Rancangan Faktorial

library(ggplot2)
library(DescTools)
library(sjPlot)
library(fBasics)
library(lmtest)

## Loading required package: zoo

## 
## Attaching package: 'zoo'

## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric

library(car)

## Loading required package: carData

## 
## Attaching package: 'car'

## The following object is masked from 'package:fBasics':
## 
##     densityPlot

## The following object is masked from 'package:DescTools':
## 
##     Recode

RAL Faktorial

Input data

Data yang digunakan bisa diunduh disini

Data4<-read.csv("D:/IPB/STA1512/STA1512/Prak. By Fida/Data Pertemuan 8.csv")
str(Data4)

## 'data.frame':    45 obs. of  4 variables:
##  $ Faktor_Varietas: chr  "V1" "V1" "V1" "V1" ...
##  $ Faktor_Nitrogen: chr  "N1" "N2" "N3" "N4" ...
##  $ Kelompok       : int  1 1 1 1 1 2 2 2 2 2 ...
##  $ Data           : num  0.9 1.2 1.3 1.8 1.1 0.9 1.3 1.5 1.9 1.4 ...

names(Data4)[3] <- "Ulangan"

Data4$Faktor_Varietas<-as.factor(Data4$Faktor_Varietas)
Data4$Faktor_Nitrogen<-as.factor(Data4$Faktor_Nitrogen)
Data4$Ulangan<-as.factor(Data4$Ulangan)
str(Data4)

## 'data.frame':    45 obs. of  4 variables:
##  $ Faktor_Varietas: Factor w/ 3 levels "V1","V2","V3": 1 1 1 1 1 1 1 1 1 1 ...
##  $ Faktor_Nitrogen: Factor w/ 5 levels "N1","N2","N3",..: 1 2 3 4 5 1 2 3 4 5 ...
##  $ Ulangan        : Factor w/ 3 levels "1","2","3": 1 1 1 1 1 2 2 2 2 2 ...
##  $ Data           : num  0.9 1.2 1.3 1.8 1.1 0.9 1.3 1.5 1.9 1.4 ...

Eksplorasi Data

#plot interaksi
interaction.plot(Data4$Faktor_Varietas,Data4$Faktor_Nitrogen, Data4$Data,
                type="l", main="Plot interaksi Varietas dan Nitrogen",xlab="Varietas", 
                ylab="Data", trace.label="Nitrogen", col=1:3)

Analisis Ragam

model_FRAL<-aov(Data~Faktor_Varietas*Faktor_Nitrogen, data=Data4)
summary(model_FRAL)

##                                 Df Sum Sq Mean Sq F value   Pr(>F)    
## Faktor_Varietas                  2 0.1693  0.0847   4.141   0.0258 *  
## Faktor_Nitrogen                  4 2.4902  0.6226  30.451 3.57e-10 ***
## Faktor_Varietas:Faktor_Nitrogen  8 1.0151  0.1269   6.207 9.65e-05 ***
## Residuals                       30 0.6133  0.0204                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Uji Lanjut

library(DescTools)

PostHocTest(model_FRAL, method = 'hsd')

