This report describes significance testing for PLS and OPLS® (orthogonal PLS) models. The testing is applicable to single-Y cases and is based on ANOVA of the cross-validated residuals (CV-ANOVA). Two variants of the CV-ANOVA are introduced. The first is based on the cross-validated predictive residuals of the PLS or OPLS model while the second works with the cross-validated predictive score values of the OPLS model. The two CV-ANOVA diagnostics are shown to work well in those cases where PLS and OPLS work well, that is, for data with many and correlated variables, missing data, etc. The utility of the CV-ANOVA diagnostic is demonstrated using three datasets related to (i) the monitoring of an industrial de-inking process; (ii) a pharmaceutical QSAR problem and (iii) a multivariate calibration application from a sugar refinery. Copyright © 2008 John Wiley & Sons, Ltd.