Power of Test Calculator

Calculate Power of Test

Test model

Tail type

Alpha

One Sample Mean Inputs

Null mean

Alternative mean

Standard deviation

Sample size

Two Independent Means Inputs

Null difference

Alternative difference

Group 1 standard deviation

Group 2 standard deviation

Group 1 sample size

Group 2 sample size

One Sample Proportion Inputs

Null proportion

Alternative proportion

Sample size

Two Independent Proportions Inputs

Group 1 null proportion

Group 2 null proportion

Group 1 alternative proportion

Group 2 alternative proportion

Group 1 sample size

Group 2 sample size

Custom Standard Error Inputs

Null center

Alternative center

Null standard error

Alternative standard error

Example Data Table

Case	Inputs	Tail	Expected Meaning
One mean	Null 100, alternative 104, sigma 10, n 64, alpha 0.05	Two tailed	Checks chance of detecting a four unit mean shift.
One proportion	Null 0.50, alternative 0.60, n 200, alpha 0.05	Two tailed	Checks chance of detecting a ten point proportion shift.
Custom error	Null 0, alternative 0.50, SE 0.20, alpha 0.05	Right tailed	Checks a planned model estimate with known uncertainty.

Formula Used

The calculator uses a normal approximation. It first converts alpha into critical z values. It then converts those z values into rejection cutoffs on the estimate scale.

Right tailed: cutoff = null center + z(1 - alpha) × SE under null.

Left tailed: cutoff = null center + z(alpha) × SE under null.

Two tailed: lower cutoff = null center + z(alpha / 2) × SE under null. Upper cutoff = null center + z(1 - alpha / 2) × SE under null.

Power: probability that the estimate falls in the rejection region when the alternative value is true.

Beta: beta = 1 - power.

How to Use This Calculator

Select the test model that matches your planned hypothesis test.
Choose a two tailed, right tailed, or left tailed test.
Enter alpha, such as 0.05 or 0.01.
Enter the null value and the alternative value.
Add sample size, standard deviation, proportions, or custom standard errors.
Press Calculate to view power, beta, critical z values, and cutoffs.
Use CSV or PDF export for records and reports.

Understanding Test Power

Test power is the chance that a study rejects a false null hypothesis. It answers a practical question. Will the design detect the effect that matters? A higher value means lower risk of missing a real difference. That missed difference is called a Type II error.

Why Power Matters

Power connects sample size, effect size, alpha, and variation. Small effects need more data. Noisy data also needs more data. A strict alpha lowers false alarms, yet it can reduce power. Balanced choices help researchers build fair tests before data collection starts.

What This Calculator Does

This calculator estimates normal approximation power for common designs. It supports one mean, two means, one proportion, two proportions, and a custom standard error model. It also handles left tailed, right tailed, and two tailed tests. The output shows power, beta, critical values, rejection cutoffs, and standardized distance.

Choosing Inputs Carefully

Use values that match the planned analysis. Enter the null value from the hypothesis. Enter the alternative value that represents a meaningful effect. For means, use a realistic standard deviation. For proportions, keep probabilities between zero and one. For custom mode, enter standard errors from a trusted design calculation.

Reading the Result

A power value near 0.80 is often used for planning. Some fields need more power. Safety studies may need stricter goals. Exploratory studies may accept less. Beta equals one minus power. It is the chance of failing to reject the null when the alternative value is true.

Planning Better Studies

Power analysis should be done before collecting data. Try several sample sizes. Compare the results. Notice how power changes when effect size or variation changes. This sensitivity check can prevent weak designs. It can also avoid using more participants than needed.

Limits of the Method

The method uses normal approximations. Results may be poor for tiny samples or extreme proportions. It does not replace a full design review. Still, it gives fast guidance. Use it as a planning aid, then confirm assumptions with your final statistical method. For publication work, document every chosen input. Save the export with the protocol. This makes later audits easier. It also shows that early sample planning was not changed after observing results.

FAQs

What is power of a test?

Power is the probability of rejecting a false null hypothesis. It shows how likely your study is to detect the chosen alternative effect.

What is a good power value?

A common planning target is 0.80. Some studies need 0.90 or higher. The right goal depends on cost, risk, and study purpose.

What does beta mean?

Beta is the probability of missing a real effect. It equals one minus power. Lower beta means stronger detection ability.

Can I use this for proportions?

Yes. Select one proportion or two independent proportions. Enter null and alternative probabilities between zero and one.

Why does alpha affect power?

A smaller alpha makes rejection harder. That can reduce false positives, but it often lowers power for the same sample size.

Does a larger sample size raise power?

Usually yes. Larger samples reduce standard error. This makes the alternative value easier to separate from the null value.

What is custom standard error mode?

Custom mode lets you enter null and alternative centers with their standard errors. It is useful for planned model estimates.

Is this exact for every test?

No. It uses normal approximations. Small samples, skewed data, and extreme proportions may need exact or simulation based methods.