Calculator Inputs
Example Data Table
This example shows a balanced design with four groups and a shared standard deviation.
| Group | Expected Mean | Planned Sample Size | Common Standard Deviation |
|---|---|---|---|
| A | 50 | 20 | 12 |
| B | 55 | 20 | 12 |
| C | 58 | 20 | 12 |
| D | 63 | 20 | 12 |
Formula Used
Balanced one-way ANOVA effect size: f = √[ Σ(μi - μ̄)2 / (kσ2) ]
Noncentrality parameter: λ = N × f2
Degrees of freedom: df1 = k - 1 and df2 = N - k
Power: 1 - FNCF(Fcritical; df1, df2, λ)
The calculator uses the central F distribution for the critical value and a Poisson mixture approximation for the noncentral F distribution.
How to Use This Calculator
- Enter the number of groups in your balanced one-way ANOVA design.
- Provide the planned sample size for each group.
- Set the significance level and your desired target power.
- Choose whether to enter Cohen's f directly or derive it from group means.
- If you derive effect size, enter one mean for each group and a common standard deviation.
- Press Calculate Power to see achieved power, critical F, and planning benchmarks.
- Use the export buttons to save the displayed results as CSV or PDF.
Why This Calculator Helps
This tool supports study design decisions before data collection. It helps researchers compare sample size plans, quantify detectable differences, and understand whether a balanced one-way ANOVA design has enough sensitivity for meaningful group comparisons.
Because it also returns required sample size and required effect size for a chosen target power, it is useful for proposal planning, pilot studies, coursework, and production experiment reviews.
FAQs
1. What does ANOVA power mean?
ANOVA power is the probability of detecting real mean differences across groups when those differences truly exist at the selected significance level.
2. What is Cohen's f in this calculator?
Cohen's f measures standardized separation among group means relative to the shared within-group standard deviation in a one-way ANOVA design.
3. Can I enter group means instead of effect size?
Yes. Choose the derived mode, enter one expected mean per group, and add a common standard deviation to compute Cohen's f automatically.
4. Does this work for unbalanced ANOVA?
No. This version assumes equal sample sizes across groups. Unequal allocation changes the noncentrality structure and requires a different implementation.
5. Why does target power affect required sample size?
Higher target power demands more information. That usually means larger per-group samples or a larger expected effect size.
6. What alpha value should I use?
Many studies use 0.05, but your field, protocol, and error tolerance should determine the final significance threshold.
7. Are the results exact?
They are numerically approximated using established distribution formulas and iterative methods, which are suitable for practical planning work.