Q&A #19164

Outlier detection

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From: Pat Ballew (for Teacher2Teacher Service)
Date: Dec 18, 2007 at 13:19:03
Subject: Re: Outlier detection


I think you have hit upon essentially the method that is used most often 
by professional statistical software, except that they use the fact that if 
the assumptions about the regression data are true, the residuals will be 
normally distributed and independent of each other.  

I think Mini-tab reports any residuals that are more than 1.5 or 2 standard 
deviations from the mean of the residuals (zero should be the mean residual)

Using normal deviation, if we assume normal distribution of the residuals, 
then the IQR is about 1.35 Sigma, and so if you use the Tukey guide 
(quartile +/- 1.5 IQR) you would have to be somewhere around 2.67 sigma to 
be an outlier.  Keep in mind this is a vertical measurement, and not 
measuring away from the line horizontally (a slightly smaller distance, I 
would think).

I think you would not be far wrong telling your students to seriously 
question data with residuals outside 2.5 sigma.  
HOWEVER>>> I think that the far more important question is to look at the 
shape of the residuals and the value of r^2 to see if we have the right 

Hope some of this is of help to you. Good luck.

 -Pat Ballew, for the T2T service

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