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Brett Shoelson (view profile)


15 Sep 2003 (Updated )

For input vector A, returns a vector B with outliers removed.

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For input vector A, returns a vector B with outliers (at the significance level alpha) removed. Also, optional output argument idx returns the indices in A of outlier values. Optional output argument outliers returns the outlying values in A.
ALPHA is the significance level for determination of outliers. If not provided, alpha defaults to 0.05.
REP is an optional argument that forces the replacement of removed elements with NaNs to preserve the length of a. (Thanks for the suggestion, Urs.)
This is an iterative implementation of the Grubbs Test that tests one value at a time. In any given iteration, the tested value is either the highest value, or the lowest, and is the value that is furthest from the sample mean. Infinite elements are discarded if rep is 0, or replaced with NaNs if rep is 1 (thanks again, Urs).
Appropriate application of the test requires that data can be reasonably approximated by a normal distribution. For reference, see:
1) "Procedures for Detecting Outlying Observations in Samples," by F.E. Grubbs; Technometrics, 11-1:1--21; Feb., 1969, and
2) _Outliers in Statistical Data_, by V. Barnett and T. Lewis; Wiley Series in Probability and Mathematical Statistics;
John Wiley & Sons; Chichester, 1994.

A good online discussion of the test is also given in NIST's Engineering Statistics Handbook:
[B,idx,outliers] = deleteoutliers([1.1 1.3 0.9 1.2 -6.4 1.2 0.94 4.2 1.3 1.0 6.8 1.3 1.2], 0.05)
B = 1.1000 1.3000 0.9000 1.2000 1.2000 0.9400 1.3000 1.0000 1.3000 1.2000
idx = 5 8 11
outliers = -6.4000 4.2000 6.8000
B = deleteoutliers([1.1 1.3 0.9 1.2 -6.4 1.2 0.94 4.2 1.3 1.0 6.8 1.3 1.2 Inf 1.2 -Inf 1.1], 0.05, 1)
B = 1.1000 1.3000 0.9000 1.2000 NaN 1.2000 0.9400 NaN 1.3000 1.0000 NaN 1.3000 1.2000 NaN 1.2000 NaN 1.1000
Written by Brett Shoelson, Ph.D.
Modified 9/23/03 to address suggestions by Urs Schwartz.
Modified 10/08/03 to avoid errors caused by duplicate "maxvals."
(Thanks to Valeri Makarov for modification suggestion.)


This file inspired Delete Outliers2.

Required Products Statistics and Machine Learning Toolbox
MATLAB release MATLAB 6.5 (R13)
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Comments and Ratings (18)
24 Mar 2015 Anna Karlsson


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24 Mar 2015 Anna Karlsson

This maybe is clear to everyone else, but what should you have for input on REP if you want to use it?

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23 Jun 2014 Muhammad khan

Nice work....

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06 May 2014 Brett Shoelson

Brett Shoelson (view profile)

This is designed to work on a vector of inputs. If you can cast your 3D points as a vector in some meaningful fashion--as distances from a central point, perhaps?--then it would work.

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06 May 2014 Hussein

Can this work on 3d points?

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07 Feb 2014 Nathan Orloff  
02 Oct 2012 Brett Baker

Thanks Brett! Works great. Love the improvements made to it as well. You saved me a chunk of time! I appreciate the sharing!

27 Jan 2012 Reza Farrahi Moghaddam  
13 Jun 2011 Mehdi Moghaddam

unfortunately doesnt work for my data which has a trend in it and I dont want to remove it from my data

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01 Oct 2009 Marcin

Marcin (view profile)

Very good. I compared your results with the one from:
on my data and got the same results. Good work!

19 Jan 2009 Hanna Modin

Thank you for a nice implementation of Grubbs test! If I might suggest an improvement that would be to make the test work with other than vectors, e.g. to remove outliers from each row in a matrix separately

16 May 2007 dali kaafar  
09 Oct 2005 s b

very useful!!!!

16 Sep 2005 James J. Cai  
07 Dec 2004 Vadim Moldavsky


25 Oct 2004 Torsten Staab

Nice job!

25 Nov 2003 Effendi Widjaja  
22 Sep 2003 Urs Schwarz (us)

very nice, brett. a few remarks re OUTPUT: there should be an option to replace outlieres with nans (to keep i/o vecs the same length); re INPUT: the option <ul> shows up in the help but doesn't seem to have a meaning (yet?); re PROCESSING: 1) nans are cut away (why? we don't know what a nan is in any context), 2) +-infs, on the other hand, are not (?).

24 Sep 2003

Addresses comments of Urs Schwartz... now provides optional input argument form maintaining vector length; also now discards Inf's.

21 Mar 2011 1.1

Fixed a typo in the description.

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