Quantitative Approach to Outliers
Some researchers use quantitative methods to exclude outliers.
For example, they exclude observations that are outside the range of ± 2 standard deviations (or even ± 1.5 SDs) around the group or design cell mean. In some areas of research, such cleaning of the data is absolutely necessary.
For example, in cognitive psychology research on reaction times, even if almost all scores in an experiment are in the range of 300-700 milliseconds, just a few distracted reactions of 10-15 seconds will completely change the overall picture. Unfortunately, defining an outlier is subjective (as it should be), and the decisions concerning how to identify them must be made on an individual basis (taking into account specific experimental paradigms and/or accepted practice and general research experience in the respective area).
In some rare cases, the relative frequency of outliers across a number of groups or cells of a design can be subjected to analysis and provide interpretable results.
For example, outliers could be indicative of the occurrence of a phenomenon that is qualitatively different than the typical pattern observed or expected in the sample. In this case, the relative frequency of outliers could provide evidence of a relative frequency of departure from the process or phenomenon that is typical for the majority of cases in a group.