Parametric inferential statistical methods are mathematical procedures for
statistical hypothesis testing which assume that the distributions of the variables being assessed have certain characteristics.
Analysis of variance 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 assumes normality.
While parametric techniques are robust – that is, they often retain considerable power to detect differences or similarities even when these assumptions are violated – some distributions violate the assumptions so markedly that a non-parametric alternative is more likely to detect a difference or similarity.
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