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 = 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.

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.

Proba Q Test Q