S Fienberg & J Tanur
International Statistical Review 1987 55 , 1, pp 75 – 96
- prev à randomization & random selection à fairness / objectivity / representativeness
o novel departure in work of Fisher, Neyman / Tchuproc à introduction of chance mechanisms à to make available probability based methods of inference at analysis stage.
- basic parallels between
o design of randomized experiments
o and
o sampling studies
- Example
o two treatment randomization design for experiment
o structure is identical to
o selection of simple random sample
- two modes of inference
o design based inference à relies on probabilistic structure associated with design
o model based inference , which introduces stochastic components as part of parametric structures.
Basic Parallels
- randomization in experiments à probability / random sampling
- both involving introduction of chance mechanisms
o for assignment of treatments to units in experiments
o choice of sample units in surveys
- two treatment experiment
o sample selection function function specifies which members of the universe are allocated to treatment 1, and which to treatment 2
o in sampling situation, allocation to T1 corresponds to being selected for inclusion in sample
§ T2 corresponds to non selection.
- purpose of randomization structure are different
o experiment
§ compare
o sampling
§ want to generalize from sample to rest of population
- experiment – thru randomization, we hold everything constant.
o thus, attribute any effects to treatment differences
- sample
o random selection and the fact that no treatment is applied à allows us to make generalization
- both à randomization structure – used to provide meaningful estimate of variability.
- split plot designs à analogous sampling technique, cluster sampling.
- conceptualization of models for total survey error can take the component of variation due to interviewer as a random effect.
More Modern Parallels : Restricted Randomization
- - blocking / randomization à introduced in agriucultural experiments à control for known heterogeneity in plots
- this restricted randomization has applicability in sampling context
o control for geographical spread of a sample
o more generally, eliminate possibility of "bad samples"
- because typical human population of interst in sampling is large and heterogenous, the simple device in restricted randomization in experimentation cannot be carried over directly.
Embedding
- embedding experiments in sampling studies or sampling in experiments
- while sampling to measure the outcome of an experiment was an intrinsic part of teachings of Fisher and of practice in agricultural experiments,
o sampling yoked with experimental design is more rare
- if experiments with surveys are to be of value, must apply the experimental principle of local control
- interpenetrating networks of samples
o design provided 5 independent estimates of economic conditions and as a consequence allowed for evaluation of the response variation associated with interviewers
- large scale sampling à largest source of response error à associated with interviewer variability
- random effects model
- this suggests to those familiar with experimental principles of local control that a useful way to embed an experiment within a survey would be to use interviewers as a form of block.
Possible Causes and curses of Specialization
- immediate analogue of treatments in sampling setting à samples
- is it advantageous to have unequal probabilities of selection.
- historically ,
o many sample surveys were designed as enumerative studies
o experiments – explore causal relationships
- because analysis of non orthogonal experiments more difficult, many experiments designed to preserve orthogonality
- surveys, rarely achieve orthogonality
- simultaneity of inference
o surveys
§ number of comparisons is enormous
§ fishing expeditions
Modeling and Inference
- reporting of information from sample surveys – often cross classifications of frequencies à descriptive or enumerative
- models are essential for dealing with non-response and attrition
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