ANOVA Calculator (General)

Enter your group data into Group 1, Group 2, and Group 3 (comma-separated values), set your significance level (α), and the ANOVA Calculator returns the F-statistic, p-value, and a full ANOVA table showing between-group and within-group sum of squares, degrees of freedom, and mean squares. Find out whether the differences between your group means are statistically significant. Also try the use the ANOVA Calculator (Biology).

Results

F-Statistic

P-Value

Result

SS Between Groups

SS Within Groups

df Between

df Within

MS Between

MS Within

Results Table

What is ANOVA and when should I use it?

ANOVA (Analysis of Variance) tests whether the means of three or more independent groups are significantly different from one another. Use one-way ANOVA when you have one categorical independent variable (factor) and a continuous dependent variable, and you want to determine if at least one group mean stands out from the rest. See also our Two-Way ANOVA Calculator.

What is the significance level (α) and which should I choose?

The significance level α is the threshold for deciding whether a result is statistically significant. A value of 0.05 is the standard choice, meaning there is a 5% chance of falsely rejecting the null hypothesis. Use 0.01 for high-precision research and 0.10 for exploratory analysis where you are willing to accept a higher risk of false positives.

How do I interpret the F-statistic and p-value?

The F-statistic compares the variance between group means to the variance within groups. A larger F-statistic suggests greater differences between groups relative to within-group variation. If the p-value is less than your chosen α, you reject the null hypothesis and conclude that at least one group mean is significantly different from the others.

Can I use ANOVA for only two groups?

Technically yes, but a two-sample t-test is preferred for comparing just two groups. ANOVA is designed for three or more groups. For two groups, ANOVA and an independent-samples t-test will produce equivalent results (F = t²), so the t-test is simpler and more conventional. You might also find our ANOVA Calculator useful.

What are the assumptions of one-way ANOVA?

One-way ANOVA assumes that observations are independent, that the dependent variable is approximately normally distributed within each group, and that the variances across groups are roughly equal (homogeneity of variances). Violating these assumptions can affect the reliability of the results.

What is the difference between one-way and two-way ANOVA?

One-way ANOVA examines the effect of a single factor on a continuous outcome. Two-way ANOVA extends this to two factors simultaneously, allowing you to assess both main effects and the interaction between the factors. Use two-way ANOVA when your experimental design includes two independent variables.

Can ANOVA tell me which specific groups are different?

No — a significant ANOVA result only tells you that at least one group mean differs, but not which pairs are different. To identify specific group differences, you need to follow up with a post-hoc test such as Tukey HSD, Bonferroni correction, or Scheffé's test.

What do SS Between and SS Within represent?

SS Between (sum of squares between groups) measures how much the group means vary from the overall mean — it captures the effect of the treatment or factor. SS Within (sum of squares within groups) measures the variation inside each group due to individual differences. The ratio of these, adjusted for degrees of freedom, produces the F-statistic.