Asymptotically distribution‐free (ADF) methods for the analyses of covariances or correlations require the calculation of an estimated variance–covariance matrix of those covariances or correlations.Formulae for this variance–covariance matrix are well known from the literature. However, it turns out that, in particular for the correlations, this matrix is quite elaborate because it seems to be necessary to compute and store fourth‐order standardized sample moments.In this paper we show that this can be avoided and that computations can be done in the data matrix directly. This may save a lot of core storage and computation time