Identifying outliers in non-normally distributed data

If you're interested in handling outliers in analytical proficiency
testing read current and past IUPAC guidance on PT (see
http://www.iupac.org/objID/Article/pac7801x0145) and particularly
references 1, 4, 5, and 11 therein, for starters. 

Although one might reasonably ask whether outliers are real or not,
bitter experience says that the vast majority of them in PT are
mistakes, so it is very widely accepted in teh PT community that if
you;re going to use consensus values, you should use some form of robust
estimate. In that context, outlier rejection is a crude robustification
- but better methods exist and are recommended.

If you're looking at data which have asymmetry for good reason, do
something ordinary (like taking logs) to get the underlying distribution
near-normal before using robust stats. If the asymmetry is just because
of the outliers, maybe you have a more awkward problem. But even then,
something like an MM-estimate or (since this is univariate) pretty much
any robust estimate using a redescending influence function will help.

Steve E

Bert Gunter <gunter.berton at gene.com> 12/30/09 7:09 PM >>>

Gents:

Whole books could be -- and have been -- written on this matter.
Personally,
when scientists start asking me about criteria for "outlier" removal, it
sends shivers up my spine and I break into a cold, clammy sweat. What is
an
"outlier" anyway?

Statisticians (of which I'm one) have promulgated the deception that
"outliers" can be defined by purely statistical criteria, and that they
can
then be "removed" from the analysis. That is a lie. The only acceptable
scientific definition of an outlier that can be legitimately removed is
of
data that can be confirmed to have been corrupted in some way, for
example,
as Jerry describes below. All purely statistical criteria are arbitrary
in
some way and therefore potentially dangerous.

The real question is: what is the scientific purpose of the analysis? --
how
are the results to be used? There are a variety of effective so-called
robust/resistant statistical procedures (e.g. see the R packages robust,
robustbase, and rrcov, among many others) that might then be useful to
accomplish the purpose even in the presence of "unusual values"
("outliers"
is a term I now avoid due to its 'political' implications). This is
almost
always a wiser course of action (there are even theoretical
justifications
for this) than using statistical criteria to "identify" and remove the
unusual values.

However, use of such tools involves subtle issues that probably cannot
be
properly aired in a forum such as this. I therefore think you would do
well
to get a competent local statistician to consult with on these matters.
Yes,
I do believe that scientists often require advanced statistical tools
that
go beyond their usual training to properly analyze even what appear to
be
"straightforward" scientific data. It is a conundrum I cannot resolve,
but
that does not mean I can deny it. 

Finally, a word of wisdom from a long-ago engineering colleague:
"Whenever I
see an outlier, I'm never sure whether to throw it away or patent it." 

 
Cheers,

Bert Gunter
Genentech Nonclinical Statistics





-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
On
Behalf Of Jerry Floren
Sent: Wednesday, December 30, 2009 9:47 AM
To: r-help at r-project.org
Subject: Re: [R] Identifying outliers in non-normally distributed data


Greetings:

I could also use guidance on this topic. I provide manure sample
proficiency
sets to agricultural labs in the United States and Canada. There are
about
65 labs in the program.

My data sets are much smaller and typically non-symmetrical with obvious
outliers. Usually, there are 30 to 60 sets of data, each with triple
replicates (90 to 180 observations).

There are definitely outliers caused by the following: reporting in the
wrong units, sending in the wrong spreadsheet, entering data in the
wrong
row, misplacing decimal points, calculation errors, etc. For each
analysis,
it is common that two to three labs make these types of errors. 

Since there are replicates, errors like misplaced decimal points are
more
obvious. However, most of the outlier errors are repeated for all three
replicates. 

I use the median and Median Absolute Deviation (MAD, constant = 1) to
flag
labs for accuracy. Labs where the average of their three reps deviates
more
than 2.5 MAD values from the median are flagged for accuracy. With this
method, it is not necessary to identify the outliers.

A collegue suggested running the data twice. On the first run, outliers
more
than 4.0 MAD units from the median are removed. On the second run,
values
exceeding 2.9 times the MAD are flagged for accuracy. I tried this in R
with
a normally distributed data set of 100,000, and the 4.0 MAD values were
nearly identical to the outliers identified with boxplot.

With my data set, the flags do not change very much if the data is run
one
time with the flags set at 2.5 MAD units compared to running the data
twice
and removing the 4.0 MAD outliers and flagging the second set at 2.9 MAD
units. Using either one of these methods might work for you, but I am
not
sure of the statistical value of these methods.

Yours,

Jerry Floren



Brian G. Peterson wrote:

John wrote:

Hello,

I've been searching for a method for identify outliers for quite some
time now. The complication is that I cannot assume that my data is
normally distributed nor symmetrical (i.e. some distributions might
have one longer tail) so I have not been able to find any good tests.
The Walsh's Test (http://www.statistics4u.info/
fundsta...liertest.html#), as I understand assumes that the data is
symmetrical for example.

Also, while I've found some interesting articles:
http://tinyurl.com/yc7w4oq ("Missing Values, Outliers, Robust
Statistics & Non-parametric Methods")
I don't really know what to use.

Any ideas? Any R packages available for this? Thanks!

PS. My data has 1000's of observations..

Take a look at package 'robustbase', it provides most of the standard
robust 
measures and calculations.

While you didn't say what kind of data you're trying to identify

outliers

in, 
if it is time series data the function Return.clean in
PerformanceAnalytics may 
be useful.

Regards,

   - Brian


-- 
Brian G. Peterson
http://braverock.com/brian/
Ph: 773-459-4973
IM: bgpbraverock

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