ANOVA Calculator

ANOVA is evaluated from Group 1, Group 2 and Group 3. The calculation reports F-Statistic, df Between and df Within.

Results

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About the ANOVA Calculator

ANOVA is treated here as a quantitative relation between Group 1, Group 2, Group 3 and Group 4 and F-Statistic, df Between, df Within and MS Between.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
Between-group variation (SSB) measures how much group means vary from grand mean. Within-group variation (SSW) measures variability within each group. F = MSB/MSW.

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

Between-group variation (SSB) measures how much group means vary from grand mean. Within-group variation (SSW) measures variability within each group. F = MSB/MSW.

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: 3 groups: fertilizer experiment (plant heights)

Inputs

group1: 10, 12, 11, 13, 9 group2: 15, 17, 14, 16, 18 group3: 20, 22, 21, 19, 23 group4: group5:
F-Statistic: 50. df Between: 2. df Within: 12. MS Between: 125. MS Within: 2.5. SS Between: 250. SS Within: 30. Conclusion: Reject H0 - significant difference between groups (p < 0.05)

With Group 1 = 10, 12, 11, 13, 9, Group 2 = 15, 17, 14, 16, 18 and Group 3 = 20, 22, 21, 19, 23 as the stated inputs, the result is F-Statistic = 50, df Between = 2 and df Within = 12. Each value corresponds to the declared output fields.

Example 2: 3 groups: drug vs placebo (similar outcomes)

Inputs

group1: 23, 25, 22, 24, 26 group2: 24, 23, 25, 24, 23 group3: 22, 24, 23, 25, 24 group4: group5:
F-Statistic: 0.1333. df Between: 2. df Within: 12. MS Between: 0.2. MS Within: 1.5. SS Between: 0.4. SS Within: 18. Conclusion: Fail to reject H0 - no significant difference (p >= 0.05)

With Group 1 = 23, 25, 22, 24, 26, Group 2 = 24, 23, 25, 24, 23 and Group 3 = 22, 24, 23, 25, 24 as the stated inputs, the result is F-Statistic = 0.1333, df Between = 2 and df Within = 12. Each value corresponds to the declared output fields.

Example 3: 4 groups: teaching methods comparison (test scores)

Inputs

group1: 72, 75, 68, 70, 73 group2: 85, 88, 82, 86, 89 group3: 78, 80, 76, 79, 81 group4: 90, 92, 88, 91, 93 group5:
F-Statistic: 63.5676. df Between: 3. df Within: 16. MS Between: 352.8. MS Within: 5.55. SS Between: 1,058.4. SS Within: 88.8. Conclusion: Reject H0 - significant difference between groups (p < 0.05)

With Group 1 = 72, 75, 68, 70, 73, Group 2 = 85, 88, 82, 86, 89, Group 3 = 78, 80, 76, 79, 81 and Group 4 = 90, 92, 88, 91, 93 as the stated inputs, the result is F-Statistic = 63.5676, df Between = 3 and df Within = 16. Each value corresponds to the declared output fields.

Example 4: 5 groups: regional salary comparison

Inputs

group1: 55000, 58000, 52000, 60000, 57000 group2: 72000, 75000, 68000, 80000, 71000 group3: 65000, 63000, 67000, 64000, 66000 group4: 45000, 48000, 42000, 50000, 47000 group5: 95000, 98000, 92000, 100000, 96000
F-Statistic: 175.3471. df Between: 4. df Within: 20. MS Between: 1,788,540,000. MS Within: 10,200,000. SS Between: 7,154,160,000. SS Within: 204,000,000. Conclusion: Reject H0 - significant difference between groups (p < 0.05)

With Group 1 = 55000, 58000, 52000, 60000, 57000, Group 2 = 72000, 75000, 68000, 80000, 71000, Group 3 = 65000, 63000, 67000, 64000, 66000 and Group 4 = 45000, 48000, 42000, 50000, 47000 as the stated inputs, the result is F-Statistic = 175.3471, df Between = 4 and df Within = 20. Each value corresponds to the declared output fields.

Common Use Cases

  • Test if multiple group means differ significantly
  • Run a one-way ANOVA for statistics class
  • Compare means across 3+ experimental groups