Parametric statistics

Parametric statistics are statistics where the population is assumed to fit any parametrized distributions (most typically the normal distribution). The opposite is non-parametric statistics.

Parametric inferential statistical methods are mathematical procedures for statistical hypothesis testing which assume that the distributions of the variables being assessed belong to known parametrized families of probability distributions. In that case we speak of parametric model.

For example, analysis of variance (ANOVA) assumes that the underlying distributions are normally distributed and that the variances of the distributions being compared are similar. The Pearson product-moment correlation coefficient also assumes normality.

Power and Robustness

A significant problem with parametric statistics is that they are frequently not robust statistics: if their assumptions are violated even slightly, they may fail utterly (see breakdown point). In these cases, a non-parametric alternative is more likely to detect a difference or similarity.

However, if the assumptions are satisfied, parametric statistics generally have more power than non-parametric alternatives.

Thus the choice between parametric and non-parametric statistics is a trade-off between power and robustness, and requires judgment about how suited the assumptions are, and how sensitive one is to deviations.