I have a general question about handling outliers when doing univariate and multivariate analysis, but I'm going to present my specific situation for discussion clarity.
I'm dealing with ecological data for roughly 100 pine trees, about evenly divided between 4 treatment groups. Approximately 20 different attributes were measured for each tree. The attributes are roughly divided into morphological measurements (i.e. tree age, size, water status, leaf size...a bunch of indicators of health) and biochemical measurements (concentration of various chemicals associated with tree stress responses). The big-picture goal of my analysis is to find the relationship between the morphological data and the biochemical data.
I performed several tests for multivariate outliers--which agreed with each other and identified 5 trees, so I removed them from the data set. Two other trees were not formally identified as multivariate outliers, but were univariate outliers (defined as |Z|>2) in >5 attributes (no other trees were >2) so I also removed those two trees from the data set. After removing those 7 trees, I am left with a few dozen univariate outlier data points scattered throughout the data.
I am performing several multivariate techniques including PCA and CCorA as well as univariate ANOVA and post hoc tests (for each attribute, based on the four treatment groups).
For the multivariate analysis, my training is to replace the outlier data points with the group mean--so that tree can continue contributing to the overall multivariate data structure (for all other attributes) but the outlier is removed so that it doesn't artificially inflate the correlation of that particular attribute.
If I handle an outlier data point in that way, should I keep it replaced with the group mean for the univariate analysis, or should I do the univariate analysis on the original data set with the outlier value included?
Also for background: I was not involved in collecting this data, so I have no experience based criteria for identifying outliers--in some cases it could be faulty instruments, or bad measurements, but it's also quite possible that a true outlier was measured (they are pretty common in plant biology--plants do lots of weird things).