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…

There are many ways of meeting this defining feature while also being capable of representing the population and having advantages for other research goals.

You’ve probably heard of some of the common design features of complex samples. It’s these features that create the complexity.

If you’ve got one or more of these, you can consider your sample complex:

- Stratification
- Clustering
- Oversampling
- Sampling Without replacement
- Finite populations
- Multistage sampling

Our next article will define each of these terms, but there are two things that are important to understand first.

First, whenever a sample is complex, **statistical estimation and analysis are more complex**.

In order for the sample’s data to accurately estimate the population, you *must* account for the design features in the analysis. This means using stat software that’s designed just for complex samples.

Second, despite this,** there are very good reasons to use complex samples**.

### Three Very Good Reasons to use Complex Samples

**1. Complex samples can be incredibly cost effective, while improving the precision of sample estimates. **

In other words, a good complex sampling design will simultaneously cost much, much less to administer *and* keep standard errors smaller than they would be in a simple random sample.

When your research budget is tight (and whose isn’t?), this is hugely important.

**2. Complex samples allow access to difficult-to-access sampling frames. **

For example, it’s very difficult to sample schoolchildren without first sampling schools or patients without sampling hospitals. Including these multiple stages of sampling means not every student or patient has an equal probability of being in the sample (making the sample complex).

** 3. Complex samples can ensure sufficient representation of small sub-population groups in the final sample. **

Let’s say you want to study color blind people over age 75 from rural areas. This group makes up a tiny, tiny proportion of the overall adult population. To have sufficient numbers in the group to make any statistical comparisons or have reasonably sized confidence intervals, you’d have to sample millions of people using simple random sampling. Oversampling this group allows you to have enough group members to study them, but it makes the overall sample complex.