Sample Size Calculator

When to use

• Use it to plan a simple proportion, mean, or two-group study before data collection.
• Use it to examine how confidence, margin of error, effect size, power, and nonresponse change required n.
• Use specialist design software for clustering, repeated measures, survival, equivalence, or complex sampling.

How to use

1. Select the planning objective and enter the corresponding proportion, variability, effect, confidence, or power inputs.
2. Enter a finite population only when sampling without replacement from a known population.
3. Calculate and inspect both the unrounded requirement and the final upward-rounded sample size.
4. Run sensitivity scenarios using defensible optimistic and conservative assumptions.

Inputs

Planning method

Determines whether the calculation targets a proportion, mean, or two-group comparison.

Margin of error or effect size

The smallest precision target or difference the design is intended to address.

Confidence and power

Probability settings that determine the critical values in the selected planning formula.

Nonresponse and population

Optional adjustments that must reflect the actual recruitment and sampling frame.

Notation

Interpretation

• The rounded result is a planning minimum under the entered assumptions.
• An achieved sample below the target can reduce precision or power but the exact impact depends on realized data.
• A calculated n does not repair biased sampling, poor measurement, attrition, or an unsuitable analysis plan.

Effect-size guidance

• Choose effect size from domain relevance or prior evidence, not a generic label alone.
• Report sensitivity across plausible variance or event-rate assumptions.
• Inflate for nonresponse after calculating analyzable observations, then round upward.

Worked examples

Assumptions

• Inputs are finite numeric values after parsing, with missing or invalid values handled according to the selected workflow.
• Planning formulas are normal-approximation estimates.
• The selected margin, power, and nonresponse assumptions are defensible for the study design.

Practical guidance

• Document every planning input and source.
• Separate recruitment target from required complete cases.
• Have complex protocols reviewed by a statistician before recruitment begins.

Common mistakes

• Using p = 0.5 without recognizing it is conservative.
• Ignoring nonresponse or dropout.

Limitations

• Power approximations are planning estimates.
• Complex survey designs and clustering are out of scope.

Related workflow links