Q test
Encyclopedia
In statistics
, Dixon's Q test, or simply the Q test, is used for identification and rejection of outlier
s. Per Dean and Dixon, and others, 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:
Where gap is the absolute difference
between the outlier in question and the closest number to it. If Qcalculated > Qtable then reject the questionable point.
Arranged in increasing order:
Outlier is 0.167. Calculate Q:
With 10 observations, Qcalculated (0.455) > Qtable (0.412), so reject it with 90% confidence. However, at 95% confidence, Qcalculated (0.455) < Qtable (0.466).
Therefore keep 0.167 at 95% confidence or reject it at 90% confidence.
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, Dixon's Q test, or simply the Q test, is used for identification and rejection of outlier
Outlier
In statistics, an outlier is an observation that is numerically distant from the rest of the data. Grubbs defined an outlier as: An outlying observation, or outlier, is one that appears to deviate markedly from other members of the sample in which it occurs....
s. Per Dean and Dixon, and others, 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:
Where gap is the absolute difference
Absolute difference
The absolute difference of two real numbers x, y is given by |x − y|, the absolute value of their difference. It describes the distance on the real line between the points corresponding to x and y...
between the outlier in question and the closest number to it. If Qcalculated > Qtable then reject the questionable point.
Example
For the data:Arranged in increasing order:
Outlier is 0.167. Calculate Q:
With 10 observations, Qcalculated (0.455) > Qtable (0.412), so reject it with 90% confidence. However, at 95% confidence, Qcalculated (0.455) < Qtable (0.466).
Therefore keep 0.167 at 95% confidence or reject it at 90% confidence.
Table
This table summarize the limit values of the test.| 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 |
| Q99%: |
0.994 |
0.926 |
0.821 |
0.740 |
0.680 |
0.634 |
0.598 |
0.568 |
External links
- Test for Outliers Main page of GNU R's package 'outlier' including 'dixon.test' function.