Three conditions, one sampling plan
The nurse's sampling plan must satisfy three conditions at once: no more than 100 households, travel to only 4 barangays, and a known chance of selection for every household in the municipality. Only a two-stage (multistage) cluster sample meets all three. In the first stage, she selects 4 barangays at random from the 18. In the second stage, she selects 25 households at random within each chosen barangay. Random selection at both stages keeps every household's chance of selection known, while the design limits travel to 4 barangays and the total to 4 × 25 = 100 households.
Why a known chance of selection matters
A probability sample is one in which every unit in the population has a known, nonzero chance of being chosen. This property allows the results to be generalized to the whole municipality and lets the researcher calculate sampling error. In a two-stage cluster sample, a household's chance equals the chance its barangay is chosen multiplied by the chance the household is chosen within that barangay. Both are known when both stages are random, even though barangays differ in size.
| Plan | Max 100 households? | Only 4 barangays? | Known chance for all? |
|---|
| 5 or 6 households in each of 18 barangays | Yes | No (18) | Yes |
| 4 random barangays, all households | No (600 or more) | Yes | Yes |
| 4 nearest barangays, 25 random households each | Yes | Yes | No |
| 4 random barangays, 25 random households each | Yes | Yes | Yes |
Why each other plan fails
Sampling 5 or 6 households in every barangay is a stratified approach that keeps probabilities known, but the team would have to visit all 18 barangays. Enrolling every household in 4 random barangays is a one-stage cluster sample; with 150 to 600 households per barangay, it gives at least 600 households, far above the limit. Choosing the 4 nearest barangays introduces convenience selection at the first stage, so households in the other 14 barangays have no chance of being selected, and the sample is no longer a probability sample. Watch out! Random selection at the second stage cannot repair a non-random first stage.
Exam takeaway
When travel limits force sampling in a few areas, use multistage cluster sampling with random selection at every stage. The trade-off is a larger sampling error than a simple random sample of the same size, because households within a barangay tend to be similar. Researchers often compensate by selecting more clusters or by weighting results according to barangay size.