Formula Used
The calculator converts the selected effect size into a planning value of Cohen f squared.
For partial eta squared: f squared = eta squared / (1 - eta squared).
For Wilks Lambda: f squared approximates (1 - Lambda^(1/s)) / Lambda^(1/s), where s = min(outcomes, groups - 1).
For Pillai trace: f squared approximates (trace / s) / (1 - trace / s).
The noncentrality parameter is lambda = effective N × f squared × allocation efficiency.
Power is estimated as 1 - Fcdf(F critical, df1, df2, lambda). The critical value uses alpha and the selected MANOVA F approximation.
How to Use This Calculator
Enter the number of study groups and dependent variables. Add covariates when the planned analysis includes them.
Select the effect size type. Enter a value from pilot data, a previous paper, or a conservative planning target.
Set alpha, target power, fixed sample size, allocation ratio, design effect, and dropout rate.
Press Calculate. Review the required complete sample, recruited sample, degrees of freedom, critical F, and achieved power.
Use CSV or PDF export to save the current planning result.
MANOVA Power Planning
Multivariate analysis of variance studies compare group means across several dependent variables. A sample size plan should reflect the number of groups, the number of outcomes, the chosen alpha level, and the expected multivariate effect. This calculator gives a practical planning estimate before data collection starts.
Why Power Matters
Power is the chance of detecting a real group difference. Low power can hide meaningful effects. Very high power can require more participants than the project can support. A balanced plan helps protect time, cost, and ethical effort.
Effect Size Choice
The tool accepts partial eta squared, Cohen f squared, Wilks Lambda, or Pillai trace. These inputs are converted to a planning f squared value. A larger effect needs fewer participants. A smaller effect needs more participants. Use pilot data, published studies, or a conservative minimum important effect.
Test Statistic Options
MANOVA may be reported with Pillai, Wilks, Hotelling Lawley, or Roy style tests. Each option uses an approximate F framework. Pillai is often stable when assumptions are imperfect. Wilks is common in reports. Hotelling Lawley and Roy can be useful with specific alternatives.
Design Controls
Covariates reduce error degrees of freedom. Unequal allocation lowers information when one group is much larger than others. A design effect can represent clustering or repeated sampling loss. Dropout inflation estimates how many people should be recruited to keep enough complete cases.
Interpreting Results
The required complete sample is the analyzed sample before dropout inflation. The enrolled sample adds the dropout allowance. Per group values assume equal allocation unless a ratio is entered. The achieved power uses the fixed total sample size entered in the form.
Best Practice
Treat this result as a planning estimate, not a final statistical guarantee. MANOVA power depends on covariance patterns, assumption quality, and true effect shape. Review the plan with a statistician when stakes are high. Save the CSV or PDF report for protocols, grant notes, or study files.
Use conservative inputs when uncertain. Run sensitivity checks across several effect sizes. Compare 0.70, 0.80, and 0.90 power targets. This makes the study plan easier to defend and easier to revise.
Document assumptions clearly so reviewers can understand every planning choice and calculation limit.
FAQs
What does MANOVA power mean?
It is the probability of finding a true multivariate group difference when the planned effect exists. Higher power lowers the chance of missing a meaningful result.
Which effect size should I use?
Use the effect size reported by a similar study when possible. If none exists, use a conservative minimum effect that would still matter for your research question.
Is partial eta squared accepted?
Yes. The calculator converts partial eta squared to Cohen f squared with eta squared divided by one minus eta squared.
Why does dropout increase the sample?
Dropout reduces the final analyzed sample. Inflation estimates how many participants should be recruited so the complete sample still reaches the target power.
What is allocation efficiency?
It estimates information loss from unequal group sizes. Balanced groups usually give the best efficiency for the same total sample size.
Should I choose Pillai or Wilks?
Pillai is often robust under assumption concerns. Wilks is widely reported. Choose the statistic that matches your planned analysis and reporting standard.
Does this replace specialist software?
No. It provides an advanced planning estimate. Complex covariance structures, repeated measures, and strict protocol work should be reviewed with statistical software or a statistician.
Can I export the results?
Yes. After calculation, use the CSV or PDF buttons to download the displayed planning summary for records, proposals, or team review.