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Dixon's Q test : ウィキペディア英語版
Dixon's Q test

In statistics, Dixon's ''Q'' test, or simply the ''Q'' test, is used for identification and rejection of outliers. This assumes normal distribution and 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:
: Q = \frac}
Where ''gap'' is the absolute difference between the outlier in question and the closest number to it. If ''Q'' > ''Q''table, where ''Q''table is a reference value corresponding to the sample size and confidence level, then reject the questionable point. Note that only one point may be rejected from a data set using a Q test.
==Example==
Consider the data set:
:0.189,\ 0.167,\ 0.187,\ 0.183,\ 0.186,\ 0.182,\ 0.181,\ 0.184,\ 0.181,\ 0.177 \,
Now rearrange in increasing order:
:0.167,\ 0.177,\ 0.181,\ 0.181,\ 0.182,\ 0.183,\ 0.184,\ 0.186,\ 0.187,\ 0.189 \,
We hypothesize that 0.167 is an outlier. Calculate ''Q'':
:Q=\frac} = \frac=0.455.
With 10 observations and at 90% confidence, ''Q'' = 0.455 > 0.412 = ''Q''table, so we conclude 0.167 is an outlier. However, at 95% confidence, ''Q'' = 0.455 < 0.466 = ''Q''table 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.
McBane〔Halpern, Arthur M. "Experimental physical chemistry : a laboratory textbook." 3rd ed. / Arthur M. Halpern , George C. McBane. New York : W. H. Freeman, c2006 (Library of Congress )〕 notes: Dixon provided related tests intended to search for more than one outlier, but they are much less frequently used than the r10 or Q version that is intended to eliminate a single outlier.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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