🎓 Statistics & Data • Hypothesis Testing
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One-Way ANOVA Calculator (F-Test)
Calculates Between-Group variance, Within-Group variance, and the F-ratio statistic for multi-group hypothesis testing.
Significance Level (α):
One-Way Analysis of Variance
One-Way ANOVA: F = MS_between / MS_within
Compare differences among 3 independent treatment groups using the F-ratio variance test.
ANOVA F-Ratio Statistic
F = 50
Reject H₀: At least one group mean is significantly different (F = 50 > crit = 3.89)
| Source | Sum of Sq (SS) | df | Mean Sq (MS) | F-Stat |
|---|---|---|---|---|
| Between Groups | 250 | 2 | 125 | 50 |
| Within Groups (Error) | 30 | 12 | 2.5 | — |
| Total | 280 | 14 | — | — |
What is ANOVA (Analysis of Variance)?
ANOVA is a statistical method used to test whether the means of three or more independent groups differ significantly from one another.
Formula & Step-by-Step Calculation
F = MS_between / MS_within = (SS_B / df_B) / (SS_W / df_W)
Ratio of explained variance between groups to unexplained error variance within groups.
Worked Step-by-Step Examples
Example 1
Compare test scores across 3 different study techniques
Solution: F = 4.25 (Statistically Significant difference across groups)
• MS_B = 120, MS_W = 28.2 ⟹ F = 120 / 28.2 = 4.25
Common Real-World & Academic Use Cases
- ✓ Clinical drug dosage multi-arm comparison
- ✓ Agricultural crop fertilizer yield trials
- ✓ Website design multi-variant UX experiments
How to Use the One-Way ANOVA Calculator (F-Test)
1
Enter Data for Each Group
Input Group 1, Group 2, and Group 3 numbers.
2
Review F-Statistic
Inspect MS Between, MS Within, and significance decision.
Frequently Asked Questions
Q: Why use ANOVA instead of multiple t-tests?
Running multiple t-tests inflates the overall Type I error rate (false positive risk); ANOVA controls the error rate across all groups simultaneously.