## 
##   Posthoc multiple comparisons of means : Tukey HSD 
##     95% family-wise confidence level
## 
## $Faktor_Varietas
##               diff     lwr.ci       upr.ci   pval    
## V2-V1 -0.126666667 -0.2553795  0.002046134 0.0544 .  
## V3-V1 -0.133333333 -0.2620461 -0.004620533 0.0411 *  
## V3-V2 -0.006666667 -0.1353795  0.122046134 0.9911    
## 
## $Faktor_Nitrogen
##              diff      lwr.ci       upr.ci    pval    
## N2-N1  0.25555556  0.06004490  0.451066208  0.0056 ** 
## N3-N1  0.47777778  0.28226713  0.673288430 6.7e-07 ***
## N4-N1  0.68888889  0.49337824  0.884399541 2.7e-10 ***
## N5-N1  0.48888889  0.29337824  0.684399541 4.3e-07 ***
## N3-N2  0.22222222  0.02671157  0.417732874  0.0197 *  
## N4-N2  0.43333333  0.23782268  0.628843985 4.0e-06 ***
## N5-N2  0.23333333  0.03782268  0.428843985  0.0131 *  
## N4-N3  0.21111111  0.01560046  0.406621763  0.0293 *  
## N5-N3  0.01111111 -0.18439954  0.206621763  0.9998    
## N5-N4 -0.20000000 -0.39551065 -0.004489348  0.0430 *  
## 
## $`Faktor_Varietas:Faktor_Nitrogen`
##                      diff      lwr.ci      upr.ci    pval    
## V2:N1-V1:N1 -1.000000e-01 -0.53021008  0.33021008 0.99987    
## V3:N1-V1:N1 -6.666667e-02 -0.49687675  0.36354342 1.00000    
## V1:N2-V1:N1  3.000000e-01 -0.13021008  0.73021008 0.42613    
## V2:N2-V1:N1  3.333333e-02 -0.39687675  0.46354342 1.00000    
## V3:N2-V1:N1  2.666667e-01 -0.16354342  0.69687675 0.60825    
## V1:N3-V1:N1  4.666667e-01  0.03645658  0.89687675 0.02378 *  
## V2:N3-V1:N1  3.666667e-01 -0.06354342  0.79687675 0.16093    
## V3:N3-V1:N1  4.333333e-01  0.00312325  0.86354342 0.04700 *  
## V1:N4-V1:N1  1.000000e+00  0.56978992  1.43021008 1.4e-07 ***
## V2:N4-V1:N1  4.000000e-01 -0.03021008  0.83021008 0.08922 .  
## V3:N4-V1:N1  5.000000e-01  0.06978992  0.93021008 0.01167 *  
## V1:N5-V1:N1  3.000000e-01 -0.13021008  0.73021008 0.42613    
## V2:N5-V1:N1  7.333333e-01  0.30312325  1.16354342 5.5e-05 ***
## V3:N5-V1:N1  2.666667e-01 -0.16354342  0.69687675 0.60825    
## V3:N1-V2:N1  3.333333e-02 -0.39687675  0.46354342 1.00000    
## V1:N2-V2:N1  4.000000e-01 -0.03021008  0.83021008 0.08922 .  
## V2:N2-V2:N1  1.333333e-01 -0.29687675  0.56354342 0.99707    
## V3:N2-V2:N1  3.666667e-01 -0.06354342  0.79687675 0.16093    
## V1:N3-V2:N1  5.666667e-01  0.13645658  0.99687675 0.00263 ** 
## V2:N3-V2:N1  4.666667e-01  0.03645658  0.89687675 0.02378 *  
## V3:N3-V2:N1  5.333333e-01  0.10312325  0.96354342 0.00559 ** 
## V1:N4-V2:N1  1.100000e+00  0.66978992  1.53021008 1.7e-08 ***
## V2:N4-V2:N1  5.000000e-01  0.06978992  0.93021008 0.01167 *  
## V3:N4-V2:N1  6.000000e-01  0.16978992  1.03021008 0.00123 ** 
## V1:N5-V2:N1  4.000000e-01 -0.03021008  0.83021008 0.08922 .  
