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Table 2 Statistics for tests of structural effect with different transformation models based on Monte Carlo simulations

From: The Box-Cox power transformation on nursing sensitive indicators: Does it matter if structural effects are omitted during the estimation of the transformation parameter?

Simulations with non negative estimate (λ) Sample size F-value for interaction effects ± STD with different model for power transformation F-test for interaction effects (Proportion with P > 0.05)
N n MeanF λ ± Std MeanF λ0 ± Std MeanF λ1 ± Std Y λ ( Y λ ) ( λ 0 ) ) ( Y λ ) ( λ 1 )
973 36 2.072 ± 1.372 1.083 ± 0.699 1.328 ± 0.922 0.687 0.885 0.938
996 54 2.460 ± 1.407 1.117 ± 0.673 1.338 ± 0.868 0.523 0.874 0.937
999 72 2.866 ± 1.475 1.126 ± 0.660 1.378 ± 0.836 0.375 0.854 0.935
1000 90 3.264 ± 1.656 1.178 ± 0.649 1.471 ± 0.865 0.343 0.823 0.927
1000 108 3.796 ± 1.686 1.219 ± 0.700 1.537 ± 0.908 0.158 0.802 0.903
1000 126 4.276 ± 1.900 1.292 ± 0.696 1.656 ± 0.951 0.100 0.748 0.899
1000 144 4.707 ± 1.984 1.336 ± 0.738 1.721 ± 0.993 0.066 0.722 0.866
1000 162 5.211 ± 2.156 1.411 ± 0.778 1.841 ± 1.073 0.043 0.697 0.852
1000 180 5.653 ± 2.080 1.444 ± 0.783 1.903 ± 1.053 0.016 0.663 0.834
1000 198 6.117 ± 2.282 1.497 ± 0.776 2.001 ± 1.114 0.009 0.624 0.798
1000 216 6.616 ± 2.324 1.570 ± 0.797 2.107 ± 1.114 0.003 0.589 0.788
  1. Notation: λ is the preset value for generating the data; λ 0 represents the estimated value for transformation parameter with no factorial treatment effect in the model; λ 1 stands for estimated value of transformation parameter with factorial treatment effect in the model. P-value is obtained from ANOVA with SAS GLM procedure. A total of 1000 datasets were generated for each fixed sample size and transformation parameter.