Design of experiments

Design effect

In survey methodology, the design effect (generally denoted as or ) is a measure of the expected impact of a sampling design on the variance of an estimator for some parameter. It is calculated as the ratio of the variance of an estimator based on a sample from an (often) complex sampling design, to the variance of an alternative estimator based on a simple random sample (SRS) of the same number of elements. The Deff (be it estimated, or known a-priori) can be used to adjust the variance of an estimator in cases where the sample is not drawn using simple random sampling. It may also be useful in sample size calculations and for quantifying the representativeness of a sample. The term "design effect" was coined by Leslie Kish in 1965. The design effect is a positive real number that indicates an inflation, or deflation in the variance of an estimator for some parameter, that is due to the study not using SRS (with , when the variances are identical). Some potential complex sampling that could introduce Deff that is different than 1 include: cluster sampling (such as when there is correlation between observations), stratified sampling, cluster randomized controlled trial, disproportional (unequal probability) sample, non-coverage, non-response, statistical adjustments of the data, etc.. Deff can be used in sample size calculations, quantifying the representative of a sample (to a target population), as well as for adjusting (often inflating) the variance of some estimator (in cases when we can calculate that estimator's variance assuming SRS). The term "Design effect" was coined by Leslie Kish in 1965. Ever since, many calculations (and estimators) have been proposed, in the literature, for describing the effect of known sampling design on the increase/decrease in the variance of estimators of interest. In general, the design effect varies between statistics of interests, such as the total or ratio mean; it also matters if the design (e.g.: selection probabilities) are correlated with the outcome of interest. And lastly, it is influenced by the distribution of the outcome itself. All of these should be considered when estimating and using design effect in practice. (Wikipedia).

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Related pages

Poisson sampling | Bessel's correction | Stratified sampling | Effective sample size | Uncorrelatedness (probability theory) | Block matrix | Point estimation | Simple random sample | Intraclass correlation | Ratio distribution | Design effect | Cluster analysis | Inverse probability weighting | Estimator | Independent and identically distributed random variables | Disjoint sets | Outlier | Parameter | Independence (probability theory) | Sampling frame | Standard error | Confidence interval | Missing data | Statistical parameter | Quota sampling | Variance inflation factor | Poisson binomial distribution | Propensity score matching | Raking | Sampling design | Leslie Kish | Sample size determination | Scaling (geometry) | Variance | Imputation (statistics) | Empirical distribution function | Simple linear regression | Inverse-variance weighting | Linear regression | Bernoulli sampling | Real number | Sampling error | Multinomial distribution | Convex combination | Cluster sampling | Horvitz–Thompson estimator | Descriptive statistics | Arithmetic mean | Standard deviation | Systematic sampling | Weighted arithmetic mean | Ratio estimator | No free lunch theorem | Random variable | Expected value | Meta-analysis | Sampling (statistics) | Correlation | Frequency (statistics) | Survey methodology | Bernoulli distribution | Optimal design | Coefficient of variation | Nonprobability sampling