Fig. 7. Required sample sizes.
Sample sizes to obtain at least 90 % power and at most 10 % error for the association strength, weight, scores and loadings. Shown estimates are constrained by the within-set variance spectrum (here aX + aY = − 2, cf. Supplementary Fig. 19 for other values). a Assuming a true between-set correlation of rtrue = 0.3 (see Supplementary Fig. 18a–d for other values) 100s to 1000s of observations are required to reach target power and error levels. Shaded areas show 95 % confidence intervals across 25 covariance matrices encoding CCA/PLS solutions with rtrue = 0.3, but varying weight vectors. b The required number of observations divided by the total number of features in X and Y scales with rtrue. For rtrue = 0.3 about 50 samples per feature are necessary to reach target power and error levels in CCA, which is much more than typically used (cf. Supplementary Fig. 2a). Every point for a given rtrue represents a different number of features and is slightly jittered for visibility. Values for a given dimensionality pX are only shown here if simulations were available for both CCA and PLS. Horizontal lines for each rtrue represent the mean across the available number of features.