ABSTRACT
Outliers are observations that are idiosyncratic in a dataset, arising for unknown reasons, and leading to potentially very different stories of what the data have to say. There are two broad classifications of violations of assumptions about error: systematic and idiosyncratic. The assumptions that errors are normally distributed with a constant variance are often seen as "robust" assumptions, in the sense that the accepted advice is that violations of the assumptions do not result in major statistical errors. The assumption that errors are normally distributed is a relatively robust assumption. But the validity of this conclusion depends on the nature of the departure of the distribution of errors from the normal one. Nonlinear but monotonic transformations of the data variable can often lead to more normally distributed errors with constant variances. Importantly, in addition to violating the assumption of normality of errors, skewed error distributions are also routinely characterized by heterogeneous variances.
