Homework3 - Questions 2,3,4 and 5
Clemen de oliveira
October 6, 2019
Question 2 # Importing data
setwd("C:/Users/clemendeoliveira/Desktop/Homework3")
data=read.table("quest2.txt",header = T,check.names = F)
str(data)## 'data.frame': 45 obs. of 4 variables:
## $ Fungicide: Factor w/ 3 levels "A","B","C": 1 1 1 1 1 2 2 2 2 2 ...
## $ Race : int 1 2 3 4 5 1 2 3 4 5 ...
## $ block : int 1 1 1 1 1 1 1 1 1 1 ...
## $ ndvi : num 0.22 0.52 0.62 0.92 0.42 0.22 0.42 0.62 0.83 0.9 ...data$Fungicide = as.factor(data$Fungicide)
data$Race = as.factor(data$Race)
data$block = as.factor(data$block)
summary(data)## Fungicide Race block ndvi
## A:15 1:9 1:15 Min. :0.0200
## B:15 2:9 2:15 1st Qu.:0.3200
## C:15 3:9 3:15 Median :0.6200
## 4:9 Mean :0.5522
## 5:9 3rd Qu.:0.7200
## Max. :0.9700attach(data)
data## Fungicide Race block ndvi
## 1 A 1 1 0.22
## 2 A 2 1 0.52
## 3 A 3 1 0.62
## 4 A 4 1 0.92
## 5 A 5 1 0.42
## 6 B 1 1 0.22
## 7 B 2 1 0.42
## 8 B 3 1 0.62
## 9 B 4 1 0.83
## 10 B 5 1 0.90
## 11 C 1 1 0.22
## 12 C 2 1 0.72
## 13 C 3 1 0.62
## 14 C 4 1 0.72
## 15 C 5 1 0.52
## 16 A 1 2 0.22
## 17 A 2 2 0.62
## 18 A 3 2 0.82
## 19 A 4 2 0.97
## 20 A 5 2 0.72
## 21 B 1 2 0.12
## 22 B 2 2 0.22
## 23 B 3 2 0.82
## 24 B 4 2 0.62
## 25 B 5 2 0.92
## 26 C 1 2 0.32
## 27 C 2 2 0.52
## 28 C 3 2 0.72
## 29 C 4 2 0.82
## 30 C 5 2 0.42
## 31 A 1 3 0.32
## 32 A 2 3 0.52
## 33 A 3 3 0.72
## 34 A 4 3 0.93
## 35 A 5 3 0.52
## 36 B 1 3 0.12
## 37 B 2 3 0.22
## 38 B 3 3 0.42
## 39 B 4 3 0.52
## 40 B 5 3 0.82
## 41 C 1 3 0.02
## 42 C 2 3 0.32
## 43 C 3 3 0.72
## 44 C 4 3 0.72
## 45 C 5 3 0.62Including histogram and boxplot
hist(data$ndvi)
boxplot(data$ndvi~data$Fungicide)
boxplot(data$ndvi~data$Race)
Anova
library(agricolae)## Warning: package 'agricolae' was built under R version 3.4.4library(lsmeans)## Warning: package 'lsmeans' was built under R version 3.4.4## Loading required package: emmeans## The 'lsmeans' package is now basically a front end for 'emmeans'.
## Users are encouraged to switch the rest of the way.
## See help('transition') for more information, including how to
## convert old 'lsmeans' objects and scripts to work with 'emmeans'.outAOV<-aov(ndvi~block+Race+Fungicide+Race*Fungicide,data = data)
