Q test
497770
163723473
2007-10-11T03:00:07Z
74.117.117.155
/* Example */
In [[statistics]], the '''''Q'' test''' is used for identification and rejection of [[outlier]]s. 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<sub>gap</sub>/Q<sub>range</sub>
Where ''Q''<sub>gap</sub> is the absolute difference between the outlier in question and the closest number to it. If ''Q''<sub>calculated</sub> > ''Q''<sub>table</sub> then reject the questionable point.
==Table==
{|
|-----
| style="vertical-align: top;" | Number of values:
| style="vertical-align: top; text-align: center;" | 3<br>
| style="vertical-align: top; text-align: center;" | 4<br>
| style="vertical-align: top; text-align: center;" | 5<br>
| style="vertical-align: top; text-align: center;" | 6<br>
| style="vertical-align: top; text-align: center;" | 7<br>
| style="vertical-align: top; text-align: center;" | 8<br>
| style="vertical-align: top; text-align: center;" | 9<br>
| style="vertical-align: top; text-align: center;" | 10<br>
|-----
| style="vertical-align: top;" | Q<sub>90%</sub>:<br>
| style="vertical-align: top; text-align: center;" | 0.941<br>
| style="vertical-align: top; text-align: center;" | 0.765<br>
| style="vertical-align: top; text-align: center;" | 0.642<br>
| style="vertical-align: top; text-align: center;" | 0.560<br>
| style="vertical-align: top; text-align: center;" | 0.507<br>
| style="vertical-align: top; text-align: center;" | 0.468<br>
| style="vertical-align: top; text-align: center;" | 0.437<br>
| style="vertical-align: top; text-align: center;" | 0.412<br>
|-----
| style="vertical-align: top;" | Q<sub>95%</sub>:<br>
| style="vertical-align: top; text-align: center;" | 0.970<br>
| style="vertical-align: top; text-align: center;" | 0.829<br>
| style="vertical-align: top; text-align: center;" | 0.710<br>
| style="vertical-align: top; text-align: center;" | 0.625<br>
| style="vertical-align: top; text-align: center;" | 0.568<br>
| style="vertical-align: top; text-align: center;" | 0.526<br>
| style="vertical-align: top; text-align: center;" | 0.493<br>
| style="vertical-align: top; text-align: center;" | 0.466<br>
|}
==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, Q<sub>calculated</sub> < Q<sub>table</sub>. Therefore keep 0.169 at 90% confidence.
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[[Category:Statistical tests]]
[[gl:Proba Q]]
[[it:Test Q]]