Double Sampling
Double Sampling (Two-Phase Sampling) · Also known as: Two-Phase Sampling
Double Sampling (also called two-phase or multistage sampling) is a survey design in which a large preliminary sample is collected using inexpensive methods or partial information, then a smaller subsample is drawn from it and measured in detail. Pioneered by Jerzy Neyman in 1938, it is particularly useful when a cheap surrogate measurement is available but true measurement is expensive.
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When to use it
Apply double sampling when a cheap auxiliary variable or covariate is available and is correlated with your study variable. Ideal in scenarios where expensive lab analysis follows cheap field screening (e.g., environmental samples, blood tests following initial screening), where administrative records exist but validation requires verification, or where you can use a pilot study to refine the main survey design. Requires that phase-one and phase-two designs are specified in advance.
Strengths & limitations
- Reduces total cost by using cheap phase-one data to guide phase-two sampling
- Improves precision compared to single-phase simple random sampling of the same total cost
- Allows optimization of sample sizes n₁ and n₂ to minimize cost for a desired precision level
- Provides flexibility to adjust phase-two sampling based on unanticipated phase-one results
- Commonly used in practice for cost-effective survey design
- Requires advance planning; changes to the design after phase one complicate analysis
- Efficiency gains depend on correlation between phase-one auxiliary data and phase-two outcome variable
- More complex estimation and variance calculation than single-phase sampling
- Data from both phases must be linked or matched, adding administrative overhead
Frequently asked
How do I choose the sizes n₁ and n₂?
Optimal allocation depends on the cost of each phase and the desired precision. Generally, if phase-one data is much cheaper than phase-two, make n₁ much larger than n₂. Statistical theory provides formulas to minimize total cost for a fixed variance target.
Is double sampling the same as stratified sampling?
No. Stratified sampling divides the population into known groups before sampling. Double sampling draws a first sample, uses that information to improve the second-phase design, then samples again. Stratified sampling is predetermined; double sampling adapts to first-phase results.
What if my phase-one surrogate is poorly correlated with the outcome?
Efficiency gains shrink as the correlation weakens. In the extreme of zero correlation, double sampling offers no advantage over simple random sampling. Always validate the surrogate before committing to a full two-phase design.
Can I change my phase-two design after seeing phase-one data?
Minor adjustments are permissible if unbiased, but major changes complicate analysis and can introduce bias. Designs should be prespecified as much as possible to ensure valid inference.
How do I estimate population mean from double-sample data?
Use a two-phase estimator that weights phase-one and phase-two data appropriately. These estimators are unbiased and have lower variance than phase-one-only or phase-two-only estimates, provided proper formulas are applied.
Sources
- Neyman, J. (1938). Contribution to the theory of sampling human populations. Journal of the American Statistical Association, 33(201), 101–116. DOI: 10.1080/01621459.1938.10503378 ↗
- Hansen, M. H., & Hurwitz, W. N. (1943). On the theory of sampling from finite populations. Annals of Mathematical Statistics, 14(4), 333–362. DOI: 10.1214/aoms/1177731356 ↗
- Cochran, W. G. (1977). Sampling Techniques (3rd ed.). John Wiley & Sons. link ↗
How to cite this page
ScholarGate. (2026, June 3). Double Sampling (Two-Phase Sampling). ScholarGate. https://scholargate.app/en/sampling/double-sampling
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
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