In our last article, we talked about simple random samples. Simple random samples are, well…simple, but they’re not always optimal or even possible.

Probability samples that don’t meet the assumptions of Simple Random Samples are called Complex Samples.

You’ll also hear the term Complex Survey, which is really just a survey that incorporates some sort of complex sampling design. Because of their size and research goals, surveys are usually* the only type of research study that uses complex samples.

(*but not always. I have seen intervention studies, for example, that used complex sampling).

### What is a Complex Sample?

The most defining feature of a complex sample is that sample members do not have equal probability of being selected.

That sounds simple enough. But… (more…)

*by Karen Grace-Martin and Trent Buskirk*

Sampling is such a fundamental concept in statistics that it’s easy to overlook. You know, like fish ignore water.

It’s just there.

But how you sample is actually very important.

There are many different ways of taking probability samples, but they come down to two basic types. Most of the statistics we’re trained on use only one of those types—the simple random sample.

If you don’t have a simple random sample, you need to incorporate that into the way you calculate your statistics in order for the statistics to accurately reflect the population.

## Why all this is important

Remember the objective of a sample is to represent the population of interest.

Simple random samples do that in a very straightforward way.

Because they’re simple, after all.

Complex samples do it as well, but in a more…roundabout way. Their roundabout nature has many other advantages, though. But you do need to make adjustments to any statistics you calculate from them.

## What is Simple random sampling?

Simple Random Samples (SRS) have a few important features.

### 1. Each element in the population has an equal probability of being selected to the sample. ** **

That’s pretty self-explanatory, but it has important consequences and requirements.

First, it requires that the list of all individuals in the population is available to the researcher.

Practically, this is never entirely true. But we can often get close. Or we can at least have reason to believe that the individuals who are available are in no systematic way different than the ones who aren’t.

That belief may or may not be reasonable, and it’s a good thing to question in your own research.

One consequence is that all observations are independent and identically distributed (i.i.d.). You’re probably familiar with this term because it’s extremely important in statistics **and modeling in particular**.

### 2. The sample is a tiny proportion of an infinite population, but…

Now, we know that most populations aren’t really infinite. But once they get to a certain size, that part doesn’t matter mathematically.

The overall samples tend to represent a very small fraction of this very, very large population. But don’t let the small sample size fool you.

That’s where the beauty of simple random sampling comes in. Your sample doesn’t have to be that large to adequately represent the population from which it is drawn if the selection was done through simple random sampling.

In fact, most polls of Americans are conducted using simple random samples of telephone numbers and a sample of roughly 1,200 adults in the U.S.

This relatively small sample is enough to represent the full population of approximately 300 million people and to estimate a binary outcome like “will you vote or not in 2014 general elections?” within 3 percentage points.

In the next post in this series, we’ll talk about the other kind of probability sample: Complex Samples.