Question

When is SRS preferred over stratified sampling? That is, under what circumstances is straified sampling inferior to SRS? My professor said "when within variance is larger, and between mean is smaller" stratified sampling isnt going to do much, and SRS would suffice. However, it is unclear what this means. Thoughts?

Answer 1

In Stratified Sampling, we divide the population into groups, called strata. Then, a Simple Random Sample is drawn from each group.

Stratified Sampling is very apt when the population is heterogeneous. Stratified Sampling is used to highlight the differences between groups in a population. In Simple Random Sampling (SRS), all members of the population have an equal probability of being sampled.

In Stratified Sampling, since the population is heterogeneous, the researcher divides the entire population into homogeneous groups, called strata.Since the researcher has divided the heterogeneous population into homogeneous strata, within variance is smaller and between mean is larger. However, if we find within variance is larger, and between mean is smaller, it indicates that the researcher has failed in his attempt to divide the heterogeneous population into homogeneous strata and thus in such a case, stratified sampling is not going to do much, and SRS would suffice.