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Appendix B. Figures showing power estimates for larger sample size.

Fig. B1.  Average power estimates for each correlation structure considered containing nine variables (Fig. 1) based on samples containing 40 observations, measured as the average proportion of rejections ( = 0.05) per 1000 tests, for normal and (exponential)3 populations. Estimates are presented according to their associated loading in the corresponding population correlation matrix. Upper values within each block of loadings represent estimates for the bootstrapped eigenvector, whereas lower values represent values for the bootstrapped broken-stick. For example, for correlation matrix 2 the loadings for variables 5–7 are the same within the first dimension, therefore their power estimates were averaged out. Values in bold indicate that a particular method showed significantly larger power based on the confidence interval for the estimate (see Methods section for details).

Fig. B2.  Average power estimates for each correlation structure considered containing nine variables (Fig. 1) based on samples containing 50 observations, measured as the average proportion of rejections ( = 0.05) per 1000 tests, for normal and (exponential)3 populations.  Estimates are presented according to their associated loading in the corresponding population correlation matrix. Upper values within each block of loadings represent estimates for the bootstrapped eigenvector, whereas lower values represent values for the bootstrapped broken-stick. For example, for correlation matrix 2 the loadings for variables 5–7 are the same within the first dimension, therefore their power estimates were averaged out. Values in bold indicate that a particular method showed significantly larger power based on the confidence interval for the estimate (see Methods section for details).

Fig. B3.  Average power estimates for each correlation structure considered containing 18 variables (Fig. 1) based on samples containing 80 observations, measured as the average proportion of rejections (alpha = 0.05) per 1000 tests, for normal and (exponential)3 populations.  Estimates are presented according to their associated loading in the corresponding population correlation matrix.  Upper values within each block of loadings represent estimates for the bootstrapped eigenvector, whereas lower values represent values for the bootstrapped broken-stick.  For example, for correlation matrix 2 the loadings for variables 9-14 are the same within the first dimension, therefore their power estimates were averaged out. Values in bold indicate that a particular method showed significantly larger power based on the confidence interval for the estimate (see methods section for details).

Fig. B4.  Average power estimates for each correlation structure considered containing 18 variables (Fig. 1) based on samples containing 100 observations, measured as the average proportion of rejections ( = 0.05) per 1000 tests, for normal and (exponential)3 populations. Estimates are presented according to their associated loading in the corresponding population correlation matrix. Upper values within each block of loadings represent estimates for the bootstrapped eigenvector, whereas lower values represent values for the bootstrapped broken-stick. For example, for correlation matrix 2 the loadings for variables 9–14 are the same within the first dimension, therefore their power estimates were averaged out. Values in bold indicate that a particular method showed significantly larger power based on the confidence interval for the estimate (see Methods section for details).

Fig. B5.  Average power estimates for each correlation structure considered containing 18 variables (Fig. 1) based on samples containing 100 observations, measured as the average proportion of rejections ( = 0.05) per 1000 tests, for normal populations. Estimates are presented according to their associated loading in the corresponding population correlation matrix. Upper values within each block of loadings represent estimates for the randomized eigenvector, whereas lower values represent values for the parallel analysis. For example, for correlation matrix 2 the loadings for variables 9–14 are the same within the first dimension, therefore their power estimates were averaged out. Values in bold indicate that a particular method showed significantly larger power based on the confidence interval for the estimate (see Methods section for details).