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}

${({Y}^{\lambda})}^{({\lambda}_{0)})}$

${\left({Y}^{\lambda}\right)}^{\left({\lambda}_{1}\right)}$


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
_{
0
}represents the estimated value for the 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. Pvalue is obtained by ShapiroWilk test with SAS Univariate procedure. A total of 1000 datasets were generated for each fixed sample size and transformation parameter.