Calculator Inputs
Example Data Table
| Scenario | Study Type | Alpha | Power | Effect Input | Dropout |
|---|---|---|---|---|---|
| Mean difference trial | Two means | 0.05 | 0.80 | Mean 100 to 110, SD 15 | 10% |
| Conversion rate study | Two proportions | 0.05 | 0.90 | Rate 0.40 to 0.55 | 5% |
| Association study | Correlation | 0.05 | 0.80 | r = 0.30 | 8% |
Formula Used
One mean: n = ((Z alpha + Z power) × SD / difference)².
Two means: n per group uses ((1 + 1 / ratio) × (Z alpha + Z power)²) / d², where d is the standardized mean difference.
One proportion: n = (Z alpha√p0q0 + Z power√p1q1)² / (p1 - p0)².
Two proportions: the calculator uses pooled null variance and alternative variance with the selected allocation ratio.
Correlation: n = ((Z alpha + Z power) / Fisher z effect)² + 3.
Dropout: adjusted sample = required sample / (1 - dropout rate).
How to Use This Calculator
- Select the study type that matches your research question.
- Choose whether to solve required sample size or achieved power.
- Enter alpha, target power, tail direction, and dropout rate.
- Complete the mean, proportion, or correlation fields needed for your design.
- Press calculate and review the result above the form.
- Use CSV or PDF download buttons to save the result.
Why Power Analysis Matters
Power analysis helps researchers plan dependable studies before data collection starts. It links sample size, effect size, significance level, and desired power. Each part affects the others. A small effect needs more observations. A higher power target also needs more observations. This calculator gives a fast planning estimate for common study designs.
Planning With Effect Size
Effect size describes the practical difference you want to detect. For mean studies, the tool converts a mean difference into Cohen style standardized difference. For proportion studies, it uses the absolute rate difference. For correlation studies, it uses Fisher transformation. These methods keep inputs simple, while still giving useful planning values.
Alpha, Tails, and Power
Alpha is the chance of rejecting a true null hypothesis. Many studies use 0.05. A two tailed test splits alpha across both directions. That choice needs a larger sample than a one tailed test. Power is the chance of detecting the planned effect. Researchers often choose 80 percent or 90 percent power.
Dropout and Allocation
Real studies often lose participants. Dropout adjustment increases the final recommended sample. The calculator divides the computed size by the expected retention rate. Two group designs also support unequal allocation. For example, a 2 ratio places twice as many participants in group two.
Interpreting The Results
The result should be viewed as a planning guide. It does not replace a full protocol review. Assumptions must match the study question. Standard deviation, baseline rate, and expected effect should come from pilot data, literature, or expert judgment. Weak assumptions can create poor sample targets.
Best Practice Notes
Use conservative inputs when information is limited. Check several effect sizes. Compare 80 percent and 90 percent power. Add a realistic dropout rate. Document every assumption in the study plan. A clear record helps reviewers understand why the chosen sample size is justified.
Using Scenario Checks
Scenario checks improve planning. Run the calculator with optimistic, expected, and conservative inputs. Save each result using the export buttons. Compare the required totals side by side. This habit shows how sensitive the design is. It also supports budget choices, recruitment planning, ethics notes, and grant explanations. It helps prevent late design changes during review and reporting later.
FAQs
What is sample size power analysis?
It estimates how many observations are needed to detect a planned effect. It can also estimate power for a sample size you already have.
What power value should I use?
Many studies use 80 percent power. Higher stakes studies may use 90 percent or more. Your choice should match the research field and protocol.
What does alpha mean?
Alpha is the allowed probability of a false positive result. A common value is 0.05, but some designs use stricter levels.
Should I choose one tailed or two tailed?
Use two tailed when effects in either direction matter. Use one tailed only when the protocol justifies one expected direction before data collection.
How does dropout adjustment work?
The calculator divides the required sample by the expected retention rate. This increases recruitment targets when some participants may leave the study.
Can this replace statistical software?
No. It is a planning helper. Complex clinical, clustered, repeated, or survival designs need dedicated statistical review and specialist software.
What standard deviation should I enter?
Use a value from pilot data, reliable literature, or a justified expert estimate. The result is only as strong as this assumption.
Why do smaller effects need larger samples?
Small effects are harder to separate from random variation. More observations reduce uncertainty and improve the chance of detecting the effect.