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Statistics · Sampling & confidence

Optimal Sample Allocation Calculator

Allocate a fixed stratified sample using proportional or Neyman allocation.

Statistics · Sampling & confidence

Enter your statistical inputs

Private in-browser calculation · explicit assumptions
Sampling design changes how much independent information the observations carry.
  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
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Enter plain numbers without measurement units. Datasets accept commas, spaces, semicolons, or line breaks and are limited to 10,000 values. Results stay in this browser.

Statistics result

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Understand sampling uncertainty

How sampling design changes precision

Optimal Sample Allocation. A headcount is not always the same as an independent information count. Clustering, unequal weights, and stratum allocation can increase or reduce precision.

Method used

Proportional nh∝Nh; Neyman nh∝NhSh.

Neyman allocation minimizes mean-estimator variance when per-unit costs are equal and SD inputs are credible.

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: Rounded allocations preserve the requested total and at least one unit per stratum; operational constraints and unequal costs require a custom design.

Quick guide

How to use this calculator

  1. Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
  2. Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
  3. 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 optimal sample allocation calculator works

Proportional nh∝Nh; Neyman nh∝NhSh.

Neyman allocation minimizes mean-estimator variance when per-unit costs are equal and SD inputs are credible.

Worked example

Optimal Sample Allocation example

A larger, more variable stratum receives more observations under Neyman allocation.

Proportional nh∝Nh; Neyman nh∝NhSh.

Supported inputs

Precision and limits

Model and design

Rounded allocations preserve the requested total and at least one unit per stratum; operational constraints and unequal costs require a custom design.

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

Neyman allocation minimizes mean-estimator variance when per-unit costs are equal and SD inputs are credible.

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.

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