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 = Q_gap/Q_range

Where "Q"_gap is the absolute difference between the outlier in question and the closest number to it. If "Q"_calculated > "Q"_table then reject the questionable point.

Table

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 at 90% confidence, Q_calculated (0.455) > Q_table (0.412). However, at 95% confidence, Q_calculated (0.455) < Q_table (0.466).
Therefore keep 0.167 at 95% confidence or reject it at 90% confidence.