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

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

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

Notation: λ is the preset value for generating the data; λ ₀represents the estimated value for transformation parameter with no factorial treatment effect in the model; λ ₁stands 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.

ISSN: 1471-2288