Hi
I measured some brain responses to different sound stimuli from 20 subjects. I have 543 observations in my dataset. I tried to fit the mixed effect model. When I did model control, both tests of normality and homogeneity of residuals failed (see also QQplot). I investigated residuals and found some outliers. If I remove 9 observations from my dataset with the largest residuals, I get the beautiful QQplot and both normality and homogeneity tests are passed. The question is: am I allowed to eliminated the outliers from the data? And if Yes, how should I report it?
Thanks for advance
Best regards
Anna
You should be very cautious removing data just because they do not fit your model.
Did you describe you exclusion criteria in your ethics proposal?
Given the large sample size, and the shape visible in your plots, I would not remove any outliers in such a case. Numerical and graphical tests are getting very sensitive for large N, whereas mean estimates are getting close to normal due to the CLT.
Let's assume s smaller sample size, then you would not even see the deviations from the straight line.
It is of course your own decision and depends on your question and your data. You may also spend some time on https://stats.stackexchange.com/ to get more insight.
Or, make a simulation in R with a sample taken from a normal, to see how "ugly" a true normal can look like:
x
Thomas Petzoldt
May I still use the model even if the normality test is failed?
Fit the model with all data and after removing the "outliers". Compare their results. Are the differences relevant? If not, use all the data. If yes, go and try to find out what may be special about these "outliers" (go back to the source, check lab-books, check for transcription errors, implausible values etc.). If you then don't find a problem there, use all the data. If you find problems, remove those values from your analysis (and document why these values were problematic, implausible or untrustworthy).
PS: Please also read about the nonsense of doing formal hypothesis tests on assumptions.
https://stats.stackexchange.com/questions/247361/normality-test-before-testing-the-difference-between-two-groups-is-it-necessary
https://stats.stackexchange.com/questions/2492/is-normality-testing-essentially-useless
http://www.pareonline.net/getvn.asp?v=18&n=11
Yes, I would use the model as is, especially as your QQ plot looks indeed very good, compare with the paper below. It is also wise to follow the suggestion of Jochen Wilhelmto improve understanding of method and data.
References:
Article Generalized Linear Mixed Models: A Practical Guide for Ecolo...
I would have thought that is is the distribution the between person residual that is important - that is for the 20 subjects but even then Normality is not a big issue but outliers could be
Ian H. Langford and Toby Lewis (1998) Outliers in Multilevel Data, Journal of the Royal Statistical Society. Series A (Statistics in Society)Vol. 161,No. 2 , pp. 121-160
Charles E. McCulloch and John M. Neuhaus (2011) Misspecifying the Shape of a Random Effects Distribution: Why Getting It Wrong May Not Matter https://arxiv.org/pdf/1201.1980.pdf
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