Enter one group per line using the format Label: values. Separate values with commas, spaces, or semicolons.
This sample dataset can be loaded into the form with one click.
| Observation | Group A | Group B | Group C |
|---|---|---|---|
| 1 | 12 | 18 | 11 |
| 2 | 15 | 20 | 10 |
| 3 | 14 | 17 | 13 |
| 4 | 13 | 22 | 12 |
| 5 | 16 | 21 | 9 |
| 6 | 15 | 19 | 14 |
The Fligner Killeen test is a robust, rank based method for checking whether several groups have equal dispersion.
1. Choose a center for each group.
For group i, compute a center value ci using the median, mean, or trimmed mean.
2. Measure absolute deviations.
For every observation xij, compute:
dij = |xij - ci|
3. Rank pooled deviations.
Pool all dij values across groups, rank them, then convert each rank to a normal score using:
aij = Φ-1((1 + Rij / (N + 1)) / 2)
4. Compute the test statistic.
Let āi be the mean score for group i, and let ā be the pooled mean score. Then:
X2 = [ Σ ni(āi - ā)2 ] / sa2
where sa2 is the sample variance of all pooled scores.
5. Get the p value.
The statistic is compared with a chi square distribution using df = k - 1, where k is the number of groups.
- Enter one group per line in the grouped data box.
- Write each line as Group Label: values.
- Choose a center method. Median is usually the safest default.
- If you select trimmed mean, set the trim percentage per tail.
- Choose your significance level α and output decimals.
- Click Run Fligner Killeen Test to generate results above the form.
- Review the statistic, p value, decision, summary table, and graph.
- Export the report using the CSV or PDF buttons.
1. What does this calculator test?
It checks whether several groups appear to have equal spread. The method focuses on dispersion rather than differences in average level.
2. When should I use the Fligner Killeen test?
Use it when you want a robust variance equality test, especially when data may be skewed, heavy tailed, or affected by outliers.
3. Why is median the default center?
Median is less sensitive to extreme observations. That usually makes the variance comparison more stable when groups contain unusual values.
4. What input format should I use?
Place each group on a new line. Add a label, a colon, and the numbers. Separate values with commas, spaces, or semicolons.
5. How do I interpret the p value?
If the p value is smaller than α, you reject equal variance. If it is larger, the data do not show strong evidence of different spread.
6. Can group sizes be different?
Yes. Unequal sample sizes are allowed. Still, each group should contain at least two observations for a meaningful spread comparison.
7. Does this test require normal data?
No. That is one reason it is popular. It is designed to stay useful when normality is questionable.
8. What does the graph show?
The Plotly box plot displays each group’s spread, center, and possible outliers. It gives a quick visual check alongside the formal test result.