|
|
| Line 1: |
Line 1: |
| In [[statistics]], '''Dixon's ''Q'' test''', or simply the '''''Q'' test''',<!--, named after [[?????? Dixon]],--> 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:
| | My name is Genie (49 years old) and my hobbies are Gongoozling and Shortwave listening.<br><br>my web-site: Fifa 15 coin generator ([http://3rascals.net/guestbook/index.php site web]) |
| | |
| : <math> Q = \frac{\text{gap}}{\text{range}} </math>
| |
| | |
| Where ''gap'' is the [[absolute difference]] between the outlier in question and the closest number to it. If ''Q'' > ''Q''<sub>table</sub>, where ''Q''<sub>table</sub> is a reference value corresponding to the sample size and confidence level, then reject the questionable point.
| |
| | |
| ==Example==
| |
| Consider the data set:
| |
| :<math>0.189,\ 0.167,\ 0.187,\ 0.183,\ 0.186,\ 0.182,\ 0.181,\ 0.184,\ 0.181,\ 0.177 \,</math>
| |
| | |
| Now rearrange in increasing order:
| |
| | |
| :<math>0.167,\ 0.177,\ 0.181,\ 0.181,\ 0.182,\ 0.183,\ 0.184,\ 0.186,\ 0.187,\ 0.189 \, </math>
| |
| | |
| We hypothesize 0.167 is an outlier. Calculate ''Q'':
| |
| | |
| :<math>Q=\frac{\text{gap}}{\text{range}} = \frac{0.177-0.167}{0.189-0.167}=0.455.</math>
| |
| | |
| With 10 observations and at 90% [[confidence interval|confidence]], ''Q'' = 0.455 > 0.412 = ''Q''<sub>table</sub>, so we conclude 0.167 is an outlier. However, at 95% confidence, ''Q'' = 0.455 < 0.466 = ''Q''<sub>table</sub> 0.167 is not considered an outlier. This means that for this example we can be 90% sure that 0.167 is an outlier, but we cannot be 95% sure.
| |
| | |
| ==Table==
| |
| This table summarizes the limit values of the test.
| |
| | |
| {|
| |
| | |
| | |
| | |
| | |
| | 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>
| |
| |-----
| |
| | style="vertical-align: top;" | Q<sub>99%</sub>:<br>
| |
| | style="vertical-align: top; text-align: center;" | 0.994<br>
| |
| | style="vertical-align: top; text-align: center;" | 0.926<br>
| |
| | style="vertical-align: top; text-align: center;" | 0.821<br>
| |
| | style="vertical-align: top; text-align: center;" | 0.740<br>
| |
| | style="vertical-align: top; text-align: center;" | 0.680<br>
| |
| | style="vertical-align: top; text-align: center;" | 0.634<br>
| |
| | style="vertical-align: top; text-align: center;" | 0.598<br>
| |
| | style="vertical-align: top; text-align: center;" | 0.568<br>
| |
| |}
| |
| | |
| ==See also==
| |
| *[[Grubbs' test for outliers]]
| |
| | |
| ==References==
| |
| *R. B. Dean and W. J. Dixon (1951) "Simplified Statistics for Small Numbers of Observations". Anal. Chem., 1951, 23 (4), 636–638. [http://pubs.acs.org/doi/abs/10.1021/ac60052a025 Abstract] [http://depa.fquim.unam.mx/amyd/archivero/ac1951_23_636_13353.pdf Full text PDF]
| |
| * Rorabacher, D.B. (1991) "Statistical Treatment for Rejection of Deviant Values: Critical Values of Dixon Q Parameter and Related Subrange Ratios at the 95 percent Confidence Level". Anal. Chem., 63 (2), 139–146. [http://pubs.acs.org/doi/pdf/10.1021/ac00002a010 PDF] (including larger tables of limit values)
| |
| | |
| ==External links==
| |
| * [http://cran.cnr.berkeley.edu/web/packages/outliers/index.html Test for Outliers] Main page of GNU R's package 'outlier' including 'dixon.test' function.
| |
| | |
| {{DEFAULTSORT:Dixon's Q Test}}
| |
| [[Category:Statistical tests]]
| |
| [[Category:Robust statistics]]
| |
| [[Category:Statistical outliers]]
| |
My name is Genie (49 years old) and my hobbies are Gongoozling and Shortwave listening.
my web-site: Fifa 15 coin generator (site web)