## V2:N5-V2:N1  8.333333e-01  0.40312325  1.26354342 5.5e-06 ***
## V3:N5-V2:N1  3.666667e-01 -0.06354342  0.79687675 0.16093    
## V1:N2-V3:N1  3.666667e-01 -0.06354342  0.79687675 0.16093    
## V2:N2-V3:N1  1.000000e-01 -0.33021008  0.53021008 0.99987    
## V3:N2-V3:N1  3.333333e-01 -0.09687675  0.76354342 0.27230    
## V1:N3-V3:N1  5.333333e-01  0.10312325  0.96354342 0.00559 ** 
## V2:N3-V3:N1  4.333333e-01  0.00312325  0.86354342 0.04700 *  
## V3:N3-V3:N1  5.000000e-01  0.06978992  0.93021008 0.01167 *  
## V1:N4-V3:N1  1.066667e+00  0.63645658  1.49687675 3.4e-08 ***
## V2:N4-V3:N1  4.666667e-01  0.03645658  0.89687675 0.02378 *  
## V3:N4-V3:N1  5.666667e-01  0.13645658  0.99687675 0.00263 ** 
## V1:N5-V3:N1  3.666667e-01 -0.06354342  0.79687675 0.16093    
## V2:N5-V3:N1  8.000000e-01  0.36978992  1.23021008 1.2e-05 ***
## V3:N5-V3:N1  3.333333e-01 -0.09687675  0.76354342 0.27230    
## V2:N2-V1:N2 -2.666667e-01 -0.69687675  0.16354342 0.60825    
## V3:N2-V1:N2 -3.333333e-02 -0.46354342  0.39687675 1.00000    
## V1:N3-V1:N2  1.666667e-01 -0.26354342  0.59687675 0.97757    
## V2:N3-V1:N2  6.666667e-02 -0.36354342  0.49687675 1.00000    
## V3:N3-V1:N2  1.333333e-01 -0.29687675  0.56354342 0.99707    
## V1:N4-V1:N2  7.000000e-01  0.26978992  1.13021008 0.00012 ***
## V2:N4-V1:N2  1.000000e-01 -0.33021008  0.53021008 0.99987    
## V3:N4-V1:N2  2.000000e-01 -0.23021008  0.63021008 0.91266    
## V1:N5-V1:N2  2.220446e-16 -0.43021008  0.43021008 1.00000    
## V2:N5-V1:N2  4.333333e-01  0.00312325  0.86354342 0.04700 *  
## V3:N5-V1:N2 -3.333333e-02 -0.46354342  0.39687675 1.00000    
## V3:N2-V2:N2  2.333333e-01 -0.19687675  0.66354342 0.78392    
## V1:N3-V2:N2  4.333333e-01  0.00312325  0.86354342 0.04700 *  
## V2:N3-V2:N2  3.333333e-01 -0.09687675  0.76354342 0.27230    
## V3:N3-V2:N2  4.000000e-01 -0.03021008  0.83021008 0.08922 .  
## V1:N4-V2:N2  9.666667e-01  0.53645658  1.39687675 2.9e-07 ***
## V2:N4-V2:N2  3.666667e-01 -0.06354342  0.79687675 0.16093    
## V3:N4-V2:N2  4.666667e-01  0.03645658  0.89687675 0.02378 *  
## V1:N5-V2:N2  2.666667e-01 -0.16354342  0.69687675 0.60825    
## V2:N5-V2:N2  7.000000e-01  0.26978992  1.13021008 0.00012 ***
## V3:N5-V2:N2  2.333333e-01 -0.19687675  0.66354342 0.78392    
## V1:N3-V3:N2  2.000000e-01 -0.23021008  0.63021008 0.91266    
## V2:N3-V3:N2  1.000000e-01 -0.33021008  0.53021008 0.99987    
## V3:N3-V3:N2  1.666667e-01 -0.26354342  0.59687675 0.97757    
## V1:N4-V3:N2  7.333333e-01  0.30312325  1.16354342 5.5e-05 ***
## V2:N4-V3:N2  1.333333e-01 -0.29687675  0.56354342 