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 1 Statistics for power transformation parameter and statistical test for structural effects based on Monte Carlo simulations

Simulations with non negative estimate (λ)	Sample size	Transformation parameter and its empirical estimate ± Standard deviation			Test for residual normality (proportion with P > 0.05)
N	n	λ	Mean (λ ₁) ± Std	Mean (λ ₀) ± Std	Y ^λ	${(Y^{λ})}^{(λ_{0)})}$	${(Y^{λ})}^{(λ_{1})}$
973	36	0.4	0.397 ± 0.160	0.296 ± 0.123	0.698	0.962	0.968
996	54	0.4	0.386 ± 0.125	0.289 ± 0.107	0.522	0.950	0.971
999	72	0.4	0.393 ± 0.104	0.295 ± 0.010	0.387	0.963	0.978
1000	90	0.4	0.395 ± 0.089	0.295 ± 0.087	0.251	0.941	0.977
1000	108	0.4	0.393 ± 0.085	0.295 ± 0.083	0.179	0.929	0.975
1000	126	0.4	0.393 ± 0.075	0.296 ± 0.074	0.120	0.920	0.976
1000	144	0.4	0.395 ± 0.068	0.299 ± 0.067	0.082	0.912	0.979
1000	162	0.4	0.395 ± 0.067	0.398 ± 0.068	0.056	0.891	0.972
1000	180	0.4	0.395 ± 0.063	0.030 ± 0.063	0.037	0.889	0.968
1000	198	0.4	0.396 ± 0.059	0.301 ± 0.059	0.018	0.880	0.971
1000	216	0.4	0.396 ± 0.057	0.302 ± 0.057	0.010	0.867	0.977

Notation: λ is the preset value for generating the data; λ ₀represents the estimated value for the 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 by Shapiro-Wilk test with SAS Univariate procedure. A total of 1000 datasets were generated for each fixed sample size and transformation parameter.

ISSN: 1471-2288