Clustersampsi Matched Pair Power Calculator

Example Data Table

Formula Used

Design effect: DE = 1 + ((m × (1 + CV²)) - 1) × ICC.

Matched pair factor: MPF = 1 - pair correlation.

Adjusted standard error: SE = √((base variance × DE × MPF) / (pairs × m)).

Power: two-sided power = Φ(z - zcrit) + Φ(-z - zcrit). One-sided power = Φ(z - zcrit).

Required pairs: pairs = base variance × DE × MPF × (zcrit + zpower)² / (effect² × m).

Detectable effect: MDE = (zcrit + zpower) × √((base variance × DE × MPF) / (pairs × m)).

How To Use This Calculator

1. Select the calculation mode.
2. Choose continuous, binary, or rate outcome.
3. Enter matched pairs and average cluster size.
4. Add intraclass correlation and cluster variation.
5. Enter the matched pair correlation.
6. Set alpha, power, and expected effect.
7. Press Calculate.
8. Download the result as CSV or PDF.

Clustered Power Planning

Cluster trials are common in applied physics studies. Labs, schools, plants, wards, or sensor arrays may act as clusters. People often compare two arms. The units inside one cluster can share noise. That shared noise reduces independent information. The intraclass correlation captures this loss. A higher value means less independent evidence per subject.

Matched Pair Adjustment

Matching pairs similar clusters before randomization can improve precision. One cluster in each pair enters each arm. The pair correlation estimates how well matching removes background variation. A strong match lowers the final variance. A weak match gives little benefit. This calculator applies that adjustment directly to the standard error.

Design Effect

The design effect is the main correction. It equals one plus the cluster size minus one, multiplied by the intraclass correlation. Unequal cluster size can raise the design effect. The coefficient of variation option handles that problem. A larger design effect raises the required clusters. It also lowers calculated power.

Outcome Choices

Continuous outcomes use the standard deviation. Binary outcomes use the control probability and treatment probability. Rate outcomes use the event rates and exposure. The calculator uses normal approximation methods. These methods are useful for planning. They are not a replacement for expert trial design.

Power, Clusters, And Effect

Use power mode when cluster counts are fixed. Use required pairs mode when you need a target power. Use detectable effect mode when budget fixes the design. The result section reports power, total clusters, total observations, standard error, z values, and adjusted design factors.

Interpreting Results

Power rises when effect size grows. It also rises when clusters increase. Larger cluster sizes help less after correlation becomes high. Better matching can save clusters. But the match correlation must be realistic. Do not assume perfect matching. Field conditions often reduce matching quality.

Good Planning Practice

Start with conservative inputs. Test low, middle, and high intraclass correlations. Compare matched and unmatched designs. Check attrition before final budgeting. Very small cluster counts can give unstable plans. For important work, confirm the plan with simulation or a statistician. Use the export buttons to save assumptions. Keep the file with proposals, lab notes, and review material. Review assumptions again whenever protocol details change during planning.