anova(outAOV)## Analysis of Variance Table
##
## Response: ndvi
## Df Sum Sq Mean Sq F value Pr(>F)
## block 2 0.06412 0.03206 2.5926 0.092684 .
## Race 4 1.92431 0.48108 38.9002 4.736e-11 ***
## Fungicide 2 0.06179 0.03090 2.4982 0.100385
## Race:Fungicide 8 0.45788 0.05723 4.6280 0.001103 **
## Residuals 28 0.34628 0.01237
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Test LSD
outfactorial<-LSD.test(outAOV, c ("Race","Fungicide"), main = "ndvi~block+Race+Fungicide+Race*Fungicide", console=TRUE)##
## Study: ndvi~block+Race+Fungicide+Race*Fungicide
##
## LSD t Test for ndvi
##
## Mean Square Error: 0.01236698
##
## Race:Fungicide, means and individual ( 95 %) CI
##
## ndvi std r LCL UCL Min Max
## 1:A 0.2533333 0.05773503 3 0.12181462 0.3848520 0.22 0.32
## 1:B 0.1533333 0.05773503 3 0.02181462 0.2848520 0.12 0.22
## 1:C 0.1866667 0.15275252 3 0.05514795 0.3181854 0.02 0.32
## 2:A 0.5533333 0.05773503 3 0.42181462 0.6848520 0.52 0.62
## 2:B 0.2866667 0.11547005 3 0.15514795 0.4181854 0.22 0.42
## 2:C 0.5200000 0.20000000 3 0.38848129 0.6515187 0.32 0.72
## 3:A 0.7200000 0.10000000 3 0.58848129 0.8515187 0.62 0.82
## 3:B 0.6200000 0.20000000 3 0.48848129 0.7515187 0.42 0.82
## 3:C 0.6866667 0.05773503 3 0.55514795 0.8181854 0.62 0.72
## 4:A 0.9400000 0.02645751 3 0.80848129 1.0715187 0.92 0.97
## 4:B 0.6566667 0.15821926 3 0.52514795 0.7881854 0.52 0.83
## 4:C 0.7533333 0.05773503 3 0.62181462 0.8848520 0.72 0.82
## 5:A 0.5533333 0.15275252 3 0.42181462 0.6848520 0.42 0.72
## 5:B 0.8800000 0.05291503 3 0.74848129 1.0115187 0.82 0.92
## 5:C 0.5200000 0.10000000 3 0.38848129 0.6515187 0.42 0.62
##
## Alpha: 0.05 ; DF Error: 28
## Critical Value of t: 2.048407
##
## least Significant Difference: 0.1859955
##
## Treatments with the same letter are not significantly different.
##
## ndvi groups
## 4:A 0.9400000 a
## 5:B 0.8800000 ab
## 4:C 0.7533333 bc
## 3:A 0.7200000 bcd
## 3:C 0.6866667 cde
## 4:B 0.6566667 cde
## 3:B 0.6200000 cde
## 2:A 0.5533333 de
## 5:A 0.5533333 de
## 2:C 0.5200000 e
## 5:C 0.5200000 e
## 2:B 0.2866667 f
## 1:A 0.2533333 f
## 1:C 0.1866667 f
## 1:B 0.1533333 foutfactorial## $statistics
## MSerror Df Mean CV t.value LSD
## 0.01236698 28 0.5522222 20.13808 2.048407 0.1859955
##
## $parameters
## test p.ajusted name.t ntr alpha
## Fisher-LSD none Race:Fungicide 15 0.05
##
## $means
## ndvi std r LCL UCL Min Max Q25 Q50 Q75
## 1:A 0.2533333 0.05773503 3 0.12181462 0.3848520 0.22 0.32 0.220 0.22 0.270
## 1:B 0.1533333 0.05773503 3 0.02181462 0.2848520 0.12 0.22 0.120 0.12 0.170
## 1:C 0.1866667 0.15275252 3 0.05514795 0.3181854 0.02 0.32 0.120 0.22 0.270
## 2:A 0.5533333 0.05773503 3 0.42181462 0.6848520 0.52 0.62 0.520 0.52 0.570
## 2:B 0.2866667 0.11547005 3 0.15514795 0.4181854 0.22 0.42 0.220 0.22 0.320
## 2:C 0.5200000 0.20000000 3 0.38848129 0.6515187 0.32 0.72 0.420 0.52 0.620
## 3:A 0.7200000 0.10000000 3 0.58848129 0.8515187 0.62 0.82 0.670 0.72 0.770
## 3:B 0.6200000 0.20000000 3 0.48848129 0.7515187 0.42 0.82 0.520 0.62 0.720
## 3:C 0.6866667 0.05773503 3 0.55514795 0.8181854 0.62 0.72 0.670 0.72 