Dixon's Q Test Calculator
Dixon’s Q test for a single outlier in 3 to 10 measurements — gap and range, Q statistic, the Rorabacher critical value at 90%, 95% or 99% and a keep/reject verdict.
How it works
Sort the data; Q = gap ÷ range = |x_suspect − x_nearest| ÷ (x_max − x_min), for the lowest or highest value (whichever gives the larger Q); reject if Q > Q_crit(n, confidence)
Dixon’s Q test is the quick outlier check of analytical chemistry: with only a handful of replicate measurements, it compares the gap between the suspect value and its nearest neighbour with the total range. The critical values are those tabulated by Rorabacher (1991) for the r₁₀ statistic, valid for 3 to 10 observations. Apply it once per data set — do not repeat it after removing a value — and always look for a physical cause before discarding a measurement.
Worked example
Ten replicate results with a low value of 0.167: Q = 0.455, which is below the 95% critical value 0.466 for n = 10, so 0.167 is kept.
Sources: Rorabacher (1991), Statistical treatment for rejection of deviant values, Analytical Chemistry · Dixon's Q test — Wikipedia
Frequently asked questions
How many values can Dixon’s Q test handle?
This version (r₁₀ statistic, Rorabacher table) is for 3 to 10 observations. For larger samples use Grubbs’ test or a boxplot rule.
Which confidence level should I use?
95% is standard in analytical chemistry. A 90% level rejects more readily; 99% only rejects very extreme values.
Can I run the test again after removing an outlier?
No. The test is designed for a single suspect value; repeating it inflates the chance of throwing away good data.
Dixon or Grubbs?
Both target a single outlier. Dixon uses only the gap and range and suits very small samples; Grubbs uses the mean and SD and needs approximately normal data.
Related calculators
Educational tool: check the test’s assumptions (sample size, independence, distribution) before relying on a result for a real decision.