Cochran Q test

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In statistics, the Q test a nonparametric statistical test 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

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, Q_calculated < Q_table. Therefore keep 0.169 at 90% confidence.

See also

• Cochran's C test