0.720
## 4:A 0.9400000 0.02645751 3 0.80848129 1.0715187 0.92 0.97 0.925 0.93 0.950
## 4:B 0.6566667 0.15821926 3 0.52514795 0.7881854 0.52 0.83 0.570 0.62 0.725
## 4:C 0.7533333 0.05773503 3 0.62181462 0.8848520 0.72 0.82 0.720 0.72 0.770
## 5:A 0.5533333 0.15275252 3 0.42181462 0.6848520 0.42 0.72 0.470 0.52 0.620
## 5:B 0.8800000 0.05291503 3 0.74848129 1.0115187 0.82 0.92 0.860 0.90 0.910
## 5:C 0.5200000 0.10000000 3 0.38848129 0.6515187 0.42 0.62 0.470 0.52 0.570
##
## $comparison
## NULL
##
## $groups
## ndvi groups
## 4:A 0.9400000 a
## 5:B 0.8800000 ab
## 4:C 0.7533333 bc
## 3:A 0.7200000 bcd
## 3:C 0.6866667 cde
## 4:B 0.6566667 cde
## 3:B 0.6200000 cde
## 2:A 0.5533333 de
## 5:A 0.5533333 de
## 2:C 0.5200000 e
## 5:C 0.5200000 e
## 2:B 0.2866667 f
## 1:A 0.2533333 f
## 1:C 0.1866667 f
## 1:B 0.1533333 f
##
## attr(,"class")
## [1] "group"Test tukey (HSD)
library(agricolae)
outHSD<-HSD.test(outAOV, c ("Race","Fungicide"), main = "ndvi~block+Race+Fungicide+Race*Fungicide", console=TRUE)##
## Study: ndvi~block+Race+Fungicide+Race*Fungicide
##
## HSD Test for ndvi
##
## Mean Square Error: 0.01236698
##
## Race:Fungicide, means
##
## ndvi std r Min Max
## 1:A 0.2533333 0.05773503 3 0.22 0.32
## 1:B 0.1533333 0.05773503 3 0.12 0.22
## 1:C 0.1866667 0.15275252 3 0.02 0.32
## 2:A 0.5533333 0.05773503 3 0.52 0.62
## 2:B 0.2866667 0.11547005 3 0.22 0.42
## 2:C 0.5200000 0.20000000 3 0.32 0.72
## 3:A 0.7200000 0.10000000 3 0.62 0.82
## 3:B 0.6200000 0.20000000 3 0.42 0.82
## 3:C 0.6866667 0.05773503 3 0.62 0.72
## 4:A 0.9400000 0.02645751 3 0.92 0.97
## 4:B 0.6566667 0.15821926 3 0.52 0.83
## 4:C 0.7533333 0.05773503 3 0.72 0.82
## 5:A 0.5533333 0.15275252 3 0.42 0.72
## 5:B 0.8800000 0.05291503 3 0.82 0.92
## 5:C 0.5200000 0.10000000 3 0.42 0.62
##
## Alpha: 0.05 ; DF Error: 28
## Critical Value of Studentized Range: 5.241876
##
## Minimun Significant Difference: 0.3365565
##
## Treatments with the same letter are not significantly different.
##
## ndvi groups
## 4:A 0.9400000 a
## 5:B 0.8800000 ab
## 4:C 0.7533333 abc
## 3:A 0.7200000 abc
## 3:C 0.6866667 abc
## 4:B 0.6566667 abc
## 3:B 0.6200000 abcd
## 2:A 0.5533333 bcde
## 5:A 0.5533333 bcde
## 2:C 0.5200000 cdef
## 5:C 0.5200000 cdef
## 2:B 0.2866667 defg
## 1:A 0.2533333 efg
## 1:C 0.1866667 fg
## 1:B 0.1533333 goutHSD## $statistics
## MSerror Df Mean CV MSD
## 0.01236698 28 0.5522222 20.13808 0.3365565
##
## $parameters
## test name.t ntr StudentizedRange alpha
## Tukey Race:Fungicide 15 5.241876 0.05
##
## $means
## ndvi std r Min Max Q25 Q50 Q75
## 1:A 0.2533333 0.05773503 3 0.22 0.32 0.220 0.22 0.270
## 1:B 0.1533333 0.05773503 3 0.12 0.22 0.120 0.12 0.170
## 1:C 0.1866667 0.15275252 3 0.02 0.32 0.120 0.22 0.270
## 2:A 0.5533333 0.05773503 3 0.52 0.62 0.520 0.52 0.570
## 2:B 0.2866667 0.11547005 3 0.22 0.42 0.220 0.22 0.320
## 2:C 0.5200000 0.20000000 3 0.32 0.72 0.420 0.52 0.620
## 3:A 0.7200000 0.10000000 3 0.62 0.82 0.670 0.72 0.770
## 3:B 0.6200000 0.20000000 3 0.42 0.82 0.520 0.62 0.720
## 3:C 0.6866667 0.05773503 3 0.62 0.72 0.670 0.72 0.720
## 4:A 0.9400000 