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:

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

Where 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, Q_calculated (0.455) > Q_table (0.412), so reject it with 90% confidence. 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.

fr:Test Q gl:Proba Q it:Test Q

---

Source: Wikipedia | The above article is available under the GNU FDL. | Edit this article