Sampling
There is no concept more fundamental to Statistics than sampling. In fact, some define Statistics as the science concerned with the collection and analysis of samples. A statistical sample is the subset of things from the statistical population that you have measured and that you will use to draw inferences about the population. On this page we will cover the properties of a statistical sample as well as some designs for collecting unbiased samples
Properties of Statistical Samples
There are three important properties that we need to understand before we can begin to use samples to answer our biological questions: 1) sample size, 2) sampling error, and 3) bias.
Sampling Designs
In order to have an unbiased sample, we can’t just jump right in and start collecting data. We need a plan. We need a plan to make sure that we collect an unbiased sample so that we can make reasonable inferences about our population. A random sampling design is the most common plan, but we will also discuss stratified random sampling and systematic sampling designs that might work better for you depending on your circumstances.
Symbols for Population Parameters and Sample Estimates
In statistics we can’t measure everything in a population, so we sample. We therefore need terms and notations (symbols) to be able to clearly identify whether we are talking about the population or the sample. As a general rule, we use Greek letters to refer to population parameters and Latin letters to refer to sample estimates. There isn’t a standard notation for the sample mean. Sometimes x-bar is used and sometimes y-bar is used.
Additional Resources
Sampling and Statistical Power - StatsTree handout
Replication - StatsTree handout
Whitlock & Schluter - The Analysis of Biological Data
Chapter 1: pages 3-10. [Sapling]
Review Questions
Why do we need to sample?
What is the difference between a population and a sample?
Monique is interested in the colors of butterflies in their local park. They catch 10 butterflies, five of which are blue and five of which are orange (i.e. half are blue). In this example, what is the population and what is the sample? Does this measure of 1/2 blue represent a parameter or an estimate?
The Next Steps
Confused?
Let’s move down the tree and review these concepts.
Ready to Move Forward?
Let’s move up the tree to the next topic.