F-statistic
0
Between-group MS ÷ within-group MS
ANOVA Calculator
Compare the means of three or more independent groups using one-way analysis of variance. Enter your observations to calculate the F-statistic, p-value, effect size, and complete ANOVA table.
One-Way ANOVA Analysis
Enter at least two numeric observations in each group.
This title will appear in the copied or downloaded report.
Most studies use an alpha level of 0.05.
Group observations
Separate values with commas, spaces, semicolons, or new lines.
P-value
0
Probability under the null hypothesis
Eta squared
0
Effect size
Total observations
0
Across 0 groups
ANOVA summary table
| Source | Sum of Squares | df | Mean Square | F | p-value |
|---|
Group descriptive statistics
| Group | Count | Mean | Standard deviation | Minimum | Maximum |
|---|
Interpretation
Private calculation
Your observations are processed locally in your browser.
Flexible input
Use commas, spaces, semicolons, tabs, or separate lines.
Educational output
Review the calculations, effect size, and conclusion.
Simple process
How the ANOVA Calculator Works
The calculator evaluates whether the differences between your group means are larger than the variation expected within the groups.
1
Enter Group Data
Add observations for each independent group. You can rename groups and create additional group fields when needed.
2
Calculate the Variance
The tool measures variation between group means and variation among observations within each group.
3
Review the Conclusion
Use the F-statistic, p-value, selected alpha level, and effect size to interpret the statistical result.
What Is a One-Way ANOVA?
A one-way analysis of variance, commonly called one-way ANOVA, is a statistical hypothesis test used to compare the means of two or more independent groups. It is especially useful when a study has one categorical independent variable and one continuous dependent variable.
For example, a researcher could use ANOVA to compare average test scores from three teaching methods, product ratings from four designs, or crop yields from several fertilizers.
Core F-ratio
F = Between-Group Variance ÷ Within-Group Variance
Null and Alternative Hypotheses
The null hypothesis states that all population group means are equal. The alternative hypothesis states that at least one population mean differs from the others.
- Null hypothesis, H₀: μ₁ = μ₂ = μ₃ = ... = μₖ
- Alternative hypothesis, H₁: At least one group mean differs
Understanding the P-Value
The p-value represents how likely it would be to observe an F-statistic at least as extreme as the calculated result when the null hypothesis is true. When the p-value is less than or equal to the selected significance level, the result is considered statistically significant.
What Does Eta Squared Mean?
Eta squared, written as η², estimates the proportion of total variation in the dependent variable that is associated with group membership. Values near zero indicate a weak effect, while larger values indicate that group membership explains more of the observed variation.
Before interpreting results
Important ANOVA Assumptions
One-way ANOVA results are most reliable when the study design and data reasonably satisfy these assumptions.
Independent Observations
Each observation should be independent and should not influence another observation in the dataset.
Approximate Normality
The dependent variable should be approximately normally distributed within each comparison group.
Equal Variances
The population variances should be reasonably similar across the groups being compared.
Common questions
ANOVA Calculator FAQs
Learn how to enter data, interpret statistical significance, and use the results responsibly.
You can compare two or more independent groups. ANOVA is most
commonly selected when comparing three or more group means because
it avoids running several separate t-tests.
Enter numeric observations separated by commas, spaces, semicolons,
tabs, or new lines. Decimal values and negative values are supported.
A significant result suggests that the population means are not all
equal. It does not identify which specific groups differ. A suitable
post-hoc comparison, such as Tukey's HSD test, may be needed.
An alpha level of 0.05 is common, but the correct choice depends on
the field, study design, consequences of errors, and any analysis
plan established before examining the results.
Yes. One-way ANOVA can analyze groups with unequal sample sizes.
However, serious differences in group variances can be more
problematic when sample sizes are also highly unequal.
No. This calculator processes the observations directly in your
browser. The entered data is not submitted to this PHP page or
stored in a database.