Sampling Theory

Sampling theory deals with the principles and techniques of selecting a subset of individuals from a population in order to make inferences about the whole. This poster summarises the core methods and the estimators associated with each.

Key Concepts

• Population vs. sample — parameters vs. statistics
• Sampling frame — the list from which the sample is drawn
• Sampling error — variability due to chance selection
• Non-sampling error — bias from design or measurement flaws

Probability Sampling Methods

Simple Random Sampling (SRS)

Every unit has an equal chance of selection. Estimates are unbiased; variance formulas are straightforward.

Systematic Sampling

Select every k-th unit from an ordered list. Simple to implement; risk of periodicity bias.

Stratified Sampling

Divide the population into homogeneous strata, then sample within each. Reduces variance when strata are internally similar.

Cluster Sampling

Randomly select groups (clusters) and observe all or a sample of units within them. Cost-effective for geographically dispersed populations.

Multistage Sampling

Combine methods across multiple stages — e.g. select clusters, then stratify within each.

Estimators

For each design the poster lists the point estimator, estimated variance, and confidence interval formula for means, totals, and proportions.