Simulations with non negative estimate (λ)

Sample size

Fvalue for interaction effects ± STD with different model for power transformation

Ftest for interaction effects (Proportion with P > 0.05)


N

n

MeanF
_{
λ
}± Std

MeanF
_{
λ0
}± Std

MeanF
_{
λ1
}± Std

Y
^{λ}

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

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


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
_{
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. Pvalue is obtained from ANOVA with SAS GLM procedure. A total of 1000 datasets were generated for each fixed sample size and transformation parameter.