I'm not convinced we want a "prediction interval" We don't want to predict... and we don't want an interval...?

Thanks and apologies I should have provided more info. We're having a look at the prediction intervals. Basically we have the length of a focal gene prediction. And the lengths of similar genes found in databases. So all numbers are positive integers. In an easy case, the distribution of the lengths is unimodal. In reality they often arent; at this stage we can suppose that that they are. Some plots of distributions are shown here: github.com/monicadragan/gene_prediction/tree/master/…

Thanks - good points. I didn't know about pairwise.wilcox.test!

"The p-value is then the proportion of the statistics that are greater than or equal to the original statistic" --> to the original statistic calculated on the full model. correct?

(yes, the gene expression values are more or less normally distributed)