Grubbs's test for outlier detection
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Grubbs's test for outlier detection
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thornahawk
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Joined: 27 Mar 2005
Posts: 569
Posted: 27 Nov 2009 08:46:26 pm    Post subject:
Grubbs's test is a quick method for testing if a certain entry in a small data set is an outlier; i.e. this test answers the question "is this entry very much different from its companions?"

The test is relatively simple to perform compared to an older outlier test, Dixon's Q test, and is now the test recommended by ISO.

Here is a short routine for performing Grubbs's test on a TI-84+SE calculator:


Code:
PROGRAM:GRUBBS
Input "DATA:",L₁
Prompt I
Input "CONFIDENCE",P
abs(L₁(I)–mean(L₁))/stdDev(L₁)→Q
dim(L₁)→N
invT(1+.5(P–1)/N,N–2)→C
(N–1)(C/√(C²+N–2))/√(N)→C
Q≤C


An output of 0 signifies L₁(I) is an outlier at the confidence level P. C is the Grubbs critical value, and Q is the test statistic. A data set to test the program can be found here.

A (slightly longer) version of this program can be done for the TI-83+ and other calculators without the invT( function, which I will post on request.

thornahawk
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Graphmastur


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Joined: 25 Mar 2009
Posts: 360
Posted: 27 Nov 2009 09:39:35 pm    Post subject:
Oh, so it's like figuring out which point is bad data for a test. Sounds interesting.
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Galandros


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Joined: 29 Aug 2008
Posts: 565
Posted: 28 Nov 2009 03:45:51 am    Post subject:
Nice program. Maybe I can use in physics experiments soon...
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