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Robust approaches to this problem have been proposed (eg, Egan & Morgan, 1998; Hadi & Simonoff, 1993; Rousseeuw & von Zomren, 1990), but these are not yet implemented in popular software packages These methods can be approximated by screening for multivariate outliers two or more times, each time dealing with cases identi ed as outliers on the previous run, until nally no new outliers are identi ed But if there seem to be too many outliers, do a trial analysis with and without later-identi ed outliers to see if they are truly changing results If not, retain them in the analysis (This is also a worthwhile strategy to apply for early-identi ed outliers if there seem to be too many of them) Once multivariate outliers are identi ed, you need to discover why the cases are extreme (You already know why univariate outliers are extreme.

) It is important to identify the variables on which the cases are deviant to help you decide whether the case is properly part of your sample and to provide an indication of the kinds of cases to which your results do not generalize If there are only a few multivariate outliers, it is reasonable to examine them one at a time through multiple regression in which a dichotomous DV is formed on the basis of the outlying case If there are several outliers, you may want to examine them as a group to see if there are any variables that consistently separate the group of outliers from the rest of the cases These procedures are illustrated in Tabachnick and Fidell (2001b) First, identify potential univariate outliers and then begin the search for multivariate outliers.

Concentrate on what is not being said as well as what is being said Remember, a lot of clues to meaning come from the speaker s tone of voice, facial expressions, and gestures People don t always say what they mean, but their body language is usually an accurate indication of their attitude and emotional state 4 Ask questions If you are not sure of what the speaker is saying, ask It s perfectly acceptable to say, Do you mean or Did I understand you to say It s also a good idea to repeat in your own words what the speaker has said, to confirm that you have understood him correctly 5 Don t let yourself be distracted by the environment or by the speaker s appearance, accent, mannerisms, or word use.

develop concrete recommendations to improve community health As it turned out, the study found that the point sources evaluated were not likely to be a signi cant contributing factor to community health concerns By not including a potentially important source of air pollution mobile sources in the study, the subcommittee did not have enough information to develop the most effective recommendations Thus it was possible that poor air quality did contribute to public health problems in South Baltimore, but by failing to look at the whole picture, the study could not answer the question in full The relationship between the limited scope of the subcommittee s work and its ability to make recommendations for improving community air quality and health was not adequately discussed, understood and agreed to at the beginning of the effort.

The solutions that eliminate univariate outliers also tend to reduce the number of multivariate outliers, but sometimes not completely because the problem with a true multivariate outlier is the combination of scores on two or more variables, not the score on any one variable To deal with multivariate outliers, rst consider the possibility that one variable is implicated for many of them If so, and the variable is highly correlated with others in a multivariate design or is not critical to the analysis, deletion of it is a good alternative Otherwise, multivariate outliers are usually deleted After the analysis is complete, look for outliers in the solution as a hint to the kinds of cases for which the solution does not work very well Outliers in the solution for ungrouped data are found through examination of residuals.