What Is a Design Effect, and What Does It Do to Your Sample Size?

Last updated October 30, 2026·4 min read

The design effect is the ratio of the variance of an estimate under the actual design to the variance of the same estimate under a simple random sample of the same size. A design effect of two means the complex design needs twice the sample to match the precision a simple random sample would have given. Its square root, sometimes called Deft, is the factor by which standard errors widen.

Where design effects come from

Two sources dominate, and most real surveys carry both:

• Clustering. Sampling groups (schools, households, clinics) and measuring many members of each is cheaper than scattering the sample, but members of a cluster resemble one another, so each additional member adds less new information than an independent case would.
• Unequal weights. Stratification with unequal sampling rates, nonresponse adjustment, and calibration all spread the weights out. The wider the spread, the more the estimate leans on a subset of the sample, and the more variance rises.

Stratification itself, done with proportional or sensible allocation, can push the other way and produce effects under one. A design effect below one is good news, and it happens, though weighting usually eats the gain.

The cluster formula

For equal cluster sizes, the classic form is:

Design effect = 1 + (m − 1) × ICC,

where m is the number sampled per cluster and ICC is the intraclass correlation, the share of total variance that sits between clusters. Worked values:

• Classes of twenty-five pupils, ICC of 0.05: 1 + 24 × 0.05 = 2.20. A sample of 1,000 pupils in forty classes carries the precision of about 455 independent cases.
• The same classes at an ICC of 0.02: 1.48. Small correlations, multiplied by large clusters, still cost real precision.
• Households of two adults, ICC of 0.30: 1.30. High correlation, tiny clusters, modest effect.

The practical moral: cluster size is the lever with the handle. More clusters of fewer members each almost always beats fewer clusters of many, at the same total n.

The weighting formula

Kish design effect prices the unequal weights alone:

Design effect from weights = n × (sum of squared weights) ÷ (sum of weights)²,

which is one plus the squared coefficient of variation of the weights. Even weights give exactly one, no cost. A weight distribution with a coefficient of variation of 0.7 gives 1.49. This is the number a weighting run reports, and it explains the trimming trade: capping the most extreme weights lowers this effect, at the price of a small bias, which is why trimming decisions are variance decisions.

Effective sample size: the number to plan and report with

Divide the nominal sample by the design effect:

• 900 completes at a design effect of 1.5: effective sample 600, and margins of error follow the 600.
• The forty-class pupil sample above: 1,000 cases, effective 455.

Reporting the nominal n beside intervals computed as if the sample were simple and random overstates precision by the full design effect. The effective sample size is the honest denominator, and any methods section can state it in one line.

Planning with the effect, not around it

Multiply the simple-random requirement by the expected design effect before fieldwork: 385 completes for a five-point margin becomes 577 at an expected effect of 1.5, and invitations follow after the response-rate division. Designs budgeted without the effect deliver surveys whose subgroups dissolve into noise and whose headline margins miss their promises by half. The effect is not a nuisance to apologize for after the fact. It is a price quoted in advance, and designs that quote it honestly are the ones whose reports hold up.

See it in a run

Analysis Studio reports the Kish design effect and the effective sample size on every weighting run, and the Sample Size and Power Planner accepts a design effect as a planning input:

Analysis StudioOpen Analysis Studio →

Sources and method notes

Definitions and formulas follow Kish: the weighting design effect as one plus the squared coefficient of variation of the weights, and the cluster form 1 + (m − 1) × ICC for equal cluster sizes. All worked values were recomputed at drafting and are re-verified at build.