PSUBFAT2DBC.RdThis function performs the analysis of a randomized block design in a split-plot with a subplot in a double factorial scheme.
PSUBFAT2DBC(
f1,
f2,
f3,
block,
resp,
alpha.f = 0.05,
alpha.t = 0.05,
norm = "sw",
homog = "bt",
mcomp = "tukey"
)Numeric or complex vector with plot levels
Numeric or complex vector with splitplot levels
Numeric or complex vector with splitsplitplot levels
Numeric or complex vector with blocks
Numeric vector with responses
Level of significance of the F test (default is 0.05)
Significance level of the multiple comparison test (default is 0.05)
Error normality test (default is Shapiro-Wilk)
Homogeneity test of variances (default is Bartlett)
Multiple comparison test (Tukey (default), LSD and Duncan)
Analysis of variance of fixed effects and multiple comparison test of Tukey, Scott-Knott, LSD or Duncan.
f1=rep(c("PD","PDE","C"), e = 40);f1=factor(f1,unique(f1))
f2=rep(c(300,400), e = 20,3);f2=factor(f2,unique(f2))
f3=rep(c("c1", "c2", "c3", "c4"), e = 5,6);f3=factor(f3,unique(f3))
bloco=rep(paste("B",1:5),24); bloco=factor(bloco,unique(bloco))
set.seed(10)
resp=rnorm(120,50,5)
PSUBFAT2DBC(f1,f2,f3,bloco,resp,alpha.f = 0.5) # force triple interaction
#> Warning: Error() model is singular
#>
#> -----------------------------------------------------------------
#> Normality of errors
#> -----------------------------------------------------------------
#> Method Statistic p.value
#> Shapiro-Wilk normality test(W) 0.9913894 0.6632354
#>
#> As the calculated p-value is greater than the 5% significance level, hypothesis H0 is not rejected. Therefore, errors can be considered normal
#>
#> -----------------------------------------------------------------
#> Homogeneity of Variances
#> -----------------------------------------------------------------
#> Method Statistic p.value
#> Bartlett test(Bartlett's K-squared) 29.86522 0.1533099
#>
#> As the calculated p-value is greater than the 5% significance level, hypothesis H0 is not rejected. Therefore, the variances can be considered homogeneous
#>
#> -----------------------------------------------------------------
#> Additional Information
#> -----------------------------------------------------------------
#>
#> CV 1 (%) = 8.29
#> CV 2 (%) = 9.01
#> Mean = 49.6176
#> Median = 49.5507
#> Possible outliers = No discrepant point
#>
#> -----------------------------------------------------------------
#> Analysis of Variance
#> -----------------------------------------------------------------
#> df SS MS F-value p
#> F1 2 200.80976 100.40488 5.9356627 0.02626955
#> block 4 72.31228 18.07807 1.0687262 0.43175774
#> Error A 8 135.32424 16.91553
#> F2 1 90.72529 90.72529 4.5377346 0.03608042
#> F3 3 61.85881 20.61960 1.0313143 0.38303103
#> F1 x F2 2 60.27090 30.13545 1.5072608 0.22744536
#> F1 x F3 6 86.85448 14.47575 0.7240219 0.63141782
#> F2 x F3 3 138.29564 46.09855 2.3056742 0.08260633
#> F1 x F2 x F3 6 115.28713 19.21452 0.9610374 0.45668802
#> Residuals 84 1679.45575 19.99352
#>
#> -----------------------------------------------------
#> Analyzing F2 inside of each level of F1 and F3
#> -----------------------------------------------------
#> Df Sum sq Mean Sq F value Pr(>F)
#> f1:f3:f2 12 4.045790e+02 3.371491e+01 1.6862919294 0.08437225
#> f1:f3:f2 PD c1 1 6.248158e+01 6.248158e+01 3.1250913552 0.08072679
#> f1:f3:f2 PDE c1 1 5.754416e-01 5.754416e-01 0.0287814019 0.86569266
#> f1:f3:f2 C c1 1 3.139833e+01 3.139833e+01 1.5704253218 0.21362233
#> f1:f3:f2 PD c2 1 1.506184e+00 1.506184e+00 0.0753335835 0.78439762
