kb/data/en.wikipedia.org/wiki/Design_effect-10.md

title	chunk	source	category	tags	date_saved	instance
Design effect	11/12	https://en.wikipedia.org/wiki/Design_effect	reference	science, encyclopedia	2026-05-05T09:49:56.844427+00:00	kb-cron

=== The design effect for complex designs ===

==== Unequal selection probabilities times Cluster sampling ==== In a 1987 paper, Kish proposed a combined design effect that incorporates both the effects due to weighting that accounts for unequal selection probabilities and cluster sampling:

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{\displaystyle {\text{Deff}}_{\text{Kish}}={\frac {n\sum \limits _{h=1}^{H}(n_{h}w_{h}^{2})}{\left(\sum \limits _{h=1}^{H}n_{h}w_{h}\right)^{2}}}\left(1+(n^{*}-1)\rho \right)={\text{Deff}}_{k}\times {\text{Deff}}_{C}}

The above uses notations similar to what is used in this article (the original 1987 publication used different notation). A model based justification for this formula was provided by Gabler et al.

==== Stratified sampling times unequal selection probabilities times Cluster sampling ==== In 2000, Liu and Aragon proposed a decomposition of unequal selection probabilities design effect for different strata in stratified sampling. In 2002, Liu et al. extended that work to account for stratified samples, where within each stratum is a set of unequal selection probability weights. The cluster sampling is either global or per stratum. Similar work was done also by Park et al. in 2003.

==== Chen-Rust Deff: Design effects to two- and three-stage designs with stratification ==== The Chen-Rust

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extends the model-based justification of Kish’s 1987 formula for design effects proposed by Gabler, el. al., applying it to two-stage designs with stratification at the first stage and to three-stage designs without stratification. The modified formulae define the overall design effect using survey weights and population intracluster correlations. These formulae allow for insightful interpretations of design effects from various sources and can estimate intracluster correlations in completed surveys or predict design effects in future surveys.

==== Henry's Deff: a design effect measure for calibration weighting in single-stage samples ==== Henry's

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proposes an extended model-assisted weighting design-effect measure for single-stage sampling and calibration weight adjustments for a case where

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{\displaystyle y_{i}=\alpha +\beta x_{i}+\epsilon _{i}}

, where

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is a vector of covariates, the model errors are independent, and the estimator of the population total is the general regression estimator (GREG) of Särndal, Swensson, and Wretman (1992). The new measure considers the combined effects of non-epsem sampling design, unequal weights from calibration adjustments, and the correlation between an analysis variable and the auxiliaries used in calibration.

==== Lohr's Deff: a design effect for a regression slope in a cluster sample ==== Lohr's

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is for ordinary least squares (OLS) and generalized least squares (GLS) estimators in the context of cluster sampling, using a random coefficient regression model. Lohr presents conditions under which the GLS estimator of the regression slope has a design effect less than 1, indicating higher efficiency. However, the design effect of the GLS estimator is highly sensitive to model specification. If an underlying random coefficient model is incorrectly specified as a random intercept model, the design effect can be seriously understated. In contrast, the OLS estimator of the regression slope and the design effect calculated from a design-based perspective are robust to misspecification of the variance structure, making them more reliable in situations where the model specification may not be accurate.

== Uses ==

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may be used when planning a future data collection, as well as a diagnostic tool: