Q test

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=\frac{\mathrm{gap}}{\mathrm{range}}.

If Qcalculated > Qtable then reject the questionable point.

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

Example

For the data:

0.189,0.169,0.187,0.183,0.186,0.182,0.181,0.184,0.181,0.177

Arranged in increasing order:

0.169,0.177,0.181,0.181,0.182,0.183,0.184,0.186,0.187,0.189

Outlier is 0.169. Calculate Q:

Q=\frac{\mathrm{gap}}{\mathrm{range}}=\frac{(0.177-0.169)}{(0.189-0.169)}=0.400.

With 10 observations at 90% confidence, Qcalculated < Qtable. Therefore keep 0.169 at 90% confidence.