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Statistics · Sampling & confidence

Sample Size for Two Means Calculator

Plan two independent group sizes for detecting a specified mean difference with normal-approximation power.

Statistics · Sampling & confidence

Enter your statistical inputs

Private in-browser calculation · explicit assumptions
Planning balances the effect worth detecting, sample size, false-positive rate, and target power.
  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
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Enter plain numbers without measurement units. Datasets accept commas, spaces, semicolons, or line breaks and are limited to 10,000 values. Results stay in this browser.

Statistics result

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Understand sampling uncertainty

How sample-size and power planning fit together

Sample Size for Two Means. Planning starts with an effect worth detecting, a significance level, a target power, and assumptions about variation or baseline rates.

Method used

n₁=[(zα+zβ)²(σ₁²+σ₂²/r)]/Δ²; n₂=r n₁.

The detectable difference should be scientifically meaningful rather than chosen to make the sample convenient.

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, independent groups, supplied planning SDs, and a fixed allocation ratio.

Quick guide

How to use this calculator

  1. Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
  2. Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
  3. 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 sample size for two means calculator works

n₁=[(zα+zβ)²(σ₁²+σ₂²/r)]/Δ²; n₂=r n₁.

The detectable difference should be scientifically meaningful rather than chosen to make the sample convenient.

Worked example

Sample Size for Two Means example

A target difference of 5 with SDs 10, 80% power and equal allocation needs about 63 per group.

n₁=[(zα+zβ)²(σ₁²+σ₂²/r)]/Δ²; n₂=r n₁.

Supported inputs

Precision and limits

Model and design

Uses a two-sided normal approximation, independent groups, supplied planning SDs, and a fixed allocation ratio.

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

The detectable difference should be scientifically meaningful rather than chosen to make the sample convenient.

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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