Calculators
One-Way ANOVA Calculator
Run a one-way ANOVA to test whether the means of three or more independent groups differ significantly. Get the F statistic, degrees of freedom, p-value, and effect size (η²) locally in your browser.
Enter values for each group, one group per box. Separate values with spaces, commas, or new lines. One-way ANOVA tests whether the means of three or more independent groups differ significantly. The F statistic, degrees of freedom, p-value, and effect size (η²) are computed locally in your browser; your values are not uploaded or stored. Assumptions: independence, normality within groups, and homogeneity of variance (equal variances across groups). With only two groups, this is equivalent to a two-sample t-test with equal variances assumed.
Compare multiple group means at once.
Enter values for each group to test whether their means are all equal. One-way ANOVA computes the F statistic as the ratio of between-group variance to within-group variance: F = MS_between / MS_within, with df1 = k − 1 and df2 = N − k. The p-value comes from the F distribution. For example, three groups with values 1.2 2.3 3.1, 2.8 3.6 4.1, and 5.2 4.8 5.5 give F ≈ 18.4, df = 2 and 6, p ≈ 0.0025, and η² ≈ 0.86. With two groups, the result matches a two-sample t-test with equal variances assumed. Assumptions: independence, normality within groups, and equal variances. Small expected counts, unequal group sizes, or variance heterogeneity can affect the Type I error rate. Enter 2 to 50 groups with at least 2 values each; total observations cannot exceed 10,000. Values must be finite numbers from -1e12 to 1e12. All calculations run locally in your browser; your values are not uploaded or stored.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
What is a one-way ANOVA?
One-way ANOVA (analysis of variance) tests whether the means of three or more independent groups are equal. It compares the variance between group means to the variance within groups using an F statistic. A significant result means at least one group mean differs from the others.
When should I use ANOVA instead of a t-test?
Use a t-test when comparing exactly two groups. Use one-way ANOVA when comparing three or more independent groups. With two groups, ANOVA gives the same p-value as a two-sample t-test with equal variances assumed.
What assumptions does ANOVA make?
The standard one-way ANOVA assumes: independence of observations within and between groups, normality of data within each group, and homogeneity of variances (equal variances across groups). Violations can affect the Type I error rate, especially with unequal group sizes.
What is the effect size η²?
Eta-squared (η²) is the proportion of total variance explained by group differences: η² = SS_between / SS_total. It ranges from 0 to 1. Common benchmarks: 0.01 is small, 0.06 is medium, and 0.14 is large, but interpret in context.
How is the p-value calculated?
The p-value is the upper-tail probability of the F distribution with df1 = k − 1 (between groups) and df2 = N − k (within groups), computed using the regularized incomplete beta function. The 0.05 critical F value is found by bisection.
What are the input limits?
Enter 2 to 50 groups, with at least 2 values per group. Total observations cannot exceed 10,000. Values must be finite numbers between -1e12 and 1e12. Groups with identical values (zero within-group variance) produce an error.
Are my data values uploaded?
No. All calculations run locally in your browser. CodeASystem does not upload or store your input values.