Dixon's Q Test Calculator
Whether that one odd measurement can be discarded.
Work out Dixon's Q Test. Whether that one odd measurement can be discarded. Written for the problem set you are stuck on.
Between 3 and 10 values, comma separated. The test only works in that range.
Q
0.842
Above the 0.71 critical value — 12 can be rejected
Q is the gap between the suspect value and its nearest neighbour, divided by the total range. Above the critical value the point can be discarded at 95% confidence. The test assumes exactly one outlier in a normally distributed set, and it applies only to the highest or lowest value. Running it repeatedly to strip several points is not what it tests — that manufactures a precision the data never had, and it is why journals ask you to report rejected points rather than quietly removing them. A failed Q test is not permission to ignore a result either. An outlier that keeps appearing is usually telling you something about the method.
How the Dixon's Q Test Calculator works
Paste three to ten measurements and this identifies the suspect value, computes Q and compares it against the 95% critical value. It also says plainly what the test does not license — repeated application to strip several points is not what it tests.
Also known as: q test calculator · outlier test calculator · how to reject an outlier · q test critical values
Frequently asked questions
How do I do a Q test?
Sort the data, take the gap between the suspect value and its nearest neighbour, and divide by the full range. If Q exceeds the critical value for your sample size, the point can be rejected at 95% confidence.
What are the critical values?
At 95% confidence: 0.970 for three points, 0.829 for four, 0.710 for five, 0.625 for six, 0.568 for seven, 0.526 for eight, 0.493 for nine and 0.466 for ten.
Can I run the test twice to remove two outliers?
No. It assumes a single outlier in a normal distribution. Applying it repeatedly manufactures precision the data does not have, which is why journals ask for rejected points to be reported rather than quietly removed.
What if I have more than ten measurements?
Use Grubbs' test, which is tabulated for larger sets and is generally preferred in modern practice. Dixon's Q is only tabulated to ten.
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