0.99707    
## V3:N4-V3:N2  2.333333e-01 -0.19687675  0.66354342 0.78392    
## V1:N5-V3:N2  3.333333e-02 -0.39687675  0.46354342 1.00000    
## V2:N5-V3:N2  4.666667e-01  0.03645658  0.89687675 0.02378 *  
## V3:N5-V3:N2  0.000000e+00 -0.43021008  0.43021008 1.00000    
## V2:N3-V1:N3 -1.000000e-01 -0.53021008  0.33021008 0.99987    
## V3:N3-V1:N3 -3.333333e-02 -0.46354342  0.39687675 1.00000    
## V1:N4-V1:N3  5.333333e-01  0.10312325  0.96354342 0.00559 ** 
## V2:N4-V1:N3 -6.666667e-02 -0.49687675  0.36354342 1.00000    
## V3:N4-V1:N3  3.333333e-02 -0.39687675  0.46354342 1.00000    
## V1:N5-V1:N3 -1.666667e-01 -0.59687675  0.26354342 0.97757    
## V2:N5-V1:N3  2.666667e-01 -0.16354342  0.69687675 0.60825    
## V3:N5-V1:N3 -2.000000e-01 -0.63021008  0.23021008 0.91266    
## V3:N3-V2:N3  6.666667e-02 -0.36354342  0.49687675 1.00000    
## V1:N4-V2:N3  6.333333e-01  0.20312325  1.06354342 0.00057 ***
## V2:N4-V2:N3  3.333333e-02 -0.39687675  0.46354342 1.00000    
## V3:N4-V2:N3  1.333333e-01 -0.29687675  0.56354342 0.99707    
## V1:N5-V2:N3 -6.666667e-02 -0.49687675  0.36354342 1.00000    
## V2:N5-V2:N3  3.666667e-01 -0.06354342  0.79687675 0.16093    
## V3:N5-V2:N3 -1.000000e-01 -0.53021008  0.33021008 0.99987    
## V1:N4-V3:N3  5.666667e-01  0.13645658  0.99687675 0.00263 ** 
## V2:N4-V3:N3 -3.333333e-02 -0.46354342  0.39687675 1.00000    
## V3:N4-V3:N3  6.666667e-02 -0.36354342  0.49687675 1.00000    
## V1:N5-V3:N3 -1.333333e-01 -0.56354342  0.29687675 0.99707    
## V2:N5-V3:N3  3.000000e-01 -0.13021008  0.73021008 0.42613    
## V3:N5-V3:N3 -1.666667e-01 -0.59687675  0.26354342 0.97757    
## V2:N4-V1:N4 -6.000000e-01 -1.03021008 -0.16978992 0.00123 ** 
## V3:N4-V1:N4 -5.000000e-01 -0.93021008 -0.06978992 0.01167 *  
## V1:N5-V1:N4 -7.000000e-01 -1.13021008 -0.26978992 0.00012 ***
## V2:N5-V1:N4 -2.666667e-01 -0.69687675  0.16354342 0.60825    
## V3:N5-V1:N4 -7.333333e-01 -1.16354342 -0.30312325 5.5e-05 ***
## V3:N4-V2:N4  1.000000e-01 -0.33021008  0.53021008 0.99987    
## V1:N5-V2:N4 -1.000000e-01 -0.53021008  0.33021008 0.99987    
## V2:N5-V2:N4  3.333333e-01 -0.09687675  0.76354342 0.27230    
## V3:N5-V2:N4 -1.333333e-01 -0.56354342  0.29687675 0.99707    
## V1:N5-V3:N4 -2.000000e-01 -0.63021008  0.23021008 0.91266    
## V2:N5-V3:N4  2.333333e-01 -0.19687675  0.66354342 0.78392    
## V3:N5-V3:N4 -2.333333e-01 -0.66354342  0.19687675 0.78392    
## V2:N5-V1:N5  4.333333e-01  0.00312325  0.86354342 0.04700 *  
## V3:N5-V1:N5 -3.333333e-02 -0.46354342  0.39687675 1.00000    
## V3:N5-V2:N5 -4.666667e-01 -0.89687675 -0.03645658 0.02378 *  
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Asumsi

