Calculadora ANOVA (entre duas médias)
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
F ≈ (Δx̄)²·n / (s₁² + s₂²) × 0,5 — aproximação didática
About this calculator
The ANOVA Calculator between two means is a didactic tool that compares two groups using a simplified version of the F-test. Instead of the full analysis of variance, it uses the approximate formula F ≈ (Δx̄)²·n / (s₁² + s₂²) × 0.5, where Δx̄ is the difference between means, n the sample size (assumed equal), and s₁², s₂² the variances of each group. The result is an approximate F value, useful for understanding the concept of variance between groups versus within groups.
This calculator was created for educational purposes, helping students and professionals visualize how the difference between means and data dispersion influence the F statistic. It is ideal for introductory statistics classes where the principle of ANOVA is demonstrated without the complexity of full calculations. The 0.5 factor adjusts the approximation for scenarios with two groups and equal sample sizes.
Important caveats: this is a didactic approximation and does not replace a full ANOVA, which requires F tables and assumptions such as normality and homogeneity of variances. The result should be interpreted cautiously, especially with small samples or very different variances. Use this calculator as a learning aid, not for formal statistical analysis.
Frequently asked questions
What does the calculated F value mean?
The approximate F value indicates the ratio of variance between groups to variance within groups. A larger F suggests stronger evidence that the means are different.
Can I use this calculator for formal hypothesis testing?
No. This is a didactic approximation. For formal tests, use a full ANOVA with F tables or statistical software.
What if the sample sizes are different?
The formula assumes equal sample sizes. If they differ, the result will be less accurate. Consider using the harmonic mean or a full ANOVA.
What is the role of the 0.5 factor in the formula?
The 0.5 factor adjusts the approximation for two groups with equal sizes, making the F value closer to the actual ANOVA calculation.
Do the data need to be normally distributed?
For a full ANOVA, yes. In this approximation, normality is not checked, but interpretation should consider this limitation.