Formula Used
The calculator uses normal approximation formulas for planning. For a two-tailed test, the critical value is Z(1 - alpha / 2). For a one-tailed test, it is Z(1 - alpha).
For achieved power, the noncentral distance is effect × information. For one sample designs, information is sqrt(n). For two group designs, information is sqrt((n1 × n2) / (n1 + n2)).
Required one sample size is ((Zcrit + Zpower) / effect)^2. Required two group size for group one is ((Zcrit + Zpower)^2 × (1 + 1 / ratio)) / effect^2. Dropout inflation divides the result by 1 - dropout rate.
Mean designs use Cohen style standardized difference. Proportion designs use Cohen h: 2 × asin(sqrt(p1)) - 2 × asin(sqrt(p2)).
How To Use This Calculator
Choose the calculation goal first. Select achieved power when sample sizes are already known. Select required sample size when planning a new study. Select minimum detectable effect when sample size is fixed.
Next, choose the study design. Enter alpha, target power, samples, means, deviations, or proportions. The tool computes the best matching standardized effect from the selected design. Press calculate. Review the result above the form. Use the export buttons to save the result.
Power Analysis Guide
Why Power Matters
Power analysis helps a researcher plan a study before data is collected. It estimates the chance of detecting a real effect. A weak study may miss an important result. A very large study may waste time and money. Good planning creates a practical balance. It also makes the research design easier to explain.
Main Inputs
The most common inputs are alpha, power, effect size, and sample size. Alpha is the chance of a false positive. Many studies use 0.05. Power is the chance of finding the effect when it is real. Many projects aim for 0.80 or 0.90. Effect size shows how large the expected difference is. Smaller effects need larger samples.
Choosing A Design
The correct design depends on the question. A one mean design compares one group with a known value. A two mean design compares two independent groups. A paired design compares related measurements from the same subjects. Proportion designs compare rates, shares, or conversion values. Pick the design that matches the data source. This keeps the result more useful.
Effect Size Meaning
For mean based tests, the calculator converts differences into a standardized effect. It divides the mean difference by a standard deviation. This makes results easier to compare across fields. For proportion based tests, the calculator uses Cohen h. That method stabilizes rates near zero or one. The final value is still an approximation. It should support planning, not replace expert judgment.
Alpha And Multiple Tests
Alpha becomes stricter when many comparisons are planned. This calculator includes a comparison adjustment. It divides alpha by the number of comparisons. That is similar to a simple Bonferroni correction. A stricter alpha reduces false positives. It also raises the sample size requirement. Use this option when several primary tests are planned.
Sample Size Planning
Required sample size grows when the effect is small. It also grows when target power is high. Two-tailed tests usually need more data than one-tailed tests. Unequal allocation can increase total sample needs. Dropout also matters. If people leave a study, the final sample becomes smaller. The dropout field inflates the starting sample to protect the final analysis.
Reading The Result
The result appears above the form after submission. It shows the main answer, adjusted alpha, effect size, critical value, and sample sizes. For achieved power, a higher percentage means better detection ability. For sample size, the result shows the planned count. For detectable effect, a lower value means the study can find smaller differences.
Using Exports
The CSV export is helpful for spreadsheets. The PDF export is useful for reports and review notes. Save both when comparing several scenarios. Change one input at a time. Then compare the exported files. This makes planning transparent. It also helps teams agree on realistic targets before the study starts.
Limits Of The Method
This calculator uses normal approximation methods. They are fast and helpful for early planning. Some studies need exact methods, simulation, or specialist models. Complex clustering, survival data, repeated measures, and nonstandard endpoints may need deeper analysis. Use this page as a strong planning aid. Confirm final designs with a qualified statistician when stakes are high.
FAQs
What is power analysis?
Power analysis estimates the chance that a study will detect a real effect. It helps choose sample size, alpha, power, and detectable effect before data collection begins.
What is a good power value?
Many studies use 80% power. Some high impact studies use 90% or more. Higher power gives better detection, but it often needs a larger sample.
What does alpha mean?
Alpha is the accepted chance of a false positive. A common value is 0.05. Smaller alpha values are stricter and usually need more participants.
What is effect size?
Effect size shows how large the expected difference is. Mean tests often use standardized differences. Proportion tests can use Cohen h for rate differences.
Why does a small effect need more data?
Small effects are harder to separate from random variation. More data reduces uncertainty. That gives the test a better chance of finding the real effect.
Should I use one-tailed or two-tailed testing?
Use two-tailed testing when effects in either direction matter. Use one-tailed testing only when one direction is justified before data collection.
What is minimum detectable effect?
Minimum detectable effect is the smallest standardized effect the study can detect at the chosen alpha, power, and sample size.
What does dropout inflation do?
Dropout inflation increases the starting sample size. It helps protect the final sample after expected withdrawals, missing data, or incomplete responses.
What is allocation ratio?
Allocation ratio compares group two size with group one size. A ratio of one means equal groups. Unequal groups can require more total subjects.
Can I use this for conversion rates?
Yes. Select a proportion design. Enter the two rates as decimals, such as 0.12 and 0.15. The calculator uses a standardized rate difference.
Why is adjusted alpha shown?
Adjusted alpha accounts for multiple comparisons. The calculator divides alpha by the comparison count. This makes the test stricter when many tests are planned.
Does this replace statistical software?
No. It is useful for planning and quick checks. Complex designs may need exact tests, simulation, or dedicated statistical review.
Why are results approximate?
The calculator uses normal approximation formulas. They are practical and fast. Exact results may differ for very small samples or unusual data.
Can I export the results?
Yes. Use the CSV button for spreadsheet work. Use the PDF button for reports, planning files, and study documentation.