Statistics

ANOVA Calculator

Calculate F-statistic, p-value, and effect sizes for one-way Analysis of Variance (ANOVA). Includes post-hoc Tukey HSD test for pairwise comparisons with step-by-step calculations.

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ANOVA Calculator - One-Way Analysis of Variance

Perform one-way ANOVA to test if there are significant differences between the means of three or more independent groups. Calculate F-statistic, p-value, effect sizes (η², ω², Cohen's f), and conduct post-hoc Tukey HSD tests with complete step-by-step calculations.

What is ANOVA?

ANOVA (Analysis of Variance) is a statistical method used to compare means across three or more groups simultaneously. Unlike multiple t-tests, ANOVA controls the Type I error rate by testing whether any group means differ significantly. The method partitions total variance into between-group variance (differences among group means) and within-group variance (individual differences within groups). If between-group variance significantly exceeds within-group variance, we conclude that at least one group mean differs.

F-Statistic Formula

F = MSB / MSW = (SSB / dfB) / (SSW / dfW)

How to Perform One-Way ANOVA

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ANOVA Applications

Clinical Trials

Compare effectiveness of multiple drug dosages or treatment protocols across patient groups.

Agricultural Research

Test different fertilizer types, irrigation methods, or crop varieties on yield outcomes.

Education Research

Compare test scores across different teaching methods, schools, or student demographics.

Quality Control

Analyze if production batches, machines, or suppliers produce significantly different results.

Frequently Asked Questions

Use ANOVA whenever you're comparing 3 or more groups. Running multiple t-tests inflates the Type I error rate (false positives). With 3 groups at α=0.05, three t-tests give ~14% overall error rate, while ANOVA maintains 5%. ANOVA is the standard approach for multi-group comparisons.