Scaled chi-square

I too think it could be useful in the armory of methods to deal with non-normality. A few riders though - non-normality often involves skewness so the utility of SE's (necessarily symmetric) becomes less (though likelihood-based CI's may still be useful). Second, careful inspection of how the data were obtained can often provide clues as to the source of non-normality, and in turn suggest alternative ways of dealing with it. A mixture of normal distributions, for example, may fit many observed distributions - and might provide insight into the generation of non-normality rather than sweeping it under the robust estimation rug. The drawback is it requires thinking :)