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I have a couple of outliers in my data and I was wanting to exclude them to see if this changes the results. In you opinion, what is the maximum number of outliers one should restrict themselves to?

Thanks! enter image description here

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  • $\begingroup$ Your graph is mangled here: the numeric labels on the y axis are missing and the legend entries are not distinct. (That may be a way of hiding unpublished data, but it doesn't help us to give you good advice.) The cryptic legend doesn't affect your question, but not knowing what scale you are working on limits the scope for useful answers. The data as shown exhibit moderate left or negative skew; this may make sense, and the apparent outliers just be consequences of that. Alternatively, it may be that you have over-transformed, e.g. used logarithms where the data don't merit that. $\endgroup$ – Nick Cox Jan 15 '15 at 16:38
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There is no maximum or minimum. Outliers should be removed if they are bad data or if there are other substantive reasons for removing them. If there are no substantive reasons, then I suggest using methods that are robust to outliers. I would not remove outliers just because they are a bit far from other points.

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    $\begingroup$ Agreed. Note tha Box, Hunter & Hunter: "Statistics for Experimenters" says that in the chemical industry, outliers often have resulted in new patents! Depending on circumstances, outliers could be the single most important piece of information in your data! Removing them should never be taken easy. $\endgroup$ – kjetil b halvorsen Jan 15 '15 at 12:33
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    $\begingroup$ Also in astrophysics. "Let's just delete the black holes and neutron stars from the data" :-). $\endgroup$ – Peter Flom - Reinstate Monica Jan 15 '15 at 12:34
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    $\begingroup$ Peter Flom: Yes! And among human beings, if there were no outliers among us, we would still be living in the stone age! $\endgroup$ – kjetil b halvorsen Jan 15 '15 at 12:40
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    $\begingroup$ In this example, note that all 7 of the labeled outliers have low values, while none have high values. That might represent problems with measurement, or it might mean something very interesting. Either way, just removing outliers here without considering what led to the low values would seem inadvisable. $\endgroup$ – EdM Jan 15 '15 at 15:24
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    $\begingroup$ I interpret the question a little differently. It does not propose removing outliers from the analysis, which is what this answer implicitly assumes. It only asks how to conduct a sensitivity analysis "to see if this changes the results." Although the advice given here about whether to remove outliers is fine--and clearly would have some bearing on subsequent decisions if it turns out the analysis is sensitive to the outliers--it does not seem to serve the O.P.'s interests in this case. $\endgroup$ – whuber Jan 15 '15 at 16:36
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I would emphasize on something that was said in an other answer and comments (I think that @Peter Flom's answers is accurate and that EdM is right on touch about measurements, among all ).

Analyzing data is something that must be done carefully. You must be very well aware of the meaning of outliers in your contact. For example, assuming that your measurement procedure was done "correctly" (I mean, you haven't introduced biases, you equipment was calibrated, the person reading the instrument did it correctly, etc. etc.), some outliers may tell something interesting and sometime very important.

Here is a made up example, please be indulgent (point them in comments) if it is not 100% right on all aspects. ;)

Say that someone is testing the effect of applying a certain amount of a substance to some cultures (populations) of bacteria. Now, "in general", the effect is to stabilize the number of bacteria in the population, but there are some outliers among the different cultures.

Imagine all your outliers indicate situations where all the bacteria are dead. Or that all outliers represent cultures where the bacteria populations have grown out of control.

What I want to point out is that the nature of your perceived outliers might be meaningful and the consequences of each are different. You might be in a situation where it is intolerable that the number of bacteria increase, or decrease.

Of course, if you noticed that some populations where wiped out by the substance, you would probably investigate on the matter since it is an easily recognizable situation. But not all phenomenon are easily detectable.

To wrap up, the notion of outliers is somewhat arbitrary, but their meanings are multiple and of different importance. Hope it will make you think on the matter... :)

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