Parametric statistics and levels of measurement.

If Y is a continuous, ordinal measure of latent variable θ and Y has a normal distribution with equal variances in several groups, then t tests and one-way analyses of variance on Y can be used to test hypotheses about population mean differences on θ in the corresponding groups. If X and Y are continuous, ordinal measures of latent variables θ and φ, and if X and Y have a bivariate normal distribution, then a test of the null hypothesis that the population correlation between X and Y is zero is also a test of the hypothesis that θ and φ are independent. (PsycINFO Database Record (c) 2010 APA, all rights reserved)