Q test
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To apply a Q test for bad data, arrange the data in order of increasing values and calculate Q as defined:
- <math>Q=\frac{gap}{range}<math>
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 |
0.560 |
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:
- <math>0.189, 0.169, 0.187, 0.183, 0.186, 0.182, 0.181, 0.184, 0.181, 0.177<math>
Arranged in increasing order:
- <math>0.169, 0.177, 0.181, 0.181, 0.182, 0.183, 0.184, 0.186, 0.187, 0.189<math>
Outlier is 0.169. Calculate Q:
- <math>Q=\frac{gap}{range}=\frac{(0.177-0.169)}{(0.189-0.169)}=0.400<math>
With 10 observations at 90% confidence, Qcalculated < Qtable. Therefore keep 0.169 at 90% confidence.
See also: List of statistical topics