Sampling Techniques and Sampling Distributions
Core rules
- Probability sampling includes simple random (with or without replacement), stratified, systematic, cluster and multistage sampling.
- Non-probability sampling includes convenience, quota and purposive or judgement sampling.
- Stratified sampling divides a heterogeneous population into homogeneous strata; cluster sampling selects whole groups.
- Sampling error arises from observing a sample; non-sampling errors include non-response, measurement and recording errors.
- Standard error of the mean: SE = σ/√n; with finite population correction SE = (σ/√n)√[(N−n)/(N−1)].
- For large n, the sampling distribution of the mean is approximately normal by the central limit theorem.
Worked example
A population has σ = 15. For n = 100, SE = 15/√100 = 1.5. If the sample is drawn without replacement from N = 500, FPC = √[(500−100)/(500−1)] = √(400/499) ≈ 0.895, so SE ≈ 1.5×0.895 ≈ 1.34. Quadrupling n to 400 would halve the standard error to about 0.75 before FPC.
Traps
- Thinking a larger sample removes bias; it mainly reduces variance.
- Confusing stratified and cluster sampling.
- Using FPC when sampling with replacement.
- Calling a data-entry mistake sampling error.
- Forgetting SE shrinks with √n, not with n.