What are the popular methods for outlier detection in univariate data, which do not assume normal distribution?

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#### Best Answer

Generally, you should avoid trimming outliers in an ad hoc fashion and instead use nonparametric or robust alternatives. A recent review with Monte Carlo studies can be found in Bakker and Wicherts (2014). At least in psychology journals, Z-score cut-offs were most popular. Of course, I wouldn't recommend that; the simulation studies in the same article demonstrate that Z-score cut-offs can inflate Type I error rates.

Although the review is focused on independent samples t-tests, most of their recommendations will apply more broadly. They concluded with the following recommendations:

• Correct or delete erroneous values.

• Based on prior research, it is not recommended to use Z scores to identify outliers. We recommend methods that suffer less from masking like the IQR or the MAD-median rule instead.

• Decide on outlier handling before seeing the results of the main analyses, and if possible, preregister the study at, for example, the Open Science Framework (http://openscienceframework.org/).

• If preregistration is not possible, report the outcomes both with and without outliers or on the basis of alternative methods.

• Report transparently about how outliers were handled.

• Do not carelessly remove outliers as this increases the probability of finding a false positive, especially when using a threshold value of Z lower than 3 or when the data are skewed.

• Use methods that are less influenced by outliers like nonparametric or robust methods such as the Mann-Whitney-Wilcoxon test and the Yuen-Welch test, or researchers may choose to conduct bootstrapping (all without removing outliers).

References:

Bakker, M., & Wicherts, J. M. (2014). Outlier removal, sum scores, and the inflation of the type I error rate in independent samples t tests: The power of alternatives and recommendations. *Psychological Methods, 19*(3), 409-427.

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