# 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.

## Table

 Number of values: 3 4 5 6 7 8 9 10 Q90%: 0.941 0.765 0.642 0.56 0.507 0.468 0.437 0.412 Q95%: 0.97 0.829 0.71 0.625 0.568 0.526 0.493 0.466

## Example

For the data:

${\displaystyle 0.189,0.169,0.187,0.183,0.186,0.182,0.181,0.184,0.181,0.177}$

Arranged in increasing order:

${\displaystyle 0.169,0.177,0.181,0.181,0.182,0.183,0.184,0.186,0.187,0.189}$

Outlier is 0.169. Calculate Q:

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

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