dixon test calculator

What is the Dixon Q test?

The Dixon Q test is a statistical method for detecting one possible outlier in a small dataset. It compares the “gap” between the suspicious extreme value and its nearest neighbor against the full range of the data. If the ratio is large enough, that value may be flagged as an outlier.

This test is popular in lab settings where sample sizes are often small and an obviously unusual measurement may come from contamination, instrument drift, or recording error.

When should you use this calculator?

• You have a small sample (usually between 3 and 30 observations).
• You suspect at most one extreme value is questionable.
• Your data are roughly from a single, approximately normal process.
• You need a quick screening check before deeper analysis.

When not to use it

• If your sample is large, use other robust methods instead.
• If you suspect multiple outliers, Dixon Q is not ideal as a one-shot test.
• If your data are strongly skewed or non-normal, interpret with caution.

How the Dixon Q statistic is computed

For sorted data x1 ≤ x2 ≤ ... ≤ xn, the common form used here is:

• Low-end test: Q_low = (x2 - x1) / (xn - x1)
• High-end test: Q_high = (xn - x(n-1)) / (xn - x1)

The calculator compares your computed Q to a critical value from a standard Dixon Q table based on sample size and chosen confidence level. If Q_calculated ≥ Q_critical, the suspected point is flagged.

How to interpret your result

If the value is flagged

This means the extreme point is statistically inconsistent with the rest of the sample at your chosen confidence level. It does not automatically prove an error. You should still check:

• measurement notes,
• instrument logs or calibration,
• sample handling steps, and
• scientific plausibility.

If the value is not flagged

The evidence is not strong enough to reject it as an outlier under this test. Keep it in the data unless there is a documented procedural reason to remove it.

Practical example

Suppose your six measurements are: 10.2, 10.3, 10.4, 10.4, 10.5, 11.7.

The highest value (11.7) looks suspicious. The test checks whether the high-end gap is large relative to the total spread. At 95% confidence, this dataset is often flagged, indicating 11.7 may be an outlier candidate.

Best practices before removing any value

• Document the reason for exclusion.
• Report analyses with and without the point when possible.
• Avoid repeatedly testing/removing values until data “look nice.”
• Use domain knowledge, not just one statistical threshold.

Quick FAQ

Can this test detect outliers in the middle of the dataset?

No. Dixon Q is designed for extreme low or high values, not interior points.

Does a 99% level mean better results?

It is stricter. You are less likely to flag a value as an outlier, which reduces false positives but may miss real issues.

Can I run the test repeatedly?

Repeated removal and retesting can inflate error rates. If you suspect multiple outliers, use a method designed for that scenario.