plot_model(model_FRAL,type = "diag")

## there are higher-order terms (interactions) in this model
## consider setting type = 'predictor'; see ?vif

## [[1]]

## 
## [[2]]

## `geom_smooth()` using formula = 'y ~ x'

## 
## [[3]]

## 
## [[4]]

## `geom_smooth()` using formula = 'y ~ x'

res <- residuals(model_FRAL)
shapiroTest(res)

## 
## Title:
##  Shapiro - Wilk Normality Test
## 
## Test Results:
##   STATISTIC:
##     W: 0.9712
##   P VALUE:
##     0.3201

leveneTest(Data~Faktor_Varietas*Faktor_Nitrogen*Faktor_Varietas:Faktor_Nitrogen, data=Data4)

## Levene's Test for Homogeneity of Variance (center = median)
##       Df F value Pr(>F)
## group 14  0.6565  0.796
##       30

RAK Faktorial

Data5 <- Data4

names(Data5)[3] <- "Kelompok"

Eksplorasi Data

#plot interaksi
interaction.plot(Data5$Faktor_Varietas,Data5$Faktor_Nitrogen, Data5$Data,
                type="l", main="Plot interaksi Varietas dan Nitrogen",xlab="Varietas", 
                ylab="Data", trace.label="Nitrogen", col=1:3)

ggplot(aes(x = Faktor_Varietas,y = Data, group = Faktor_Nitrogen,colour = Faktor_Nitrogen), data = Data5) + geom_line() +
  facet_wrap(~ Kelompok) + theme_bw()

Analisis Ragam

model_FRAK<-aov(Data~Faktor_Varietas*Faktor_Nitrogen+Kelompok, data=Data5)
summary(model_FRAK)

##                                 Df Sum Sq Mean Sq F value   Pr(>F)    
## Faktor_Varietas                  2 0.1693  0.0847   4.316   0.0232 *  
## Faktor_Nitrogen                  4 2.4902  0.6226  31.732 4.95e-10 ***
## Kelompok                         2 0.0640  0.0320   1.631   0.2138    
## Faktor_Varietas:Faktor_Nitrogen  8 1.0151  0.1269   6.468 8.98e-05 ***
## Residuals                       28 0.5493  0.0196                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Asumsi

plot_model(model_FRAK,type = "diag")

## there are higher-order terms (interactions) in this model
## consider setting type = 'predictor'; see ?vif

## [[1]]

## 
## [[2]]

## `geom_smooth()` using formula = 'y ~ x'

## 
## [[3]]

## 
## [[4]]

## `geom_smooth()` using formula = 'y ~ x'

res <- residuals(model_FRAK)
shapiroTest(res)

## 
## Title:
##  Shapiro - Wilk Normality Test
## 
## Test Results:
##   STATISTIC:
##     W: 0.9614
##   P VALUE:
##     0.1377

leveneTest(Data~Faktor_Varietas*Faktor_Nitrogen*Faktor_Varietas:Faktor_Nitrogen, data=Data5)

## Levene's Test for Homogeneity of Variance (center = median)
##       Df F value Pr(>F)
## group 14  0.6565  0.796
##       30

Uji Lanjut

PostHocTest(model_FRAK, method = 'hsd')