#> f1:f3:f2 PDE c2 1 2.056254e+00 2.056254e+00 0.1028460179 0.74923713
#> f1:f3:f2 C c2 1 8.697023e-03 8.697023e-03 0.0004349921 0.98340962
#> f1:f3:f2 PD c3 1 7.579835e+01 7.579835e+01 3.7911457435 0.05486583
#> f1:f3:f2 PDE c3 1 1.254129e+02 1.254129e+02 6.2726766866 0.01419419
#> f1:f3:f2 C c3 1 3.714302e+00 3.714302e+00 0.1857752589 0.66756041
#> f1:f3:f2 PD c4 1 4.318861e+01 4.318861e+01 2.1601300773 0.14536832
#> f1:f3:f2 PDE c4 1 2.700789e-01 2.700789e-01 0.0135083189 0.90775141
#> f1:f3:f2 C c4 1 5.816824e+01 5.816824e+01 2.9093543955 0.09176244
#> residuals 84 1.679456e+03 1.999352e+01
#>
#>
#> ------------------------------------------
#> F2 within the combination of levels PD of F1 and c1 of F3
#> ------------------------------------------
#> resp groups
#> 300 48.15854 a
#> 400 43.15928 a
#>
#>
#> ------------------------------------------
#> F2 within the combination of levels PD of F1 and c2 of F3
#> ------------------------------------------
#> resp groups
#> 400 47.71108 a
#> 300 46.93489 a
#>
#>
#> ------------------------------------------
#> F2 within the combination of levels PDE of F1 and c1 of F3
#> ------------------------------------------
#> resp groups
#> 300 49.36217 a
#> 400 48.88240 a
#>
#>
#> ------------------------------------------
#> F2 within the combination of levels PDE of F1 and c2 of F3
#> ------------------------------------------
#> resp groups
#> 400 50.78703 a
#> 300 49.88011 a
#>
#>
#> ------------------------------------------
#> F2 within the combination of levels C of F1 and c1 of F3
#> ------------------------------------------
#> resp groups
#> 300 52.23990 a
#> 400 48.69599 a
#>
#>
#> ------------------------------------------
#> F2 within the combination of levels C of F1 and c2 of F3
#> ------------------------------------------
#> resp groups
#> 300 51.78121 a
#> 400 51.72223 a
#>
#> -----------------------------------------------------
#> Analyzing F3 inside of each level of F1 and F2
#> -----------------------------------------------------
#> Df Sum sq Mean Sq F value Pr(>F)
#> f1:f2:f3 18 402.29605 22.349781 1.1369762 0.3301216
#> f1:f2:f3: PD 300 3 118.75284 39.584281 2.0137282 0.1171401
#> f1:f2:f3: PDE 300 3 47.47222 15.824074 0.8050010 0.4941058
#> f1:f2:f3: C 300 3 26.13741 8.712471 0.4432201 0.7226428
#> f1:f2:f3: PD 400 3 71.11234 23.704112 1.2058736 0.3118617
#> f1:f2:f3: PDE 400 3 57.90185 19.300616 0.9818593 0.4047110
#> f1:f2:f3: C 400 3 80.91939 26.973129 1.3721748 0.2559524
#> residuals 96 1887.09227 19.657211
#>
#>
#> ------------------------------------------
#> F3 within the combination of levels PD of F1 and 300 of F2
#> ------------------------------------------
#> resp groups
#> c3 47.84186 a
#> c2 47.71108 a
#> c4 46.19138 a
#> c1 43.15928 a
#>
#>
#> ------------------------------------------
#> F3 within the combination of levels PD of F1 and 400 of F2
#> ------------------------------------------
#> resp groups
#> c3 47.84186 a
#> c2 47.71108 a
#> c4 46.19138 a
#> c1 43.15928 a
#>
#>
#> ------------------------------------------
#> F3 within the combination of levels PDE of F1 and 300 of F2
#> ------------------------------------------
#> resp groups
#> c2 50.78703 a
#> c4 49.73344 a
#> c1 48.88240 a
#> c3 46.19361 a
#>
#>
#> ------------------------------------------
#> F3 within the combination of levels PDE of F1 and 400 of F2
#> ------------------------------------------
#> resp groups
#> c2 50.78703 a
#> c4 49.73344 a
#> c1 48.88240 a
#> c3 46.19361 a
#>
#>
#> ------------------------------------------
