Sampling Methods and Survey Design

By the end of this lesson, you will be able to distinguish between population and sample, identify types of sampling (random, stratified, cluster, systematic, convenience), recognize sources of bias, and evaluate the quality of a statistical study.

The Big Idea

Statistics is the science of drawing conclusions about populations from samples. The validity of any statistical conclusion depends entirely on how the sample was collected. A biased sample produces biased conclusions, no matter how sophisticated the analysis. Sampling design is therefore the most important step in any study.

Key Terms

Population: the entire group of interest (all students, all voters, all adults).

Sample: the subset actually studied.

Parameter: a numerical summary of the population (unknown, estimated from data).

Statistic: a numerical summary of the sample (the estimate of the parameter).

Sampling Methods

Simple Random Sample (SRS)

Every individual in the population has an equal chance of being selected. The gold standard.

Method: assign numbers to everyone, use a random number generator.

Stratified Random Sample

Divide the population into groups (strata) based on a relevant characteristic, then randomly sample from each stratum.

Use: when the population has natural subgroups and you want to ensure each is represented.

Cluster Sample

Divide the population into clusters (geographic areas, classrooms), randomly select some clusters, then sample everyone in the selected clusters.

Use: when it's expensive to travel across a large population.

Systematic Sample

Select every $k$th individual from a list, after a random starting point.

Use: when you have an ordered list of the population.

Convenience Sample

Select whoever is easiest to reach.

Problem: almost always biased. Rarely valid for inference.

Sources of Bias

Selection bias: the sample systematically excludes certain groups.

Example: surveying online when studying elderly populations (fewer online users).