ANOVA Calculator

Run a one-way ANOVA across two or more groups with F-statistic, p-value, variance breakdown, and eta-squared.

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What This Calculator Does

This calculator performs a one-way ANOVA from grouped observations entered as text. It reports the between-group and within-group sums of squares, mean squares, F statistic, p-value, and effect size.

It combines Grouped Samples to estimate F Statistic, p-Value, SS Between.

Formula & Method

Core equations:

F=\frac{MS_B}{MS_W}

where

MS_B=\frac{SS_B}{k-1}

and

MS_W=\frac{SS_W}{N-k}

. Effect size is

\eta^2=\frac{SS_B}{SS_T}

Notation used in the formulas: $R$ = F Statistic; $x_{1}$ = Grouped Samples.

Method summary: inputs are normalized to consistent units, core equations are evaluated, then secondary values are derived and rounded for display.

Use it when you need to test whether the means of several independent groups differ more than random variation would suggest.

Reference Book

Introduction to Mathematical Statistics

Global Edition

Robert V. Hogg, Joseph McKean, and Allen T. Craig · Pearson

A standard reference for probability distributions, estimation, hypothesis testing, regression, and ANOVA.

View Book

Inputs Used

Grouped Samples: Used directly in the calculation.

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