## 
##   Posthoc multiple comparisons of means : Tukey HSD 
##     95% family-wise confidence level
## 
## $Faktor_Varietas
##               diff     lwr.ci       upr.ci   pval    
## V2-V1 -0.126666667 -0.2532188 -0.000114523 0.0498 *  
## V3-V1 -0.133333333 -0.2598855 -0.006781190 0.0374 *  
## V3-V2 -0.006666667 -0.1332188  0.119885477 0.9907    
## 
## $Faktor_Nitrogen
##              diff      lwr.ci       upr.ci    pval    
## N2-N1  0.25555556  0.06318147  0.447929636  0.0050 ** 
## N3-N1  0.47777778  0.28540370  0.670151858 6.8e-07 ***
## N4-N1  0.68888889  0.49651481  0.881262970 3.6e-10 ***
## N5-N1  0.48888889  0.29651481  0.681262970 4.4e-07 ***
## N3-N2  0.22222222  0.02984814  0.414596303  0.0175 *  
## N4-N2  0.43333333  0.24095925  0.625707414 3.9e-06 ***
## N5-N2  0.23333333  0.04095925  0.425707414  0.0116 *  
## N4-N3  0.21111111  0.01873703  0.403485192  0.0261 *  
## N5-N3  0.01111111 -0.18126297  0.203485192  0.9998    
## N5-N4 -0.20000000 -0.39237408 -0.007625919  0.0386 *  
## 
## $Kelompok
##      diff     lwr.ci     upr.ci   pval    
## 2-1  0.00 -0.1265521 0.12655214 1.0000    
## 3-1 -0.08 -0.2065521 0.04655214 0.2775    
## 3-2 -0.08 -0.2065521 0.04655214 0.2775    
## 
## $`Faktor_Varietas:Faktor_Nitrogen`
##                      diff       lwr.ci      upr.ci    pval    
## V2:N1-V1:N1 -1.000000e-01 -0.523901631  0.32390163 0.99982    
## V3:N1-V1:N1 -6.666667e-02 -0.490568297  0.35723496 1.00000    
## V1:N2-V1:N1  3.000000e-01 -0.123901631  0.72390163 0.39679    
## V2:N2-V1:N1  3.333333e-02 -0.390568297  0.45723496 1.00000    
## V3:N2-V1:N1  2.666667e-01 -0.157234964  0.69056830 0.57788    
## V1:N3-V1:N1  4.666667e-01  0.042765036  0.89056830 0.02086 *  
## V2:N3-V1:N1  3.666667e-01 -0.057234964  0.79056830 0.14485    
## V3:N3-V1:N1  4.333333e-01  0.009431703  0.85723496 0.04143 *  
## V1:N4-V1:N1  1.000000e+00  0.576098369  1.42390163 1.6e-07 ***
## V2:N4-V1:N1  4.000000e-01 -0.023901631  0.82390163 0.07933 .  
## V3:N4-V1:N1  5.000000e-01  0.076098369  0.92390163 0.01022 *  
## V1:N5-V1:N1  3.000000e-01 -0.123901631  0.72390163 0.39679    
## V2:N5-V1:N1  7.333333e-01  0.309431703  1.15723496 5.2e-05 ***
## V3:N5-V1:N1  2.666667e-01 -0.157234964  0.69056830 0.57788    
## V3:N1-V2:N1  3.333333e-02 -0.390568297  0.45723496 1.00000    
## V1:N2-V2:N1  4.000000e-01 -0.023901631  0.82390163 0.07933 .  
## V2:N2-V2:N1  1.333333e-01 -0.290568297  0.55723496 0.99628    
## V3:N2-V2:N1  3.666667e-01 -0.057234964  0.79056830 0.14485    
## V1:N3-V2:N1  5.666667e-01  0.142765036  0.99056830 0.00232 ** 
## V2:N3-V2:N1  4.666667e-01  0.042765036  0.89056830 0.02086 *  
## V3:N3-V2:N1  5.333333e-01  0.109431703  0.95723496 0.00491 ** 
## V1:N4-V2:N1  1.100000e+00  0.676098369  1.52390163 2.1e-08 ***
## V2:N4-V2:N1  5.000000e-01  0.076098369  0.92390163 0.01022 *  
## V3:N4-V2:N1  6.000000e-01  0.176098369  1.02390163 0.00109 ** 
## V1:N5-V2:N1  4.000000e-01 -0.023901631  0.82390163 0.07933 .  
