Rancangan Split Plot

2024-11-05

Data yang digunakan pada contoh dapat diunduh disini

Split Plot RAL

Bobot<-read.csv("D:/IPB/STA1512/STA1512/Prak. By Fida/Data Pertemuan 10.csv")
str(Bobot)

## 'data.frame':    27 obs. of  4 variables:
##  $ Pukan     : chr  "k1" "k1" "k1" "k2" ...
##  $ Benih     : chr  "j1" "j2" "j3" "j1" ...
##  $ Ulangan   : int  1 1 1 1 1 1 1 1 1 2 ...
##  $ Bobot_Biji: num  63.8 66.4 67.8 65.3 68 ...

Bobot$Pukan<-as.factor(Bobot$Pukan)
Bobot$Benih<-as.factor(Bobot$Benih)
Bobot$Ulangan<-as.factor(Bobot$Ulangan)
str(Bobot)

## 'data.frame':    27 obs. of  4 variables:
##  $ Pukan     : Factor w/ 3 levels "k1","k2","k3": 1 1 1 2 2 2 3 3 3 1 ...
##  $ Benih     : Factor w/ 3 levels "j1","j2","j3": 1 2 3 1 2 3 1 2 3 1 ...
##  $ Ulangan   : Factor w/ 3 levels "1","2","3": 1 1 1 1 1 1 1 1 1 2 ...
##  $ Bobot_Biji: num  63.8 66.4 67.8 65.3 68 ...

library(lme4)

## Loading required package: Matrix

library(agricolae)
library(dplyr)

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

aovSPlot1<-aov(Bobot_Biji~Pukan*Benih+Error(Ulangan:Pukan),data=Bobot)

## Warning in aov(Bobot_Biji ~ Pukan * Benih + Error(Ulangan:Pukan), data =
## Bobot): Error() model is singular

summary(aovSPlot1)

## 
## Error: Ulangan:Pukan
##           Df Sum Sq Mean Sq F value  Pr(>F)   
## Pukan      2 20.873  10.436   18.46 0.00273 **
## Residuals  6  3.392   0.565                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Error: Within
##             Df Sum Sq Mean Sq F value  Pr(>F)   
## Benih        2 16.418   8.209   10.79 0.00208 **
## Pukan:Benih  4 11.345   2.836    3.73 0.03395 * 
## Residuals   12  9.125   0.760                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

library(ggplot2)
ggplot2::ggplot(aes(x = Benih, y = Bobot_Biji, group = Pukan, colour = Pukan), data = Bobot) + geom_line()+ theme_bw()

ggplot2::ggplot(aes(x = Benih, y = Bobot_Biji, group = Pukan, colour = Pukan), data = Bobot) + geom_line() + 
  facet_wrap(~ Ulangan) + theme_bw()

Split Plot RAK

aovSPlot2<-aov(Bobot_Biji~Pukan*Benih+Ulangan+Error(Ulangan:Pukan),data=Bobot)

## Warning in aov(Bobot_Biji ~ Pukan * Benih + Ulangan + Error(Ulangan:Pukan), :
## Error() model is singular

summary(aovSPlot2)

## 
## Error: Ulangan:Pukan
##           Df Sum Sq Mean Sq F value Pr(>F)  
## Pukan      2 20.873  10.436  14.978 0.0139 *
## Ulangan    2  0.605   0.303   0.434 0.6751  
## Residuals  4  2.787   0.697                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Error: Within
##             Df Sum Sq Mean Sq F value  Pr(>F)   
## Benih        2 16.418   8.209   10.79 0.00208 **
## Pukan:Benih  4 11.345   2.836    3.73 0.03395 * 
## Residuals   12  9.125   0.760                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

sp <- with(Bobot,sp.plot(block=Ulangan, pplot=Pukan, splot=Benih, Y=Bobot_Biji))

## 
## ANALYSIS SPLIT PLOT:  Bobot_Biji 
## Class level information
## 
## Pukan    :  k1 k2 k3 
## Benih    :  j1 j2 j3 
## Ulangan  :  1 2 3 
## 
## Number of observations:  27 
## 
## Analysis of Variance Table
## 
## Response: Bobot_Biji
##             Df  Sum Sq Mean Sq F value   Pr(>F)   
## Ulangan      2  0.6050  0.3025  0.3978 0.680332   
## Pukan        2 20.8727 10.4364 14.9782 0.013876 * 
## Ea           4  2.7871  0.6968                    
## Benih        2 16.4178  8.2089 10.7947 0.002079 **
## Pukan:Benih  4 11.3448  2.8362  3.7296 0.033947 * 
## Eb          12  9.1255  0.7605                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## cv(a) = 1.3 %, cv(b) = 1.3 %, Mean = 65.84037

Uji Lanjut

Prep_df = sp$gl.a
Prep_df

## [1] 4

Temp_df = sp$gl.b
Temp_df

## [1] 12

Prep_JKG = sp$Ea
Prep_JKG

## [1] 0.6967704

Temp_JKG = sp$Eb
Temp_JKG

## [1] 0.7604574

uj <- with(Bobot,LSD.test(Bobot_Biji,
                         Pukan,
                         DFerror = Prep_df, 
                         MSerror = Prep_JKG,
                         console = TRUE))

