Sampling Methods and Bias
Define and compare probability sampling methods: SRS, stratified, cluster, and systematic. Identify sources of bias: voluntary response, convenience, undercoverage, and nonresponse bias. Understand that larger samples reduce sampling variability but do not fix bias.
A lesson of AP Statistics, in Collecting Data, about 10 minutes.
Sampling Methods
By the end of this lesson, you will be able to describe common probability and non-probability sampling methods, identify sources of bias, and explain why random sampling is essential for valid inference.
Why Sampling Matters
A population is the entire group we want to study. A sample is the subset we actually observe. Good statistical inference requires a sample that represents the population.
Parameter: a number describing a population (e.g., μ, p). Usually unknown.
Statistic: a number computed from a sample (e.g., $\bar{x}$, $\hat{p}$). Used to estimate the parameter.
Probability Sampling Methods
In probability sampling, every member of the population has a known, nonzero probability of being selected. Only probability samples allow valid statistical inference.
Simple Random Sample (SRS): every possible sample of size n has an equal probability of selection. The gold standard. Use a random number generator or a random number table.
Stratified random sample: divide the population into non-overlapping strata (groups) based on a relevant characteristic; take an SRS from each stratum. Ensures representation from each subgroup; often reduces variability.
Cluster sample: divide the population into clusters; randomly select whole clusters; observe every member of selected clusters. Practical when the population is geographically spread out. Less precise than SRS if clusters are heterogeneous.
Systematic random sample: choose every kth member after a random start. Simple to implement; can be biased if there's a periodic pattern in the population.
Multistage sample: combine several sampling methods (e.g., cluster then SRS within clusters). Used in large-scale national surveys.
Non-Probability Sampling (Avoid for Inference)
Convenience sample: select whoever is easiest to reach. Almost always biased.
Voluntary response sample: participants self-select (call-in polls, online surveys). Systematically over-represents those with strong opinions.
These cannot support valid statistical inference.