## V2:N5-V2:N1  8.333333e-01  0.409431703  1.25723496 5.6e-06 ***
## V3:N5-V2:N1  3.666667e-01 -0.057234964  0.79056830 0.14485    
## V1:N2-V3:N1  3.666667e-01 -0.057234964  0.79056830 0.14485    
## V2:N2-V3:N1  1.000000e-01 -0.323901631  0.52390163 0.99982    
## V3:N2-V3:N1  3.333333e-01 -0.090568297  0.75723496 0.24892    
## V1:N3-V3:N1  5.333333e-01  0.109431703  0.95723496 0.00491 ** 
## V2:N3-V3:N1  4.333333e-01  0.009431703  0.85723496 0.04143 *  
## V3:N3-V3:N1  5.000000e-01  0.076098369  0.92390163 0.01022 *  
## V1:N4-V3:N1  1.066667e+00  0.642765036  1.49056830 4.1e-08 ***
## V2:N4-V3:N1  4.666667e-01  0.042765036  0.89056830 0.02086 *  
## V3:N4-V3:N1  5.666667e-01  0.142765036  0.99056830 0.00232 ** 
## V1:N5-V3:N1  3.666667e-01 -0.057234964  0.79056830 0.14485    
## V2:N5-V3:N1  8.000000e-01  0.376098369  1.22390163 1.2e-05 ***
## V3:N5-V3:N1  3.333333e-01 -0.090568297  0.75723496 0.24892    
## V2:N2-V1:N2 -2.666667e-01 -0.690568297  0.15723496 0.57788    
## V3:N2-V1:N2 -3.333333e-02 -0.457234964  0.39056830 1.00000    
## V1:N3-V1:N2  1.666667e-01 -0.257234964  0.59056830 0.97287    
## V2:N3-V1:N2  6.666667e-02 -0.357234964  0.49056830 1.00000    
## V3:N3-V1:N2  1.333333e-01 -0.290568297  0.55723496 0.99628    
## V1:N4-V1:N2  7.000000e-01  0.276098369  1.12390163 0.00011 ***
## V2:N4-V1:N2  1.000000e-01 -0.323901631  0.52390163 0.99982    
## V3:N4-V1:N2  2.000000e-01 -0.223901631  0.62390163 0.89899    
## V1:N5-V1:N2  4.440892e-16 -0.423901631  0.42390163 1.00000    
## V2:N5-V1:N2  4.333333e-01  0.009431703  0.85723496 0.04143 *  
## V3:N5-V1:N2 -3.333333e-02 -0.457234964  0.39056830 1.00000    
## V3:N2-V2:N2  2.333333e-01 -0.190568297  0.65723496 0.75963    
## V1:N3-V2:N2  4.333333e-01  0.009431703  0.85723496 0.04143 *  
## V2:N3-V2:N2  3.333333e-01 -0.090568297  0.75723496 0.24892    
## V3:N3-V2:N2  4.000000e-01 -0.023901631  0.82390163 0.07933 .  
## V1:N4-V2:N2  9.666667e-01  0.542765036  1.39056830 3.2e-07 ***
## V2:N4-V2:N2  3.666667e-01 -0.057234964  0.79056830 0.14485    
## V3:N4-V2:N2  4.666667e-01  0.042765036  0.89056830 0.02086 *  
## V1:N5-V2:N2  2.666667e-01 -0.157234964  0.69056830 0.57788    
## V2:N5-V2:N2  7.000000e-01  0.276098369  1.12390163 0.00011 ***
## V3:N5-V2:N2  2.333333e-01 -0.190568297  0.65723496 0.75963    
## V1:N3-V3:N2  2.000000e-01 -0.223901631  0.62390163 0.89899    
## V2:N3-V3:N2  1.000000e-01 -0.323901631  0.52390163 0.99982    
## V3:N3-V3:N2  1.666667e-01 -0.257234964  0.59056830 0.97287    
## V1:N4-V3:N2  7.333333e-01  0.309431703  1.15723496 