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Outliers are cases that have an atypical score either for a single variable (univariate outliers) or for a combination of variables (multivariate outliers). Outliers generally have a large impact on the solution, i.e. the outlier case can conceivably change the value or score that we would predict for every other case in the study. Our concern with outliers is to answer the question of whether our analysis is more valid with the outlier case included or more valid with the outlier case excluded.
To answer this question, we must have methods for detecting and assessing outliers. The method for detecting univariate outliers is to convert the scores on the variable to standard scores and scan for very large positive and negative standard scores. We will normally apply this strategy to the analysis of a metric dependent variable. The detection of multivariate outliers is used to detect unusual cases for the combined set of metric independent variables, using a multivariate distance measure analogous to standard score distance from the mean of the sample.
The decision to exclude or retain the outlier case is based on our understanding of the cause of the outlier and the impact it is having on the results. If the outlier is a data entry error or an obvious misstatement by a respondent, it probably should be excluded. If the outlier is an unusual but probable value, it should be retained. We can improve our understanding of the impact of the outlier by running an analysis twice, one with the outlier included and again with the outlier excluded..