Outlier Tests

Dixon Q Test

Outlier test for very small samples (n = 3..30) based on range ratios.

Statusvalidated

Version1.0.0

Minitab equivalentStat > Basic Statistics > Outlier Test (Dixon)

Description

Dixon Q is a classical outlier test that compares the gap between the suspected value and its neighbour with the data range. Depending on n it switches between variants r10 (n=3..7), r11 (8..10), r21 (11..13), and r22 (14..30); critical values come from the Rorabacher (1991) tables. Widely used in analytical chemistry (DIN 53804).

Formulas

Q (r10)

Q = \frac{x _{(n)} - x _{(n - 1)}}{x _{(n)} - x _{(1)}}

Standard variant for n = 3..7 (upper outlier)

r11

r_{11} = \frac{x _{(n)} - x _{(n - 1)}}{x _{(n)} - x _{(2)}}

Variant for n = 8..10

r22

r_{22} = \frac{x _{(n)} - x _{(n - 2)}}{x _{(n)} - x _{(3)}}

Variant for n = 14..30

Assumptions

Independent, approximately normal data
Sample size 3 ≤ n ≤ 30

Limitations

Outside n = 3..30 no tabulated values → use Grubbs or Generalized ESD
Only one outlier per call

References

Dixon, W. J. (1953), Processing data for outliers, Biometrics 9(1), 74–89
Rorabacher, D. B. (1991), Statistical treatment for rejection of deviant values, Anal. Chem. 63(2), 139–146
DIN 53804-1:2002, Statistische Auswertung von Daten — Teil 1: Stetige Merkmale