Competence Centre for Methodology and Statistics
“The nuisance parameter nuisance”
A great deal of statistical debate concerns ‘univariate’ error, or disturbance, terms in models. I put ‘univariate’ in inverted commas because as soon as one writes a model of the form (say) Yi =Xiβ + Єi, i = 1 … n and starts to raise questions about the distribution of the disturbance terms, Єi one is frequently led into multivariate speculations, such as, ‘is the variance identical for every disturbance term?’ and, ‘are the disturbance terms independent?’ and not just speculations such as, ‘is the distribution of the disturbance terms Normal?’. Aris Spanos might also want me to put inverted commas around ‘disturbance’ (or ‘error’) since what I ought to be thinking about is the joint distribution of the outcomes, Yi conditional on the predictors.
However, in my statistical world of planning and analysing clinical trials, the differences made to inferences according to whether one uses parametric versus non-parametric methods is often minor. Of course, using non-parametric methods does nothing to answer the problem of non-independent observations but for experiments, as opposed to observational studies, you can frequently design-in independence. That is a major potential pitfall avoided but then there is still the issue of Normality. However, in my experience, this is rarely where the action is. Inferences rarely change dramatically on using ‘robust’ approaches (although one can always find examples with gross-outliers where they do). However, there are other sorts of problem that can affect data which can make a very big difference. Continue reading