Q test
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In statistics, the Q test is used for identification 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:
- <math>Q=\frac{\mathrm{gap}}{\mathrm{range}}.</math>
If Qcalculated > Qtable then reject the questionable point.
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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 |
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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{\mathrm{gap}}{\mathrm{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.it:test Q