In this paper, the statistical significance of the contribution of variables to the principal components in principal components analysis (PCA) is assessed nonparametrically by the use of permutation tests. We compare a new strategy to a strategy used in previous research consisting of permuting the columns (variables) of a data matrix independently and concurrently, thus destroying the entire correlational structure of the data. This strategy is considered appropriate for assessing the significance of the PCA solution as a whole, but is not suitable for assessing the significance of the contribution of single variables. Alternatively, we propose a strategy involving permutation of one variable at a time, while keeping the other variables fixed. We compare the two approaches in a simulation study, considering proportions of Type I and Type II error. We use two corrections for multiple testing: the Bonferroni correction and controlling the False Discovery Rate (FDR). To assess the significance of the variance accounted for by the variables, permuting one variable at a time, combined with FDR correction, yields the most favorable results. This optimal strategy is applied to an empirical data set, and results are compared with bootstrap confidence intervals.