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Statistics

ANOVA One Way Calculator

Run one-way ANOVA summary statistics for multiple groups.

Last validated: 2026-02-14

One-Way ANOVA Calculator compares means across three or more groups to test whether at least one group mean differs from the others. ANOVA separates total variation into between-group variation, which reflects differences among group averages, and within-group variation, which reflects scatter inside each group. The F-statistic is the ratio of these two variance estimates; a large F value suggests group means are farther apart than expected from ordinary within-group noise. The p-value indicates how surprising that F-statistic would be if all group means were equal. ANOVA identifies evidence of a difference somewhere among the groups, but follow-up comparisons are needed to determine which groups differ. Independence, variance similarity, and distribution shape affect interpretation.

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Input Pattern

Enter values in the left panel, keep units explicit, run the calculation, then copy or share the result. Invalid fields are highlighted immediately.

One-way ANOVA Input

Use semicolons between groups, commas/spaces within group.

Result

F statistic: 7.92307692

DF between/within: 2 / 6

MS between: 11.444444

MS within: 1.444444

Interpret with an F table or statistical package for p-values.

How to use this tool

  1. Enter Groups for the anova one way calculator, keeping units, dates, or text format consistent with the form labels.
  2. Confirm sample size, ordering, and distribution assumptions before relying on the calculated result.
  3. Click "Run the tool" and review One-way ANOVA Input, Result for the primary output.
  4. Check the statistical assumptions and sample context before using the result in a report or decision.

Worked Example

Auto-generated from the tool's current default or entered inputs.

Example Inputs

  • Groups: 12,14,15; 9,11,10; 13,14,12
  • Group count: 3
  • Ss between: 22.888888888888882
  • Ss within: 8.666666666666668
  • Df between: 2
  • Df within: 6
  • Ms between: 11.444444444444441
  • Ms within: 1.4444444444444446

Expected Outputs

  • Parsed groups 0 0: 12
  • Parsed groups 0 1: 14
  • Parsed groups 0 2: 15
  • Parsed groups 1 0: 9

Interpretation

Confidence and limitations

Formula References

Assumptions

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