Describe › Outliers

Reed–Dixon (Dixon's Q)

Dixon's Q test flags a single extreme value in a very small sample (3 ≤ n ≤ 30) by comparing its gap from the nearest neighbour against the full range.

What is Reed–Dixon (Dixon's Q)?

Dixon designed Q for tiny samples (lab replicates, n = 3 to 7 is the classic case) where Grubbs' SD-based statistic is itself too noisy to be useful. The test compares the gap from the suspect value to its nearest neighbour against the total range — a simple geometric framing that needs almost no distributional setup.

Several Dixon variants exist (Q, Q₁₁, Q₂₁ etc.) for different sample sizes; modern implementations pick the right variant automatically. The method here picks the standard r₁₀ / r₁₁ / r₂₁ / r₂₂ ratios from Rorabacher's tables based on n.

When should I use Reed–Dixon (Dixon's Q)?

Lab-style data with 3 ≤ n ≤ 30 and a single suspect value.
When you need a defensible single-outlier test on data too small for Grubbs to be reliable.

What data does it need?

One numeric column (3 ≤ n ≤ 30) + significance level α.

What does it report?

Q statistic, the suspect value, and a p-value / critical-value verdict.

What does it assume?

Independent observations.
Data are approximately normal apart from the candidate outlier.
Exactly one outlier is suspected — masking is a problem with two.

Formula

Q = |suspect − nearest| / (max − min)   (for n ≤ 7)

How do I interpret the result?

Significant Q indicates the suspect is too far from its neighbours to be a member of the same population. As with Grubbs, document the deletion reason; never re-apply iteratively.

References

Dixon (1950). Analysis of extreme values. Annals of Mathematical Statistics 21(4).
Rorabacher (1991). Statistical treatment for rejection of deviant values. Analytical Chemistry 63(2).