How does stratified sampling differ from simple random sampling?
Instruction: Describe the differences between stratified sampling and simple random sampling, including scenarios where each would be preferable.
Updated
Official answer
In simple random sampling without replacement, every possible sample of the specified size has the same selection probability. Equal individual inclusion probabilities alone are not enough to define this design: other sampling schemes can also have that property.
Stratified sampling divides the population into non-overlapping groups that cover the population, then samples within each group. It can secure useful sample sizes for small groups and improve precision when the stratification relates to the outcome. It requires a sampling frame with reliable stratum information.
Allocation need not be proportional. Suppose a population is 90% group A and 10% group B, but the sample takes equal numbers from each. For an overall mean, use the population shares: 0.9 × mean(A) + 0.1 × mean(B), rather than an unweighted average of the two sample means. Variance estimation must also reflect the design.
Choose simple random sampling for a suitable complete frame and straightforward overall estimates; stratify when subgroup precision or an efficient allocation justifies the additional design work. Neither method automatically cures nonresponse or coverage bias.