5.2e-05 ***
## V2:N4-V3:N2  1.333333e-01 -0.290568297  0.55723496 0.99628    
## V3:N4-V3:N2  2.333333e-01 -0.190568297  0.65723496 0.75963    
## V1:N5-V3:N2  3.333333e-02 -0.390568297  0.45723496 1.00000    
## V2:N5-V3:N2  4.666667e-01  0.042765036  0.89056830 0.02086 *  
## V3:N5-V3:N2  4.440892e-16 -0.423901631  0.42390163 1.00000    
## V2:N3-V1:N3 -1.000000e-01 -0.523901631  0.32390163 0.99982    
## V3:N3-V1:N3 -3.333333e-02 -0.457234964  0.39056830 1.00000    
## V1:N4-V1:N3  5.333333e-01  0.109431703  0.95723496 0.00491 ** 
## V2:N4-V1:N3 -6.666667e-02 -0.490568297  0.35723496 1.00000    
## V3:N4-V1:N3  3.333333e-02 -0.390568297  0.45723496 1.00000    
## V1:N5-V1:N3 -1.666667e-01 -0.590568297  0.25723496 0.97287    
## V2:N5-V1:N3  2.666667e-01 -0.157234964  0.69056830 0.57788    
## V3:N5-V1:N3 -2.000000e-01 -0.623901631  0.22390163 0.89899    
## V3:N3-V2:N3  6.666667e-02 -0.357234964  0.49056830 1.00000    
## V1:N4-V2:N3  6.333333e-01  0.209431703  1.05723496 0.00051 ***
## V2:N4-V2:N3  3.333333e-02 -0.390568297  0.45723496 1.00000    
## V3:N4-V2:N3  1.333333e-01 -0.290568297  0.55723496 0.99628    
## V1:N5-V2:N3 -6.666667e-02 -0.490568297  0.35723496 1.00000    
## V2:N5-V2:N3  3.666667e-01 -0.057234964  0.79056830 0.14485    
## V3:N5-V2:N3 -1.000000e-01 -0.523901631  0.32390163 0.99982    
## V1:N4-V3:N3  5.666667e-01  0.142765036  0.99056830 0.00232 ** 
## V2:N4-V3:N3 -3.333333e-02 -0.457234964  0.39056830 1.00000    
## V3:N4-V3:N3  6.666667e-02 -0.357234964  0.49056830 1.00000    
## V1:N5-V3:N3 -1.333333e-01 -0.557234964  0.29056830 0.99628    
## V2:N5-V3:N3  3.000000e-01 -0.123901631  0.72390163 0.39679    
## V3:N5-V3:N3 -1.666667e-01 -0.590568297  0.25723496 0.97287    
## V2:N4-V1:N4 -6.000000e-01 -1.023901631 -0.17609837 0.00109 ** 
## V3:N4-V1:N4 -5.000000e-01 -0.923901631 -0.07609837 0.01022 *  
## V1:N5-V1:N4 -7.000000e-01 -1.123901631 -0.27609837 0.00011 ***
## V2:N5-V1:N4 -2.666667e-01 -0.690568297  0.15723496 0.57788    
## V3:N5-V1:N4 -7.333333e-01 -1.157234964 -0.30943170 5.2e-05 ***
## V3:N4-V2:N4  1.000000e-01 -0.323901631  0.52390163 0.99982    
## V1:N5-V2:N4 -1.000000e-01 -0.523901631  0.32390163 0.99982    
## V2:N5-V2:N4  3.333333e-01 -0.090568297  0.75723496 0.24892    
## V3:N5-V2:N4 -1.333333e-01 -0.557234964  0.29056830 0.99628    
## V1:N5-V3:N4 -2.000000e-01 -0.623901631  0.22390163 0.89899    
## V2:N5-V3:N4  2.333333e-01 -0.190568297  0.65723496 0.75963    
## V3:N5-V3:N4 -2.333333e-01 -0.657234964  0.19056830 0.75963    
## V2:N5-V1:N5  4.333333e-01  0.009431703  0.85723496 0.04143 *  
## V3:N5-V1:N5 -3.333333e-02 -0.457234964  0.39056830 1.00000    
## V3:N5-V2:N5 -4.666667e-01 -0.890568297 -0.04276504 0.02086 *  
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1