#> F3 within the combination of levels C of F1 and 300 of F2
#> ------------------------------------------
#> resp groups
#> c4 54.06542 a
#> c2 51.72223 a
#> c3 49.99311 a
#> c1 48.69599 a
#>
#>
#> ------------------------------------------
#> F3 within the combination of levels C of F1 and 400 of F2
#> ------------------------------------------
#> resp groups
#> c4 54.06542 a
#> c2 51.72223 a
#> c3 49.99311 a
#> c1 48.69599 a
#>
#> -----------------------------------------------------
#> Analyzing F1 inside of each level of F2 and F3
#> -----------------------------------------------------
#> Df Sum sq Mean Sq F value Pr(>F)
#> f3:f2:f1 2 59.625599 29.812800 1.52038077 0.22412954
#> f3:f2:f1: 300 c1 2 43.979354 21.989677 1.12142039 0.33027695
#> f3:f2:f1: 400 c1 2 105.740063 52.870031 2.69624387 0.07284810
#> f3:f2:f1: 300 c2 2 59.625599 29.812800 1.52038077 0.22412954
#> f3:f2:f1: 400 c2 2 44.042312 22.021156 1.12302576 0.32975990
#> f3:f2:f1: 300 c3 2 14.716266 7.358133 0.37524700 0.68817777
#> f3:f2:f1: 400 c3 2 36.301384 18.150692 0.92564145 0.39997561
#> f3:f2:f1: 300 c4 2 3.296073 1.648036 0.08404588 0.91946036
#> f3:f2:f1: 400 c4 2 155.521212 77.760606 3.96560306 0.02232123
#> Residuals combined 91 1784.398248 19.608772
#>
#>
#> ------------------------------------------
#> F1 within the combination of levels 300 of F2 and c1 of F3
#> ------------------------------------------
#> resp groups
#> C 52.23990 a
#> PDE 49.36217 a
#> PD 48.15854 a
#>
#>
#> ------------------------------------------
#> F1 within the combination of levels 300 of F2 and c2 of F3
#> ------------------------------------------
#> resp groups
#> C 51.78121 a
#> PDE 49.88011 a
#> PD 46.93489 a
#>
#>
#> ------------------------------------------
#> F1 within the combination of levels 300 of F2 and c3 of F3
#> ------------------------------------------
#> resp groups
#> PD 53.34816 a
#> PDE 53.27635 a
#> C 51.21201 a
#>
#>
#> ------------------------------------------
#> F1 within the combination of levels 300 of F2 and c4 of F3
#> ------------------------------------------
#> resp groups
#> PD 50.34775 a
#> PDE 50.06212 a
#> C 49.24180 a
#>
#>
#> ------------------------------------------
#> F1 within the combination of levels 400 of F2 and c1 of F3
#> ------------------------------------------
#> resp groups
#> PDE 48.88240 a
#> C 48.69599 a
#> PD 43.15928 a
#>
#>
#> ------------------------------------------
#> F1 within the combination of levels 400 of F2 and c2 of F3
#> ------------------------------------------
#> resp groups
#> C 51.72223 a
#> PDE 50.78703 a
#> PD 47.71108 a
#>
#>
#> ------------------------------------------
#> F1 within the combination of levels 400 of F2 and c3 of F3
#> ------------------------------------------
#> resp groups
#> C 49.99311 a
#> PD 47.84186 a
#> PDE 46.19361 a
#>
#>
#> ------------------------------------------
#> F1 within the combination of levels 400 of F2 and c4 of F3
#> ------------------------------------------
#> resp groups
#> C 54.06542 a
#> PDE 49.73344 a
#> PD 46.19138 a
PSUBFAT2DBC(f1,f2,f3,bloco,resp,alpha.f = 0.4) # force double interaction
#> Warning: Error() model is singular
#>
#> -----------------------------------------------------------------
#> Normality of errors
#> -----------------------------------------------------------------
#> Method Statistic p.value
#> Shapiro-Wilk normality test(W) 0.9913894 0.6632354
#>
#> As the calculated p-value is greater than the 5% significance level, hypothesis H0 is not rejected. Therefore, errors can be considered normal
#>
