Power Analysis Calculator | Sample Size, Power & MDE

Q: What inputs matter most for a power analysis?

The key assumptions are significance level alpha, one-sided versus two-sided testing, target power, and a realistic effect size. For means, the effect size depends on the expected difference relative to sigma. For proportions, the baseline rate and target rate determine the effect size.

Q: Does this page use exact t-test or chi-square power formulas?

No. This first release uses a normal-approximation workflow for speed and clarity. It is useful for planning, but you should confirm assumptions with a method that matches your final study design if the decision is high stakes.

Q: When should I choose one-sided instead of two-sided?

Choose one-sided only when the direction of interest is fixed before data collection and an effect in the opposite direction would not count as success. Otherwise use two-sided because it is the safer default.

How to use

Choose the data structure first: one mean, two means, one proportion, or two proportions.
Choose what you want to solve: required sample size, achieved power, or minimum detectable effect.
Set alpha, tails, and a realistic effect assumption, then use the result as a planning baseline before moving to analysis.

Wave 3 statistics expansion

Four normal-approximation power workflows

Use one mean when you plan a single average against a reference value and you already have a defensible sigma assumption.

Inputs

Use this for one planned mean against a reference value when sigma is known or defensibly approximated.

Estimated sigma σ Minimum effect to detect

Assumptions summary

Use alpha, tails, and a realistic effect assumption to size the study before data collection.
For two-group modes, the first release assumes balanced group sizes.
For proportion modes, the page converts baseline and target rates into a standardized effect internally.

What the page computes

The selected mode maps your study design to a normal-approximation test statistic.
Alpha and tails determine the critical threshold.
The page then solves for required sample size, achieved power, or minimum detectable effect.

Power analysis vs sample size

Sample size answers a precision question such as “How many responses do we need so the estimate is within ±3 points?” This page answers a detection question such as “How many users do we need to detect a +2 point lift with 80% power at alpha 5%?”

If the language in the decision meeting is about confidence interval width, use the sample-size page first. If it is about detecting or ruling out a practical effect, use power analysis.

How to think about effect size

Choose an effect that would change a decision, not merely a tiny effect that happens to be nonzero.
For means, the practical effect depends on the expected difference relative to sigma.
For proportions, baseline and target rates matter. A 5-point lift from 10% to 15% is not the same standardized effect as a 5-point lift from 60% to 65%.
If your sigma or baseline rate is uncertain, run a small range of scenarios rather than treating one number as fixed truth.

What to do after planning

After planning the design, move to the matching analysis page once data collection is complete.

Sample Size Calculator
Use this instead when the planning target is confidence interval width rather than test sensitivity.
T-Test Calculator
Move here after collection when the outcome is a mean and you need confidence intervals or a test result.
ANOVA Calculator
Move here when the design compares mean outcomes across three or more groups.
Chi-Square Test Calculator
Move here for count-based comparisons and contingency tables after collection.
Statistics (inference & tests)
Return to the topic hub for neighboring inference, regression, and distribution tools.

FAQ

How is power analysis different from the sample-size page?

The sample-size page is about estimation precision and confidence interval width. This page is about hypothesis-test sensitivity: required n, achieved power, or minimum detectable effect under a chosen alpha and tails setting.

What inputs matter most for a power analysis?

Enter the smallest effect that would change a real decision. For means, think in original units relative to sigma. For proportions, use a realistic baseline and target rate rather than an arbitrary percentage-point gap without context.

When should I choose one-sided instead of two-sided?

One-sided testing puts all alpha into one tail, so the critical threshold is lower. That only makes sense when the direction is fixed in advance and the opposite direction would not count as a meaningful success case.

Does this page use exact t-test or chi-square power formulas?

No. The first release uses a normal-approximation workflow for speed and clarity. It is good for planning, but if the final decision is high stakes you should confirm assumptions with a method aligned to the final study design.

Does the share URL include my numeric assumptions?

No. The share URL stores only lightweight settings such as mode, solve target, alpha, tails, direction, and target power. Numeric inputs stay in your browser.

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