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I have a model as follows:

Y ~ X + town

One town in data has only outlying values for X variable, 5 in total, causing a wide gap between the outliers and the X values of other towns. My data includes 6000 subjects, distributed between 15 towns. Removing the town with outlying X values would result in 5800 subjects.

Model including the outliers show no association between X and Y.

Model excluding the outliers show clear association between X and Y.

Would it be reasonable to exclude the outlying town from the analysis, since these values would not allow the regression to make precise predictions (wide gap between values)?

Also, these outlying X values are correct, but produced by a different mechanism from other towns. This mechanism is not likely affecting our study population, but can affect other populations (e.g. children versus adults). May this justify the exclusion?

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    $\begingroup$ That depends on your precise goals, but on this information I would work with the logarithm of the variable. Excluding big values from analyses because they are awkward is usually a bad idea. $\endgroup$
    – Nick Cox
    Aug 11, 2020 at 7:43
  • $\begingroup$ Have you looked at robust regression methods ? They may allow you to perform your analysis on the whole data while avoiding too influencial points. $\endgroup$
    – Pohoua
    Aug 11, 2020 at 8:28
  • $\begingroup$ You seem to be proposing reducing a sample of size 15 to one of size 10. This needs more on your data for better advice to be possible. $\endgroup$
    – Nick Cox
    Aug 11, 2020 at 9:14
  • $\begingroup$ Thank you for your comments! My data includes 6000 subjects, distributed between 15 towns. Removing the town with outlying X values would result in 5800 subjects. $\endgroup$
    – st4co4
    Aug 11, 2020 at 10:08
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    $\begingroup$ It would be better to edit your question to include the additional information you have supplied in comments. $\endgroup$
    – mdewey
    Aug 11, 2020 at 14:59

1 Answer 1

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There are potentially two reasons why you check for outliers.

If you detect outliers, you should check whether the data collection was done correctly. It is possible that any outlier represents a mistake in the experiment, protocol etc.

However, if such mistakes are not detected, removing outliers is not justified. It may mean that your sampling is not homogeneous. If it is not possible to improve data collection, then as Nick Cox said, a transformation may help.

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    $\begingroup$ Thanks for the mention. Please check whether my small edits preserve your meaning. $\endgroup$
    – Nick Cox
    Aug 11, 2020 at 8:23
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    $\begingroup$ Very helpful, thank you! These outlying X values are correct, but produced by a different mechanism from other towns. This mechanism is not likely affecting our study population, but can affect other populations (e.g. children versus adults). May this justify the exclusion? $\endgroup$
    – st4co4
    Aug 11, 2020 at 8:54

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