Understand sampling uncertainty
How sampling design changes precision
Stratified Sampling Estimator. A headcount is not always the same as an independent information count. Clustering, unequal weights, and stratum allocation can increase or reduce precision.
1Describe the population structure2Apply the declared design adjustment3Report both nominal size and effective precision
Method used
ȳst=ΣWhȳh; Var=ΣWh²(1−fh)sh²/nh.
Stratification can improve precision when strata are internally coherent and population weights are correct.
What the result cannot establish
A design effect summarizes a specified design; it does not correct selection bias, nonresponse, coverage error, or a poorly defined target population.
Assumption: Enter aligned population sizes, sample sizes, sample means, and sample SDs; each stratum uses simple random sampling without replacement.
Quick guide
How to use this calculator
- Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
- Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
- Read the result together with its assumptions and interpretation. Statistical output summarizes uncertainty under a model; it does not repair biased data or establish causation.
Calculation method
How the stratified sampling estimator calculator works
ȳst=ΣWhȳh; Var=ΣWh²(1−fh)sh²/nh.
Stratification can improve precision when strata are internally coherent and population weights are correct.
Worked example
Stratified Sampling Estimator example
Two equally sized strata with means 10 and 20 estimate an overall mean of 15.
ȳst=ΣWhȳh; Var=ΣWh²(1−fh)sh²/nh.
Supported inputs
Precision and limits
Model and design
Enter aligned population sizes, sample sizes, sample means, and sample SDs; each stratum uses simple random sampling without replacement.
Numerical scope
Inputs use double-precision numerical methods with guarded domains. Datasets accept up to 10,000 finite plain-decimal values. Extremely large parameters or probabilities deep in a numerical tail may require specialist statistical software.
Interpretation
Stratification can improve precision when strata are internally coherent and population weights are correct.
Decision boundary
The calculator does not validate how data were collected, diagnose dependence or bias, choose a scientifically meaningful effect, or replace review by a qualified statistician for consequential research, medical, regulatory, safety, or policy decisions.
Privacy
Entered values and calculated results stay in this browser and are not sent to an analytics service.
Continue calculating
Related calculators
