ANOVA Calculator

Perform one-way ANOVA analysis of variance with F-statistic and p-value.

By Konstantin Iakovlev · Updated April 2026 · Source: Khan Academy

F-Statistic

10.8000

Significant?

Likely (F>3.15)

ANOVA Table

SS Between360.00
SS Within950.00
MS Between180.00
MS Within16.67
F-Statistic10.8000

Use the ANOVA Calculator above to calculate your results. Enter your values and see instant results — all calculations run in your browser.

Disclaimer: This calculator is for informational purposes only and does not constitute tax, financial, or legal advice. Results are estimates based on the information you provide and current rates. Always consult a qualified tax professional or financial advisor for advice specific to your situation.

How It Works

Analysis of variance answers a single, focused question: when you have three or more independent groups, are the differences in their means large enough to be statistically significant, or could they have arisen by chance? Researchers lean on this test constantly to judge whether different treatments or conditions actually produce different outcomes, which is why it sits at the center of so much experimental design and data analysis.

The engine behind the test is the F-statistic, computed by dividing the 'between-group variability' by the 'within-group variability'. When that ratio climbs, it tells you the spread between the group means outweighs the spread inside the individual groups, which points toward a genuine difference rather than random noise.

The results only hold up when the data respects ANOVA's three assumptions: observations must be independent, residuals roughly normal, and variances reasonably equal across groups. Ignoring these conditions can quietly distort your conclusions, so when the data clearly breaks them, reach for Welch's ANOVA or a non-parametric alternative instead.

Example: Comparing Sales Strategies

  1. 1 A marketing company tested three different advertising strategies (A, B, C) and recorded the weekly sales in thousands of dollars for each. Strategy A: 12, 15, 11, 14, 13 Strategy B: 18, 20, 19, 17, 21 Strategy C: 10, 9, 12, 11, 10
  2. 2 The ANOVA calculator would take these sales figures as input for each group. It would then compute the sum of squares between groups (SSB), sum of squares within groups (SSW), degrees of freedom, mean squares, and finally the F-statistic and its corresponding p-value.
  3. 3 Let's assume the calculator outputs an F-statistic of 25.3 and a p-value of 0.0001. This p-value is significantly less than the typical alpha level of 0.05.
  4. 4 Since the p-value (0.0001) is less than 0.05, we reject the null hypothesis. This means there is a statistically significant difference in weekly sales among the three advertising strategies. A post-hoc test would then be needed to determine which specific strategies differ from each other.

Source: Khan Academy · Last updated: April 2026

Frequently Asked Questions

When should I use ANOVA instead of a t-test?
Use ANOVA when comparing means across three or more groups. A t-test compares only two groups. Running multiple t-tests inflates the chance of a false positive, while ANOVA controls for this by testing all groups simultaneously.
What does a significant F-statistic mean in ANOVA?
A significant F-statistic (p-value below your threshold, typically 0.05) means at least one group mean is significantly different from the others. It does not tell you which groups differ. You need post-hoc tests like Tukey HSD to identify specific differences.
What are the assumptions of one-way ANOVA?
One-way ANOVA assumes independent observations, normally distributed data within each group, and roughly equal variances across groups (homoscedasticity). ANOVA is robust to moderate violations of normality with larger sample sizes.

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