample size was needed.

## Cluster Sampling

Cluster sampling is often confused with stratified sampling, because they both involve "groups". In reality, they're very different. In stratified sampling, we split the population up into groups (strata) based on some characteristic.

A **cluster sample** is obtained by selecting
all individuals within a randomly selected collection or group of individuals.

In essence, we use cluster sampling when our population is already broken
up into groups (*clusters*), and each cluster represents the population.
That way, we just select a certain number of clusters.

With our visual, let's suppose the 12 individuals are paired up just as they were sitting in the original population.

Since we want a random sample of size four, we just select two of the clusters. We would number the clusters 1-6 and use technology to randomly select two random numbers. It might look something like this:

For another take, watch this YouTube video:

One situation where cluster sampling would apply might be in manufacturing. Suppose your company makes light bulbs, and you'd like to test the effectiveness of the packaging. You don't have a complete list, so simple random sampling doesn't apply, and the bulbs are already in boxes, so you can't order them to use systematic. And all the bulbs are essentially the same, so there aren't any characteristics with which to stratify them.

To use cluster sampling, a quality control inspector might select a certain
number of entire boxes of bulbs and test each bulb within those boxes. In
this case, the boxes are the *clusters*.

## Convenience Sampling

Other methods do exist for finding samples of populations. In fact, you've
seen some already. Probably the most common is the so-called **convenience
sample**. Convenience samples are just what they sound like - convenient.
Unfortunately, they're rarely representative. Think of the radio call-in
show, those people in the shopping malls trying to survey you about your
purchasing habits, or even the voting on American
Idol!

Here's a specific example. It's a poll on beliefnet.com, titled "What Evangelicals Want". All online polls use, by nature, convenience sampling. According to the article, "The poll was promoted on Beliefnet’s web site and through its newsletters." Only those evangelicals who visit this particular web site and actually answer the survey are included. Beware any poll result taken with convenience sampling.

## Multistage Sampling

Often one technique isn't possible, so many professional polling agencies
use a technique called **multistage sampling**. The strategy
is relatively self-explanatory - two or more sampling techniques are used.

For example, consider the light-bulb example we looked at earlier with cluster sampling. Let's suppose that the bulbs come off the assembly line in boxes that each contain 20 packages of four bulbs each. One strategy would be to do the sample in two stages:

**Stage 1:** A quality control engineer removes every 200th box coming off
the line. (The plant produces 5,000 boxes daily. (This is *systematic* sampling.)

**Stage 2:** From each box, the engineer then samples three packages to inspect.
(This is an example of **cluster** sampling.)

The US Census also uses multistage sampling. If you haven't already (you should have!), read Section 1.4 in your text for more details.

## Summary

Here's a visual summary of the four main sampling strategies:

## Simple Random:

## Stratified:

## Systematic:

## Cluster: