Calculator
Example Data Table
| Example | Values | End checked | Alpha | Expected note |
|---|---|---|---|---|
| Lab replicate set | 10.08, 10.11, 10.09, 10.10, 10.43 | High end | 0.05 | Large high-end gap may be flagged. |
| Low suspect set | 4.12, 4.45, 4.48, 4.50, 4.53 | Low end | 0.10 | Lowest value is compared with its neighbor. |
| Balanced set | 7.21, 7.24, 7.25, 7.27, 7.29 | Both ends | 0.05 | No strong end gap is expected. |
Formula Used
Sort the observations from smallest to largest.
Range: xmax − xmin
Lower-end Q: Q = (x2 − x1) / (xmax − xmin)
Upper-end Q: Q = (xn − x(n−1)) / (xmax − xmin)
If Q calculated is greater than Q critical, the selected end value is flagged as a possible outlier.
This calculator uses a common Dixon Q critical table for sample sizes 3 through 30. A custom critical value can override the table.
How to Use This Calculator
Enter at least 3 and no more than 30 numeric observations.
Choose whether to test the lowest value, highest value, or both ends.
Select the alpha level that matches your reporting rule.
Leave the custom critical field blank unless your method uses another table.
Press Calculate to review the decision above the form.
Use the CSV or PDF button to export the same calculation.
About the Dixon Q Test Calculator
The Dixon Q test is a simple method for checking one doubtful value in a small data set. It is often used in chemistry, quality control, and laboratory reporting. This calculator helps you sort the data, locate the widest end gap, and compare the Q statistic with a selected critical value.
Why the Test Matters
Small samples can be sensitive to one unusual reading. A single bad result may change the mean, range, and final decision. The test gives a structured screening step before you remove a value. It should support judgment, not replace it.
How the Calculator Works
Enter all observations as numbers. You may separate them with commas, spaces, or line breaks. The tool sorts the data from low to high. It checks the low end, the high end, or both ends. The selected confidence level controls the critical value. If the calculated Q is greater than the critical Q, the suspect value is flagged.
Good Statistical Practice
Use this test only when one value looks doubtful. Do not repeat the test until the data look clean. That practice can remove valid observations. Also check the experiment notes. A known instrument fault, sample mix-up, or recording error gives stronger evidence than any test alone.
Interpreting Results
A flagged value is not automatically wrong. It means the end gap is large compared with the full range. Review the source data before excluding it. Keep a record of the raw values, sorted values, Q statistic, critical value, and confidence level. This makes the decision easier to audit later.
Limitations
Dixon Q is designed for small samples. It assumes the remaining observations are from one population. It also focuses on an end value only. Values in the middle are not tested. For larger samples, consider Grubbs, Rosner, or robust methods. Always match the method to the study design.
Reporting Tips
Report the decision in plain language. State whether the minimum value, maximum value, or larger end gap was tested. Mention the sample size and chosen alpha level. When exporting results, keep the CSV with the worksheet. Save the PDF with the final report. Clear records reduce later confusion. They also support calm peer review.
FAQs
What is the Dixon Q test?
It is a statistical screening test for one suspected outlier at the low or high end of a small sorted data set.
What sample size can I use?
This calculator supports 3 to 30 values because the included critical table covers that range.
Can I test both ends?
Yes. Choose both ends to calculate lower and upper Q values. Review each decision separately and document the reason for testing.
When is a value rejected?
A suspect value is flagged when the calculated Q value is greater than the selected critical Q value.
Should I remove every flagged value?
No. A flag is evidence for review. Check notes, instruments, and method rules before removing any observation.
What does alpha mean?
Alpha is the chosen significance level. Smaller alpha values require stronger evidence before a value is flagged.
Why is sorting needed?
The Dixon Q formula compares an end gap with the full range. Sorting identifies the lowest and highest candidates.
Can I use my own critical value?
Yes. Enter a custom critical Q value when your laboratory method, textbook, or protocol uses a different table.