ANOVA Calculator & Visualizer
A comprehensive tool for one-way Analysis of Variance (ANOVA) with step-by-step explanations and interactive visualizations
What is ANOVA?
Analysis of Variance (ANOVA) is a statistical test used to determine whether there are significant differences between the means of three or more independent groups. It analyzes the variance within groups versus the variance between groups to determine if the group means are different enough to be statistically significant.
Assumptions for ANOVA:
- Independence: Observations in each group are independent of each other
- Normality: Data in each group follows a normal distribution
- Homogeneity of variance: Variances across groups are approximately equal
Enter Your Data
Enter numeric values for each group (one value per line). You can add up to 6 groups.
Group 1
Group 2
Group 3
Results
ANOVA Table
| Source | Sum of Squares | df | Mean Square | F | p-value |
|---|
Visualization
Understanding the Results
Sum of Squares (SS)
Measures the total variation in the data. It's partitioned into:
- SS Between: Variation due to differences between group means
- SS Within: Variation within each group (error)
Degrees of Freedom (df)
Number of independent values that can vary:
- df_between: Number of groups - 1
- df_within: Total observations - Number of groups
Mean Square (MS)
Average variance, calculated by dividing Sum of Squares by degrees of freedom:
F-Statistic
The test statistic that compares the variance between groups to the variance within groups:
A larger F-value indicates that the group means are more different relative to the variation within groups.
p-value
The probability of observing an F-statistic as extreme as (or more extreme than) the one calculated, assuming the null hypothesis is true (that all group means are equal).
- p < 0.05: Strong evidence against null hypothesis (groups likely differ)
- p ≥ 0.05: Insufficient evidence to reject null hypothesis (groups may be similar)