ClarityHow to use this tool
- Enter sample a, sample b, sample c, significance level.
- Select Calculate to view the result.
- Check the method and assumptions below before using the result.
Input reference and sample values
Use the units and choices shown for each field. Sample values are provided for practice, not as recommendations.
| Input | Format and units | Sample |
|---|---|---|
| Sample A | Keep the structure and separators shown in the sample. Line breaks are retained in this input. | 8, 10, 9, 12, 11 |
| Sample B | Keep the structure and separators shown in the sample. Line breaks are retained in this input. | 5, 7, 6, 8, 9 |
| Sample C | Keep the structure and separators shown in the sample. Line breaks are retained in this input. | 12, 14, 13, 16, 15 |
| Significance level | Numeric value. Minimum: 0.0001. Maximum: 0.2. | 0.05 |
Result for these sample inputs
0.0000560929223 probability
- Test statistic
- 24.6666667
- Degrees of freedom
- 2 and 12
- Decision at chosen alpha
- Reject the null hypothesis
- Between-group SS
- 123.333333
- Within-group SS
- 30
- Eta squared
- 0.804347826
The p-value is not the probability that the null hypothesis is true. Choose the hypothesis and significance level before inspecting the result; statistical significance does not measure practical importance.
Select Try the example in the form to load these values and calculate them again. This replaces the current form inputs. Compare the result with the method and worked explanation below.
The method, explained
F = [between-group sum of squares/(k−1)] / [within-group sum of squares/(N−k)]. This page uses three groups, so numerator df is 2.
Using sample a = 8, 10, 9, 12, 11, sample b = 5, 7, 6, 8, 9, sample c = 12, 14, 13, 16, 15, significance level = 0.05, the result is 0.0000560929223 probability. Change these example inputs to match your task; use the method above to check each step.
What to keep in mind
Exactly three independent groups with approximately normal errors and equal population variances. A significant omnibus test does not identify which groups differ. A descriptive or probability calculation under the stated assumptions. Check the sample design and model before interpreting results.
Reference: NIST: statistical methods handbook
Common questions
Does a small p-value tell me which group is different?
No. The omnibus null hypothesis is that all three population means are equal. Identifying specific differences requires planned contrasts or suitable post-hoc comparisons with multiplicity control.
Can the three groups contain different numbers of values?
Yes. Each group needs at least two observations. The calculation weights group means by their actual sample counts; the equal-variance assumption still applies.
Methodology maintained by ClarityKit. How these tools are built and checked.