Example Data Table
| Scenario | Study type | Alpha | Tail | Main inputs | Planning use |
|---|---|---|---|---|---|
| Drug response score | Two means | 0.05 | Two | Mean 100 vs 108, SD 15, n 64 each | Estimate achieved power |
| Email conversion test | Two proportions | 0.05 | Two | Rate 0.40 vs 0.55, n 170 each | Check beta risk |
| Training improvement | Two means | 0.01 | One | Mean 72 vs 78, SD 12, target 90% | Estimate required sample |
| Survey adoption | Two proportions | 0.05 | Two | Rate 0.22 vs 0.30, allocation 2 | Plan unequal groups |
Formula Used
Normal Critical Value
For a two tailed test, the calculator uses z = inverse normal of 1 minus alpha divided by 2. For a one tailed test, it uses z = inverse normal of 1 minus alpha.
Power For Mean Difference
Standard error equals square root of SD1 squared over n1 plus SD2 squared over n2. The noncentral value equals absolute mean difference divided by standard error. Two tailed power equals P(Z greater than critical Z) plus P(Z less than negative critical Z) under that shifted normal curve.
Sample Size For Mean Difference
Group 1 sample size equals (z alpha plus z target power) squared times SD1 squared plus SD2 squared divided by allocation ratio, all divided by expected difference squared. Group 2 sample size equals allocation ratio times group 1 sample size.
Power For Proportion Difference
Standard error equals square root of p1(1 minus p1) over n1 plus p2(1 minus p2) over n2. The noncentral value equals absolute proportion difference divided by standard error. Cohen h equals two arcsine square root p2 minus two arcsine square root p1.
How To Use This Calculator
- Select whether your study compares two means or two proportions.
- Choose whether you need achieved power or required sample size.
- Enter alpha, target power, and the test tail.
- Enter expected means and standard deviations, or expected proportions.
- For power, enter group sample sizes.
- For sample planning, enter the allocation ratio between groups.
- Press Calculate to show results below the header and above the form.
- Download the result table as CSV or PDF for records.
Statistics Power Planning Guide
Understanding Statistical Power
Statistical power shows the chance that a study will detect a real effect when that effect exists. A strong plan usually targets 80% or 90% power. Higher power lowers beta risk, but it usually requires more participants, trials, or observations. This calculator helps compare that tradeoff before the study starts.
Why Power Matters
Low power can hide useful findings. It can also make positive results unstable. A powered design gives the researcher a clearer path. It links the expected effect, sample size, variation, and significance level. When those pieces are transparent, the final result becomes easier to defend.
Choosing Inputs
Start with the main outcome and the smallest effect that matters. For mean comparisons, enter the two expected means and standard deviations. For proportion comparisons, enter both expected rates. Choose the alpha level that matches your tolerance for false positives. Select a one tailed test only when the direction is justified before seeing data.
Sample Size Planning
When sample size is unknown, use the target power option. The calculator estimates group sizes using a normal approximation. The allocation ratio allows unequal groups, which is useful when one group is costly or harder to recruit. After rounding sample sizes upward, the tool also estimates achieved power.
Interpreting Results
Power is not proof that an effect exists. It is a planning measure. A high value means the design has a better chance of detecting the chosen effect. Beta is the chance of missing that effect. Minimum detectable effect shows the effect size needed for the chosen sample size and target power.
Practical Notes
Use conservative standard deviations when past evidence is limited. Try several scenarios rather than one optimistic case. Compare 80%, 90%, and 95% power to see how fast sample needs rise. For small samples, rare events, or complex models, confirm the design with specialist software or simulation. This tool is best for early planning and clear teaching examples.
Reporting the Plan
Record every assumption before data collection. Note the selected test direction, alpha level, target power, expected effect, and variance source. This record prevents later confusion. It also helps reviewers see whether the sample was chosen scientifically rather than guessed after results appeared during peer review later.
FAQs
What is statistical power?
Statistical power is the probability of detecting a real effect when that effect truly exists. Many studies use 80% or 90% as planning targets.
What does beta risk mean?
Beta risk is the chance of missing the chosen effect. It equals one minus power. Lower beta means a stronger chance of detection.
Can I use one tailed testing?
Use one tailed testing only when the effect direction is justified before data collection. It should not be chosen after seeing results.
What alpha level should I enter?
Alpha is the tolerated false positive rate. A common value is 0.05, but stricter studies may use 0.01 or another justified threshold.
Does higher power need more samples?
Usually yes. Higher power reduces beta risk, but it normally increases required sample size, cost, time, and operational effort.
What is allocation ratio?
Allocation ratio describes the size of group 2 relative to group 1. A value of 2 means group 2 has twice as many observations.
Can this handle paired tests?
This version focuses on independent group comparisons. Paired designs need correlation or paired difference variation, so they require a different formula.
Are the results exact?
The results use normal approximations. They are useful for planning, teaching, and screening designs. Complex studies may need simulation or specialist review.