Effective Size Calculator for ANOVA

The Effective Size Calculator for ANOVA estimates the required sample size based on effect size, significance level, power, and number of groups. This tool helps academic researchers and statisticians plan robust studies. Whether you are applying for grants, designing experiments, or ensuring adequate statistical power, this calculator provides accurate results. It simplifies complex power analysis for better research outcomes.

Small (0.10), Medium (0.25), Large (0.40) - The standardized measure of the magnitude of the phenomenon
Probability of Type I error (typically 0.05)
Probability of correctly rejecting a false null hypothesis (typically 0.80)
Number of groups or categories in your ANOVA design
Number of control variables (for ANCOVA designs)

How Required Sample Size Is Calculated

The required sample size represents the minimum number of participants needed to detect a real difference between groups with confidence. This calculation uses the noncentral F distribution to ensure your study is strong enough to find meaningful results without wasting resources on too many subjects.

N = (λ + f² * df₁) / f²

Where:

  • N = Total sample size required
  • λ = Noncentrality parameter (lambda)
  • f = Effect size (Cohen's f)
  • df₁ = Degrees of freedom (groups - 1 + covariates)

The method first determines degrees of freedom based on your groups and covariates. It then calculates lambda using your desired power and alpha level. Finally, it solves for N to show the exact number of participants needed to achieve your statistical goals.

What Your Required Sample Size Means

This number tells you exactly how many subjects you must recruit to avoid a failed study. A higher number usually means you are looking for a small, hard-to-detect effect or want very high certainty.

Common Sample Size Ranges

High Sample Size (200+): You are likely detecting small effects (f=0.1) or want very high power. This is common in social sciences where differences are subtle.

Moderate Sample Size (50-150): Ideal for detecting medium effects (f=0.25). This range balances cost with the ability to find statistically significant results.

Low Sample Size (<50): Only sufficient if you expect a large, obvious effect (f=0.4) or are conducting a pilot study.

Important: Always add 10-20% extra to your calculated number to account for participants dropping out or providing incomplete data.

This calculator provides estimates for educational purposes only. Actual sample size requirements may vary based on data characteristics and specific research assumptions. Please consult a statistician for complex designs or critical applications.