Q‑Test (Dixon’s Q Test) Calculator
Enter your sample data (comma‑separated numbers) and select whether to test the lowest or the highest value as a potential outlier.
* Note: The test is typically used for small samples (3 ≤ n ≤ 30).
Step 1: Enter Your Data
e.g., 4.2, 4.5, 4.7, 4.8, 7.2
Select Candidate Outlier:
How It Works
The Q‑statistic is calculated as:
- Lowest value test: \( Q = \frac{x_2 – x_1}{x_n – x_1} \)
- Highest value test: \( Q = \frac{x_n – x_{n-1}}{x_n – x_1} \)
where \(x_1\) is the smallest, \(x_2\) is the second smallest, \(x_{n-1}\) is the second largest, and \(x_n\) is the largest value in the sorted sample.
Critical Values for the Q-Test of a Single Outlier (Q10)
The following table provides critical values for Q(α, n), where α is the probability of incorrectly rejecting the suspected outlier and n is the number of samples in the data set.
| n ⇓ / α ⇒ | 0.10 | 0.05 | 0.04 | 0.02 | 0.01 |
|---|---|---|---|---|---|
| 3 | 0.941 | 0.970 | 0.976 | 0.988 | 0.994 |
| 4 | 0.765 | 0.829 | 0.846 | 0.889 | 0.926 |
| 5 | 0.642 | 0.710 | 0.729 | 0.780 | 0.821 |
| 6 | 0.560 | 0.625 | 0.644 | 0.698 | 0.740 |
| 7 | 0.507 | 0.568 | 0.586 | 0.637 | 0.680 |
| 8 | 0.468 | 0.526 | 0.543 | 0.590 | 0.634 |
| 9 | 0.437 | 0.493 | 0.510 | 0.555 | 0.598 |
| 10 | 0.412 | 0.466 | 0.483 | 0.527 | 0.568 |