ANOVA Calculator

Calculate one-way analysis of variance with F-statistic and p-value

Data Input

Results

What is ANOVA?

Analysis of Variance (ANOVA) is a statistical method used to compare means across multiple groups. It tests whether there are statistically significant differences between the means of three or more independent groups. ANOVA is an extension of the t-test for comparing more than two groups.

ANOVA Formula

The F-statistic for one-way ANOVA is calculated as:

F = MSB / MSW

Where:

  • MSB = Mean Square Between (variance between groups)
  • MSW = Mean Square Within (variance within groups)

How to Use the Calculator

  1. Enter data for each group (separate by commas or spaces)
  2. Set your significance level (α)
  3. Click "Calculate" to get the ANOVA results
  4. View the F-statistic, p-value, and ANOVA table
  5. Interpret the results

Interpreting Results

  • p-value < α: Reject the null hypothesis (significant differences between groups)
  • p-value ≥ α: Fail to reject the null hypothesis (no significant differences)
  • F > critical value: Reject the null hypothesis
  • F ≤ critical value: Fail to reject the null hypothesis

Applications

  • Experimental Design: Comparing treatment effects
  • Quality Control: Comparing production methods
  • Medical Research: Comparing treatment outcomes
  • Education: Comparing teaching methods
  • Marketing: Comparing customer satisfaction across groups