Loading required packages

library(agricolae)
library(ExpDes)
## 
## Attaching package: 'ExpDes'
## The following objects are masked from 'package:agricolae':
## 
##     lastC, order.group, tapply.stat

Reading and preparing the data

#RCBD without sub-sample
rcbd <- read.csv("rcbd.csv") 
rcbd$Trt <- factor(rcbd$TRT)
rcbd$Block <- factor(rcbd$PLOT)

#RCBD with sub-samples
rcbdsub <- read.csv("rcbdsub.csv") 
rcbdsub$Trt <- factor(rcbdsub$TRT)
rcbdsub$Block <- factor(rcbdsub$BLOCK)

#Latin square design
additives <- read.csv("additives.csv")
additives$Driver <- factor(additives$Driver)
additives$Car <- factor(additives$Car)
additives$Treatment <- additives$Trt

ANOVA for RCBD without sub-samples

out1 <- aov(SEEDLINGS ~ Trt + Block,
            data = rcbd) #default aov () function
summary(out1)
##             Df Sum Sq Mean Sq F value   Pr(>F)    
## Trt          2   1832   916.0  211.38 2.74e-06 ***
## Block        3    438   146.0   33.69 0.000377 ***
## Residuals    6     26     4.3                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
HSD.test(out1, "Trt", console =TRUE)#post-hoc for Trt effect
## 
## Study: out1 ~ "Trt"
## 
## HSD Test for SEEDLINGS 
## 
## Mean Square Error:  4.333333 
## 
## Trt,  means
## 
##   SEEDLINGS      std r Min Max
## 1        58 7.831560 4  48  66
## 2        87 7.788881 4  78  94
## 3        80 5.715476 4  72  85
## 
## Alpha: 0.05 ; DF Error: 6 
## Critical Value of Studentized Range: 4.339195 
## 
## Minimun Significant Difference: 4.516378 
## 
## Treatments with the same letter are not significantly different.
## 
##   SEEDLINGS groups
## 2        87      a
## 3        80      b
## 1        58      c
# Using the rbd() function in the ExpDes package
with(rcbd, rbd(Trt, Block, SEEDLINGS,
               quali=TRUE,
               mcomp="tukey")) 
## ------------------------------------------------------------------------
## Analysis of Variance Table
## ------------------------------------------------------------------------
##            DF   SS     MS      Fc      Pr>Fc
## Treatament  2 1832 916.00 211.385 0.00000274
## Block       3  438 146.00  33.692 0.00037669
## Residuals   6   26   4.33                   
## Total      11 2296                          
## ------------------------------------------------------------------------
## CV = 2.78 %
## 
## ------------------------------------------------------------------------
## Shapiro-Wilk normality test
## p-value:  0.5130488 
## According to Shapiro-Wilk normality test at 5% of significance, residuals can be considered normal.
## ------------------------------------------------------------------------
## 
## ------------------------------------------------------------------------
## Homogeneity of variances test
## p-value:  0.7764982 
## According to the test of oneillmathews at 5% of significance, the variances can be considered homocedastic.
## ------------------------------------------------------------------------
## 
## Tukey's test
## ------------------------------------------------------------------------
## Groups Treatments Means
## a     2   87 
##  b    3   80 
##   c   1   58 
## ------------------------------------------------------------------------

ANOVA for RCBD with sub-samples

out2 <- aov(worms ~ Trt + Block + Trt:Block,
            data = rcbdsub)
summary(out2)
##             Df Sum Sq Mean Sq F value   Pr(>F)    
## Trt          2  293.4  146.72  16.113 5.28e-06 ***
## Block        4  151.2   37.79   4.150  0.00603 ** 
## Trt:Block    8  196.2   24.53   2.694  0.01641 *  
## Residuals   45  409.8    9.11                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
HSD.test(out2, "Trt", console = TRUE)
## 
## Study: out2 ~ "Trt"
## 
## HSD Test for worms 
## 
## Mean Square Error:  9.105556 
## 
## Trt,  means
## 
##         worms      std  r Min Max
## c        5.25 2.935715 20   0  12
## control  9.70 5.068998 20   4  22
## s        4.80 2.353050 20   1   9
## 
## Alpha: 0.05 ; DF Error: 45 
## Critical Value of Studentized Range: 3.427507 
## 
## Minimun Significant Difference: 2.312686 
## 
## Treatments with the same letter are not significantly different.
## 
##         worms groups
## control  9.70      a
## c        5.25      b
## s        4.80      b

ANOVA for Latin Square Design

out3 <- aov(Reduction ~ Treatment + Driver + Car,
            data = additives)
anova(out3)
## Analysis of Variance Table
## 
## Response: Reduction
##           Df Sum Sq Mean Sq F value   Pr(>F)   
## Treatment  3     40  13.333     2.5 0.156490   
## Driver     3    216  72.000    13.5 0.004466 **
## Car        3     24   8.000     1.5 0.307174   
## Residuals  6     32   5.333                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#Using the latsd() function in the ExpDes package
with(additives, latsd(Treatment, Driver, Car, Reduction,
                      quali = TRUE,
                      mcomp = "tukey"))
## ------------------------------------------------------------------------
## Analysis of Variance Table
## ------------------------------------------------------------------------
##            DF  SS     MS   Fc    Pr>Fc
## Treatament  3  40 13.333  2.5 0.156490
## Row         3 216 72.000 13.5 0.004466
## Column      3  24  8.000  1.5 0.307174
## Residuals   6  32  5.333              
## Total      15 312                     
## ------------------------------------------------------------------------
## CV = 11.55 %
## 
## ------------------------------------------------------------------------
## Shapiro-Wilk normality test
## p-value:  0.3260439 
## According to Shapiro-Wilk normality test at 5% of significance, residuals can be considered normal.
## ------------------------------------------------------------------------
## 
## According to the F test, the means can not be considered distinct.
##   Levels Means
## 1      A    18
## 2      B    22
## 3      C    21
## 4      D    19
## ------------------------------------------------------------------------