A Priori Power Calculator

Calculator Inputs

Calculation mode

Test family

Tail setting

Alpha

Target power

Effect size d or r

Expected physical difference

Standard deviation

Sample size or group 1 n

Allocation ratio n2/n1

Design effect

Attrition percent

Formula Used

The calculator uses normal approximation formulas for early planning. For a mean based design, the critical value is z_alpha = inverse normal of 1 minus alpha divided by tails.

For one sample or paired mean tests, required effective n = ((z_alpha + z_power) / d)^2. For two means, group 1 effective n = ((z_alpha + z_power)^2 x (1 + 1 / allocation ratio)) / d^2.

For correlation planning, Fisher z is atanh(r). Required effective n = ((z_alpha + z_power) / atanh(r))^2 + 3. Design effect and attrition then adjust the planned sample.

Achieved power uses Power = normal CDF(noncentral value minus z_alpha). Minimum detectable effect reverses the same equations.

How to Use This Calculator

Select whether you need sample size, achieved power, or minimum detectable effect.
Choose the test family that best matches the physics study.
Enter alpha, power, tails, effect size, and sample settings.
Use expected difference and standard deviation when you want d to be derived.
Click Calculate, then use CSV or PDF download for records.

Example Data Table

Scenario	Mode	Family	Alpha	Power	Effect	Extra Setting
Detector calibration shift	Required sample size	Paired mean	0.05	0.80	0.40	Design effect 1.00
Two chamber pressure study	Achieved power	Two means	0.05	Not needed	0.55	Ratio 1.50
Voltage and temperature link	Minimum detectable effect	Correlation	0.01	0.90	Calculated	n = 80

A Priori Power Planning for Physics

Why power matters

A priori power calculation is used before a physics experiment starts. It helps estimate how many observations are needed to detect a planned effect. This matters when a laboratory run is costly, slow, or limited by equipment time. A clear power target also protects weak studies from being too small.

Inputs used by the calculator

The calculator uses a normal approximation for common planning cases. You can plan a one sample mean test, paired measurement test, two group mean comparison, or correlation study. Enter alpha, target power, tails, design effect, and an expected effect. For mean based work, you may enter a standardized effect directly. You may also enter an expected physical difference and a standard deviation. The tool then derives the standardized effect.

Physics examples

In physics, the expected effect may be a change in voltage, decay rate, temperature, resistance, pressure, or detector response. The standard deviation should match the same unit. A small standard deviation increases sensitivity. A larger standard deviation requires more observations. Two tailed tests need stronger evidence than one tailed tests. That usually increases the required sample size.

Design effect and attrition

Design effect is useful when measurements are not fully independent. Repeated readings from one device, shared batches, or clustered samples can reduce effective information. Use one for independent measurements. Use a larger value when clustering is expected. Attrition adjusts the planned sample upward. It is helpful when sensor failures, unusable samples, or missing readings are likely.

Using results responsibly

The achieved power mode checks an existing plan. It estimates whether a proposed sample can detect the chosen effect. The minimum detectable effect mode works backward. It shows the smallest standardized effect that a fixed sample can detect at the selected power. These modes help compare practical limits with scientific goals.

Results are planning estimates, not guarantees. Real experiments may violate assumptions. Distribution shape, unequal variances, calibration drift, and systematic error can change performance. Treat the output as an early design guide. Then combine it with pilot data, domain knowledge, and a written analysis plan. Good planning makes physics studies clearer. It also makes resource requests easier to defend. Keep notes beside each exported report.

FAQs

What is a priori power?

It is planned statistical power estimated before data collection. It helps decide sample size, effect targets, and study feasibility.

Which effect size should I enter?

For mean tests, enter standardized difference d. You can also enter expected physical difference and standard deviation. For correlation studies, enter expected r.

Should I choose one tailed or two tailed?

Use two tailed when effects in either direction matter. Use one tailed only when the opposite direction is not scientifically relevant.

What does design effect mean?

Design effect adjusts for reduced information from clustering, repeated batches, or dependent readings. Use 1 when observations are independent.

Why add attrition?

Attrition covers expected missing, failed, or unusable measurements. It increases the planned sample so final usable data remains adequate.

Can this replace full statistical software?

No. It gives normal approximation planning estimates. Complex models, exact tests, or unusual distributions need deeper analysis.

What is minimum detectable effect?

It is the smallest effect a fixed sample can detect at the chosen alpha, tails, and target power.

Why is this useful in physics?

Physics experiments often cost time and resources. Power planning helps justify runs, sensors, samples, and measurement schedules.