Sampling Size Estimation Calculator
Prospective independently specified normal approximation mean sample budget ceil(z²σ²/E²), independent animals/random sampling/variance assumptions; not finite population, t-distribution or cure selection.
Description
Estimating a population mean requires a precision target, variability estimate and sampling model.
Estimating a population mean requires a precision target, variability estimate and sampling model.1
This tool calculates a normal-approximation sample budget from an independently specified two-sided error probability, pilot standard deviation and mean error margin.
When to use Sampling Size Estimation Calculator
Use this tool to calculate a normal-approximation sample budget from an independently specified two-sided error probability, pilot standard deviation and mean error margin.
How to use Sampling Size Estimation Calculator and how it works
- Establish the observations, units, reference context and assumptions described below.
- Enter callerTwoSidedAlpha, callerPilotStandardDeviation, callerIndependentlySpecifiedMeanErrorMargin and run the tool.
- Read result.value using the meanings and sign conventions below.
- Correct any rejected inputs and rerun; independently review the result under the stated scope.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| callerTwoSidedAlpha | Two-sided error probability alpha strictly between zero and one; use 0.05 rather than 5 for five percent. | number | Required; finite; fraction 0–1 inclusive; branch conditions below |
| callerPilotStandardDeviation | Positive pilot standard deviation in the mean measurement unit. | number | Required; finite; strictly positive; branch conditions below |
| callerIndependentlySpecifiedMeanErrorMargin | Positive desired absolute mean error margin in the standard deviation unit. | number | Required; finite; strictly positive; branch conditions below |
Require two-sided alpha strictly between zero and one, positive pilot standard deviation and positive mean error margin in the same measurement unit. Use the approximate inverse-normal quantile at 1-alpha/2, square its product with standard deviation/error margin, and round upward to an integer sample budget. The normal approximation assumes the supplied variability and independent sampling model; it includes neither a finite-population correction nor a t adjustment. Extremely small alpha can make the quantile argument round to one and be rejected.
sampleBudget=ceil((Phi_inverse(1-alpha/2)*pilotSD/errorMargin)^2) Use the stated ordering, units and branch conditions.
| Output field | Meaning | Value type |
|---|---|---|
| result | Object containing the fields below. | object |
| result.value | Integer normal-approximation sample budget rounded upward. | number |
{
"input": {
"callerTwoSidedAlpha": 0.05,
"callerPilotStandardDeviation": 2,
"callerIndependentlySpecifiedMeanErrorMargin": 1
},
"output": {
"result": {
"value": 16
}
}
}Limitations and assumptions
The calculation depends on independently established observations, coefficients and the matching units. It does not collect data, choose a treatment or target, establish model applicability or provide a validated forecast. Interpret its result within the branch conditions and assumptions above.
Supply explicit values and dense aligned arrays. Unexpected fields, wrong types and nonfinite scalar values are rejected; fixed-token, alignment and other branch conditions are explained above. A successful false flag, empty match list or unknown-evidence list differs from an input error. Extremely large inputs or nonrepresentable results may fail.
Alternative or Complementary methods
Use Attribute Sampling Deviation Rate Size Computation for a related operation: An observed attribute-sampling deviation rate is the fraction of examined items with recorded deviations.
Use Block Stratified Selection Coverage Adequacy Checker for a related operation: Stratified coverage must be considered by block as well as in aggregate.
References
-
Sampling Size Estimation Calculator — tool.io
Similar or alternative tools
- Attribute Sampling Deviation Rate Size Computation
An observed attribute-sampling deviation rate is the fraction of examined items with recorded deviations.
- Block Stratified Selection Coverage Adequacy Checker
Stratified coverage must be considered by block as well as in aggregate.