Dixon Q Test Calculator
Use this tool to test whether the smallest or largest value in a small sample is a statistical outlier.
What is the Dixon Outlier Test?
The Dixon Q test is a quick statistical method for checking whether one extreme value in a small dataset is likely an outlier. It is commonly used in chemistry, lab quality control, and small experimental datasets where you only have a handful of observations.
Unlike broad outlier detection tools, Dixon's test is designed for small samples (typically 3 to 30 points) and focuses on the lowest or highest value. It compares the gap between the suspected outlier and its nearest neighbor against the total range of the data.
How this Dixon Q calculator works
Step 1: Sort the sample
Your input values are sorted from smallest to largest. Let the sorted list be: x1 ≤ x2 ≤ ... ≤ xn.
Step 2: Compute test statistics
The calculator computes:
- Qlow = (x2 - x1) / (xn - x1) for a possible low-end outlier.
- Qhigh = (xn - x(n-1)) / (xn - x1) for a possible high-end outlier.
Step 3: Compare against a critical value
Based on your sample size and confidence level (90%, 95%, or 99%), the tool looks up a critical value Qcrit. If Qcalc ≥ Qcrit, the tested extreme value is flagged as an outlier.
How to use the calculator
- Enter numbers separated by commas, spaces, semicolons, or line breaks.
- Choose a confidence level (95% is the usual default).
- Select auto mode or choose whether to test the highest or lowest value.
- Click Calculate Dixon Test to get the decision and full intermediate values.
Interpreting your result
If a value is flagged, it means that under Dixon's assumptions, the extreme value is statistically inconsistent with the rest of the sample at your chosen confidence level. This is evidence to investigate the point, not automatic permission to delete it.
Always combine statistical output with domain context. A flagged value could indicate a recording error, contamination, instrument drift, or a real but rare event that should remain in analysis.
Assumptions and limitations
- Best for small samples (n between 3 and 30).
- Assumes roughly normal measurement behavior.
- Designed to evaluate one suspected outlier at an extreme.
- Not ideal for large datasets or multiple outliers.
When to use alternatives
For larger datasets or repeated outlier checks, consider robust approaches such as modified Z-score, IQR-based screening, Grubbs' test, or model-based diagnostics. Dixon's test is excellent for quick small-sample checks, but not a complete outlier strategy.
Practical example
Suppose your readings are 2.1, 2.2, 2.3, 2.4, and 4.9. The high-end gap is large relative to the full range, so the highest value will likely exceed Qcrit at 95% confidence and be flagged. Use the Load Example button to try this instantly.