What is cluster sampling?
Cluster sampling selects whole groups first, such as schools or villages, and then surveys people inside the selected groups. It makes fieldwork dramatically cheaper, because interviews happen in a few places instead of everywhere, but it costs precision: people in the same cluster tend to be alike, so the sample must grow to compensate. The design effect measures that penalty.
Almost every real education survey is a cluster survey. Nobody can test 385 children scattered one-per-village across a state; you go to schools, and each school hands you a roomful of children at once. The catch is statistical: thirty children from one school tell you a lot about that school and less about the state, because they share teachers, textbooks and a neighbourhood. Each additional child from the same school adds less new information than a child from a fresh school would.
The design effect (DEFF)
A worked example
You need an effective sample of 385 children for a state learning survey. You plan to test 20 children per school, and learning outcomes in your context have an ICC of about 0.2.
- DEFF = 1 + (20 - 1) × 0.2 = 4.8
- Children needed = 385 × 4.8 ≈ 1,848
- Schools needed = 1,848 / 20 ≈ 93
Now shrink the per-school take to 10 children: DEFF = 1 + 9 × 0.2 = 2.8, so children needed = 385 × 2.8 ≈ 1,078 across about 108 schools. More schools to visit, but 770 fewer children to test. Whether that trade is worth it depends on your travel costs, which is exactly the calculation how many schools to survey walks through.
When clustering is the right call
- When respondents are naturally grouped and travel between groups is the dominant cost: schools, anganwadi centres, villages, health facilities.
- When no complete list of individuals exists, but a complete list of clusters does. You can sample schools from an official directory even if you cannot list every child in the state.
- Almost always in combination: stratify by district first, then sample schools within each district, then children within schools. That is two-stage cluster sampling, the workhorse of large education surveys.
Frequently asked questions
What is the design effect?
The factor by which clustering inflates your required sample compared with simple random sampling: DEFF = 1 + (m - 1) × ICC. It grows with both cluster size m and the intra-cluster correlation ICC. A clustered sample of 1,000 with DEFF 2.5 carries the information of only 400 truly independent people.
Why use cluster sampling if it needs more people?
Because cost lives in travel, not interviews. Testing 20 children in one school takes a morning; testing 20 children in 20 scattered villages takes weeks. The design effect is the price of that convenience, and for most field surveys it is a price worth paying, as long as it is budgeted honestly.
More clusters or more people per cluster?
More clusters, almost always. Since people within a cluster are alike, piling on more of them adds little; new clusters add fresh information. Keep at least 25 to 30 clusters per group you want to compare, and let the per-cluster take be modest.
Feel the design effect for yourself
Sampling Shala's Learn mode lets you drag the ICC and cluster size and watch the required sample react.
Open Learn mode