Understand sampling uncertainty
How sample-size and power planning fit together
Paired-Sample Size. Planning starts with an effect worth detecting, a significance level, a target power, and assumptions about variation or baseline rates.
1Define the smallest meaningful effect2Set alpha, power, and allocation3Round sample requirements upward and allow for attrition
Method used
n=ceil[((zα+zβ)σd/Δ)²].
Power is driven by the variability of paired differences, not the marginal SD of either measurement alone.
What the result cannot establish
Power is a long-run probability under the assumed effect and model. It is not a guarantee of significance, data quality, or practical importance.
Assumption: Uses a two-sided normal approximation and independent, approximately modeled pair differences; inflate for incomplete pairs separately.
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 paired-sample size calculator works
n=ceil[((zα+zβ)σd/Δ)²].
Power is driven by the variability of paired differences, not the marginal SD of either measurement alone.
Worked example
Paired-Sample Size example
A paired difference of 2 with difference SD 5, 80% power and alpha 0.05 needs about 50 complete pairs.
n=ceil[((zα+zβ)σd/Δ)²].
Supported inputs
Precision and limits
Model and design
Uses a two-sided normal approximation and independent, approximately modeled pair differences; inflate for incomplete pairs separately.
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
Power is driven by the variability of paired differences, not the marginal SD of either measurement alone.
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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