# ConductScience Sample Size & Power Calculator: method and validation record

This record fixes the calculation behind the free Sample Size & Power Calculator at https://conductscience.com/tools/sample-size-calculator, and the worked examples that check it.

## What the tool computes

For two-sided tests at significance level α:

- the sample size needed to reach a target power, or the power reached with a given sample size;
- for t-tests (two independent groups, or paired), exactly from the noncentral t distribution, given Cohen's d;
- for two proportions, from the normal-approximation formula without continuity correction, given p₁ and p₂.

The page also offers an ANOVA option; it is an approximation and is not part of this record.

## Files

| File | Contents |
| --- | --- |
| `METHODS.md` | Formulas, numerics, conventions, references, and changes from the page before this record |
| `cases.json`, `cases.csv` | The worked examples: inputs, expected outputs and where each expected answer comes from |
| `validation-report.json` | The engine's output for every case, pass or fail, and the SHA-256 of each engine file |
| `engine/` | The calculation source files the report fingerprints (when included) |
| `data_dictionary.csv` | Columns of `cases.csv` |
| `CITATION.cff`, `LICENSE`, `MANIFEST.json` | Citation metadata, licence, and byte count and SHA-256 of every file |

## How to cite

ConductScience. ConductScience Sample Size & Power Calculator [software]. 2026. https://doi.org/10.55157/csd.tool.samplesize.2026.001

In a methods section: "Sample size was determined with the ConductScience Sample Size & Power Calculator (https://doi.org/10.55157/csd.tool.samplesize.2026.001), which computes t-test power from the noncentral t distribution, for [power]% power at a two-sided α of [alpha] to detect Cohen's d = [value]."