Formula Used
The calculator estimates power as the probability of rejecting the null hypothesis when the expected alternative value is true.
For mean tests, the standardized shift is:
Shift = Effect / Standard Error
For one mean tests, standard error equals SD / sqrt(n).
For two mean tests, standard error equals SD × sqrt(1/n1 + 1/n2).
For proportion tests, the rejection boundary is built from the null proportion, then evaluated under the expected proportion.
For correlation tests, Fisher transformation is used:
z = 0.5 × ln((1 + r) / (1 - r))
Beta risk equals 1 minus power.
The target sample estimate uses the selected alpha level, target power, effect size, and variability assumptions.
How to Use This Calculator
Select the test type first. Choose the alternative direction. Enter alpha and target power.
For mean tests, enter sample size, null value, expected value, and standard deviation.
For proportion tests, enter proportions and sample sizes.
For correlation tests, enter the null correlation, expected correlation, and sample size.
Press the calculate button. Review the power, beta risk, standard error, critical rule, and target sample estimate.
Use the CSV or PDF buttons to save the result.
Why Test Power Matters
A hypothesis test can miss a real effect when the study is too small. Power describes the chance of detecting that effect when the alternative assumption is true. A high value means the design has better protection against a false negative. This calculator helps you review that risk before data collection starts.
What the Calculator Estimates
The tool works with common planning cases. You can evaluate one sample means, two sample means, one proportion, two proportions, and correlation tests. Each case uses the null assumption, the expected true value, sample size, alpha level, and selected tail direction. The output shows power, beta risk, critical boundary details, standardized effect, and an estimated sample target.
How Inputs Affect Power
Power increases when sample size rises, variability falls, or the expected effect becomes larger. A smaller alpha level usually lowers power because the test needs stronger evidence. Two sided tests also need more evidence than one sided tests. For that reason, the same study can look acceptable under one setting and weak under another setting.
Using R Style Planning
Researchers often use R functions to study power before running an analysis. This page follows the same planning idea. It turns study assumptions into a probability of rejection under the alternative. The result is not a promise about future data. It is a planning estimate based on the values entered by the user.
Interpreting Results Carefully
A power near 80 percent is often treated as a useful planning target. Higher power may be needed when missing an effect is costly. Lower power may be acceptable in early screening work. Always choose inputs from sound prior studies, pilot data, or practical scientific judgment. Poor assumptions can make any power calculation misleading.
Good Design Practice
Run several scenarios before choosing a final design. Try smaller and larger effects. Adjust standard deviation, proportions, alpha, and sample sizes. Compare the beta risk and required sample target across cases. This habit shows how sensitive the plan is to uncertainty. It also helps communicate design choices to supervisors, reviewers, and collaborators.
Document each selected value. Save exports with notes. This creates a clear record for audits, reports, grant applications, and repeated team reviews later discussion sessions.
FAQs
What is power in a hypothesis test?
Power is the chance that a test rejects the null hypothesis when the alternative value is true. It measures how likely your design is to detect the expected effect.
What is beta risk?
Beta risk is the chance of missing a real effect. It equals one minus power. A beta of 0.20 means power is 0.80.
Which alpha level should I use?
Many studies use 0.05, but the best value depends on risk, field standards, and study goals. Smaller alpha values require stronger evidence.
Can this replace professional study design?
No. It supports planning and comparison. Complex trials, clustered designs, survival outcomes, and repeated measures need specialized statistical review.
Why does power increase with sample size?
Larger samples reduce standard error. That makes the same effect easier to separate from random variation, so the rejection probability increases.
What does two sided mean?
A two sided test checks for effects in both directions. It usually needs stronger evidence than a one sided test with the same alpha level.
Why are results approximate?
The calculator uses normal and Fisher approximations. They work well for many planning tasks, but may be less reliable with tiny samples or extreme proportions.
How should I choose the expected effect?
Use prior research, pilot data, clinical importance, business impact, or scientific judgment. Avoid choosing an effect only to force a desired sample size.