Q test

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In statistics, the Q test is used for identification and rejection of outliers. This test should be used sparingly and never more than once in a data set. To apply a Q test for bad data, arrange the data in order of increasing values and calculate Q as defined:

Q = Qgap/Qrange

Where Qgap is the absolute difference between the outlier in question and the closest number to it. If Qcalculated > Qtable then reject the questionable point.

[edit] Table

Number of values:  3
 4
 5
 6
 7
 8
 9
 10
Q90%:
 0.941
 0.765
 0.642
 0.560
 0.507
 0.468
 0.437
 0.412
Q95%:
 0.970
 0.829
 0.710
 0.625
 0.568
 0.526
 0.493
 0.466
Q99%:
 0.994
 0.926
 0.821
 0.740
 0.680
 0.634
 0.598
 0.568

[edit] Example

For the data:

0.189,0.167,0.187,0.183,0.186,0.182,0.181,0.184,0.181,0.177

Arranged in increasing order:

0.167,0.177,0.181,0.181,0.182,0.183,0.184,0.186,0.187,0.189

Outlier is 0.167. Calculate Q:

Q=\frac{\mathrm{gap}}{\mathrm{range}}=\frac{(0.177-0.167)}{(0.189-0.167)}=0.455.

With 10 observations, Qcalculated (0.455) > Qtable (0.412), so reject it with 90% confidence. However, at 95% confidence, Qcalculated (0.455) < Qtable (0.466).
Therefore keep 0.167 at 95% confidence or reject it at 90% confidence.

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