#> -----------------------------------------------------------------
#> Homogeneity of Variances
#> -----------------------------------------------------------------
#> Method Statistic p.value
#> Bartlett test(Bartlett's K-squared) 29.86522 0.1533099
#>
#> As the calculated p-value is greater than the 5% significance level, hypothesis H0 is not rejected. Therefore, the variances can be considered homogeneous
#>
#> -----------------------------------------------------------------
#> Additional Information
#> -----------------------------------------------------------------
#>
#> CV 1 (%) = 8.29
#> CV 2 (%) = 9.01
#> Mean = 49.6176
#> Median = 49.5507
#> Possible outliers = No discrepant point
#>
#> -----------------------------------------------------------------
#> Analysis of Variance
#> -----------------------------------------------------------------
#> df SS MS F-value p
#> F1 2 200.80976 100.40488 5.9356627 0.02626955
#> block 4 72.31228 18.07807 1.0687262 0.43175774
#> Error A 8 135.32424 16.91553
#> F2 1 90.72529 90.72529 4.5377346 0.03608042
#> F3 3 61.85881 20.61960 1.0313143 0.38303103
#> F1 x F2 2 60.27090 30.13545 1.5072608 0.22744536
#> F1 x F3 6 86.85448 14.47575 0.7240219 0.63141782
#> F2 x F3 3 138.29564 46.09855 2.3056742 0.08260633
#> F1 x F2 x F3 6 115.28713 19.21452 0.9610374 0.45668802
#> Residuals 84 1679.45575 19.99352
#> Multiple Comparison Test: Tukey HSD
#>
#> Warning: Error() model is singular
#>
#> -----------------------------------------------------
#> Analyzing F2 inside of each level of F1
#> -----------------------------------------------------
#> Df Sum sq Mean Sq F value Pr(>F)
#> f1:f2 3 1.509962e+02 5.033206e+01 2.517419e+00 0.06364890
#> f1:f2: PD 1 1.205087e+02 1.205087e+02 6.027388e+00 0.01614866
#> f1:f2: PDE 1 3.048749e+01 3.048749e+01 1.524868e+00 0.22032730
#> f1:f2: C 1 2.072023e-06 2.072023e-06 1.036347e-07 0.99974391
#> Residuals 84 1.679456e+03 1.999352e+01
#>
#> -----------------------------------------------------
#> Analyzing F1 inside of each level of F2
#> -----------------------------------------------------
#> Df Sum sq Mean Sq F value Pr(>F)
#> f2:f1 4 261.0806555 65.27016 3.3395896 0.013547392
#> f2:f1: 300 2 20.9535457 10.47677 0.5677075 0.572104140
#> f2:f1: 400 2 240.1271098 120.06355 6.5059141 0.004051541
#> Residuals combined 34 0.5427802 18.45453
#>
#> -----------------------------------------------------
#> Analyzing F3 inside of each level of F2
#> -----------------------------------------------------
#> Df Sum sq Mean Sq F value Pr(>F)
#> f2 1 90.72529 90.72529 4.537735 0.03608042
#> f2:f3 6 200.15445 33.35907 1.668494 0.13882429
#> f2:f3: 300 3 91.69873 30.56624 1.528808 0.21301183
#> f2:f3: 400 3 108.45571 36.15190 1.808181 0.15191196
#> Residuals 84 1679.45575 19.99352
#>
#> -----------------------------------------------------
#> Analyzing F2 inside of each level of F3
#> -----------------------------------------------------
#> Df Sum sq Mean Sq F value Pr(>F)
#> f3 3 6.185881e+01 20.61960309 1.031314255 0.383031028
#> f3:f2 4 2.290209e+02 57.25523189 2.863689304 0.028136793
#> f3:f2: c1 1 6.784462e+01 67.84461738 3.393330159 0.068989287
#> f3:f2: c2 1 2.198162e+00 2.19816232 0.109943733 0.741034050
#> f3:f2: c3 1 1.588826e+02 158.88262698 7.946705733 0.006006889
#> f3:f2: c4 1 9.552089e-02 0.09552089 0.004777592 0.945058275
#> Residuals 84 1.679456e+03 19.99352088
#>
#> ======================
#> Multiple comparasion
#> ======================
#> 300 400
#> c1 49.92 aA 46.913 aA
#> c2 49.532 aA 50.073 aA
#> c3 52.612 aA 48.01 aB
#> c4 49.884 aA 49.997 aA