How many discoveries have been lost by ignoring modern statistical methods?

Hundreds of articles in statistical journals have pointed out that standard analysis of variance, Pearson productmoment correlations, and least squares regression can be highly misleading and can have relatively low power even under very small departures from normality. In practical terms, psychology journals are littered with nonsignificant results that would have been significant if a more modern method had been used. Modern robust techniques, developed during the past 30 years, provide very effective methods for dealing with nonnormality, and they compete very well with conventional procedures when standard assumptions are met. In addition, modern methods provide accurate confidence intervals for a much broader range of situations, they provide more effective methods for detecting and studying outliers, and they can be used to get a deeper understanding of how variables are related. This article outlines and illustrates these results.