## 
## Study: Bobot_Biji ~ Pukan
## 
## LSD t Test for Bobot_Biji 
## 
## Mean Square Error:  0.6967704 
## 
## Pukan,  means and individual ( 95 %) CI
## 
##    Bobot_Biji      std r        se      LCL      UCL   Min   Max   Q25   Q50
## k1   65.71222 1.239100 9 0.2782426 64.93970 66.48475 63.83 67.83 65.00 65.83
## k2   66.97556 1.495895 9 0.2782426 66.20303 67.74808 65.00 69.20 65.83 66.67
## k3   64.83333 1.123365 9 0.2782426 64.06081 65.60586 63.00 66.50 64.17 65.00
##      Q75
## k1 66.43
## k2 68.00
## k3 65.50
## 
## Alpha: 0.05 ; DF Error: 4
## Critical Value of t: 2.776445 
## 
## least Significant Difference: 1.092516 
## 
## Treatments with the same letter are not significantly different.
## 
##    Bobot_Biji groups
## k2   66.97556      a
## k1   65.71222      b
## k3   64.83333      b

uj2 <- with(Bobot,LSD.test(Bobot_Biji,
                          Benih,
                          DFerror = Prep_df, 
                          MSerror = Prep_JKG,
                          console = TRUE))

## 
## Study: Bobot_Biji ~ Benih
## 
## LSD t Test for Bobot_Biji 
## 
## Mean Square Error:  0.6967704 
## 
## Benih,  means and individual ( 95 %) CI
## 
##    Bobot_Biji       std r        se      LCL      UCL   Min   Max   Q25   Q50
## j1   65.11000 0.5890246 9 0.2782426 64.33747 65.88253 63.83 65.83 65.00 65.33
## j2   66.92111 1.4104294 9 0.2782426 66.14859 67.69364 65.00 69.20 65.83 66.50
## j3   65.49000 1.8043351 9 0.2782426 64.71747 66.26253 63.00 67.83 64.17 65.83
##      Q75
## j1 65.50
## j2 68.00
## j3 66.67
## 
## Alpha: 0.05 ; DF Error: 4
## Critical Value of t: 2.776445 
## 
## least Significant Difference: 1.092516 
## 
## Treatments with the same letter are not significantly different.
## 
##    Bobot_Biji groups
## j2   66.92111      a
## j3   65.49000      b
## j1   65.11000      b

uj3 <- with(Bobot,LSD.test(Bobot_Biji,
                          interaction(Pukan,Benih),
                          DFerror = Prep_df, 
                          MSerror = Prep_JKG,
                          console = TRUE))

## 
## Study: Bobot_Biji ~ interaction(Pukan, Benih)
## 
## LSD t Test for Bobot_Biji 
## 
## Mean Square Error:  0.6967704 
## 
## interaction(Pukan, Benih),  means and individual ( 95 %) CI
## 
##       Bobot_Biji       std r        se      LCL      UCL   Min   Max    Q25
## k1.j1   64.77667 0.8571075 3 0.4819303 63.43861 66.11472 63.83 65.50 64.415
## k1.j2   66.36333 0.5033223 3 0.4819303 65.02528 67.70139 65.83 66.83 66.130
## k1.j3   65.99667 1.7559423 3 0.4819303 64.65861 67.33472 64.33 67.83 65.080
## k2.j1   65.38667 0.4178915 3 0.4819303 64.04861 66.72472 65.00 65.83 65.165
## k2.j2   68.62333 0.6013596 3 0.4819303 67.28528 69.96139 68.00 69.20 68.335
## k2.j3   66.91667 0.7414400 3 0.4819303 65.57861 68.25472 66.33 67.75 66.500
## k3.j1   65.16667 0.4384442 3 0.4819303 63.82861 66.50472 64.67 65.50 65.000
## k3.j2   65.77667 0.7514209 3 0.4819303 64.43861 67.11472 65.00 66.50 65.415
## k3.j3   63.55667 0.5870548 3 0.4819303 62.21861 64.89472 63.00 64.17 63.250
##         Q50    Q75
## k1.j1 65.00 65.250
## k1.j2 66.43 66.630
## k1.j3 65.83 66.830
## k2.j1 65.33 65.580
## k2.j2 68.67 68.935
## k2.j3 66.67 67.210
## k3.j1 65.33 65.415
## k3.j2 65.83 66.165
## k3.j3 63.50 63.835
## 
## Alpha: 0.05 ; DF Error: 4
## Critical Value of t: 2.776445 
## 
## least Significant Difference: 1.892293 
## 
## Treatments with the same letter are not significantly different.
## 
##       Bobot_Biji groups
## k2.j2   68.62333      a
## k2.j3   66.91667     ab
## k1.j2   66.36333     bc
## k1.j3   65.99667     bc
## k3.j2   65.77667     bc
## k2.j1   65.38667    bcd
## k3.j1   65.16667    bcd
## k1.j1   64.77667     cd
## k3.j3   63.55667      d