simple random sample

Target Population and Sampling Frame in Survey Sampling

February 9th, 2015 by

Author: Trent Buskirk, PhD.

As it is in history, literature, criminology and many other areas, context is important in statistics.  Knowing from where your data comes gives clues about what you can do with that data and what inferences you can make from it.

In survey samples context is critical because it informs you about how the sample was selected and from what population it was selected.   (more…)

Sampling Error in Surveys

February 6th, 2015 by

Author: Trent Buskirk, PhD.

What do you do when you hear the word error?  Do you think you made a mistake?

Well in survey statistics, error could imply that things are as they should be.  That might be the best news yet–error could mean that things are as they should be.

Let’s break this down a bit more before you think this might be a typo or even worse, an error. (more…)

What is a Complex Sample? Part 1: Simple Random Samples

January 2nd, 2014 by

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.


Stratified Sampling for Oversampling Small Sub-Populations

June 11th, 2012 by

by Ritu Narayan

Sampling is a critical issue in any research study design. Most of us have grappled with balancing costs, time and of course, statistical power when deciding our sampling strategies.

How do we know when to go for a simple random sample or to go for stratification or for clustering? Let’s talk about stratified sampling here and one research scenario when it is useful.

One Scenario for Stratified Sampling

Suppose you are studying minority groups and their behavior, say Yiddish speakers in the U.S. and their voting.  Yiddish speakers are a small subset of the US population, just .6%. (more…)