0.02645751 3 0.92 0.97 0.925 0.93 0.950
## 4:B 0.6566667 0.15821926 3 0.52 0.83 0.570 0.62 0.725
## 4:C 0.7533333 0.05773503 3 0.72 0.82 0.720 0.72 0.770
## 5:A 0.5533333 0.15275252 3 0.42 0.72 0.470 0.52 0.620
## 5:B 0.8800000 0.05291503 3 0.82 0.92 0.860 0.90 0.910
## 5:C 0.5200000 0.10000000 3 0.42 0.62 0.470 0.52 0.570
##
## $comparison
## NULL
##
## $groups
## ndvi groups
## 4:A 0.9400000 a
## 5:B 0.8800000 ab
## 4:C 0.7533333 abc
## 3:A 0.7200000 abc
## 3:C 0.6866667 abc
## 4:B 0.6566667 abc
## 3:B 0.6200000 abcd
## 2:A 0.5533333 bcde
## 5:A 0.5533333 bcde
## 2:C 0.5200000 cdef
## 5:C 0.5200000 cdef
## 2:B 0.2866667 defg
## 1:A 0.2533333 efg
## 1:C 0.1866667 fg
## 1:B 0.1533333 g
##
## attr(,"class")
## [1] "group"Computing graph bar
library(ggplot2)
graph<-lsmeans(outAOV, ~Race*Fungicide, adjust='Tukey')
graph<-summary(graph)
graph$Race <- factor(graph$Race, levels = c( "1","2","3","4","5"))
ggplot(graph, aes(x=Race, y=lsmean, fill=Fungicide)) +
geom_bar(position=position_dodge(0.9), stat="identity",
colour="black", # Use black outlines
size=.3) + scale_fill_brewer() +
geom_errorbar(aes(ymin=lsmean-SE, ymax=lsmean+SE),
size=.5, # Thinner lines
colour="black",
width=.2,
position=position_dodge(.9)) +
xlab("Race") +
ylab("NDVI") +
ggtitle("ndvi homework3") +
annotate("text",x=0.65,y=0.4,label="a", size=6)+
annotate("text",x=1,y=0.4,label="ab", size=6)+
annotate("text",x=1.4,y=0.4,label="abc", size=6)+
annotate("text",x=1.78,y=0.7,label="abc", size=6)+
annotate("text",x=2,y=0.5,label="abc", size=6)+
annotate("text",x=2.3,y=0.7,label="abc", size=6)+
annotate("text",x=2.7,y=0.95,label="abcd", size=6)+
annotate("text",x=3,y=0.75,label="bcde", size=6)+
annotate("text",x=3.3,y=0.85,label="bcde", size=6)+
annotate("text",x=3.6,y=1.05,label="cdef", size=6)+
annotate("text",x=4,y=0.8,label="cdef", size=6)+
annotate("text",x=4.3,y=0.9,label="defg", size=6)+
annotate("text",x=4.3,y=0.8,label="efg", size=6)+
annotate("text",x=5,y=1,label="fg", size=6)+
annotate("text",x=5.2,y=0.74,label=" g", size=6)+
theme_bw() +
theme(axis.text.x = element_text(angle = 45, hjust = 1))+
theme(axis.title=element_text( size = rel(2.1) , color="black")) +
theme(axis.text = element_text(colour = "black", size="20")) +
theme(legend.title = element_text(size = "14"))+
theme(legend.position = "none")+
theme(plot.title = element_text(size = rel(2)))
Question 3
setwd("C:/Users/clemendeoliveira/Desktop/Homework3")
data3=read.table("quest3.txt",header = T,check.names = F)
str(data3)## 'data.frame': 90 obs. of 5 variables:
## $ fungicide: Factor w/ 3 levels "A","B","C": 1 1 1 1 1 2 2 2 2 2 ...
## $ race : int 1 2 3 4 5 1 2 3 4 5 ...
## $ block : int 1 1 1 1 1 1 1 1 1 1 ...
## $ year : int 1 1 1 1 1 1 1 1 1 1 ...
## $ ndvi : num 0.22 0.52 0.62 0.92 0.42 0.22 0.42 0.62 0.83 0.9 ...data3$race=as.factor(data3$race)
data3$fungicide=as.factor(data3$fungicide)
data3$block = as.factor(data3$block)
data3$year= as.factor(data3$year)
summary(data3)## fungicide race block year ndvi
## A:30 1:18 1:30 1:45 Min. :0.0200
## B:30 2:18 2:30 2:45 1st Qu.:0.3200
## C:30 3:18 3:30 Median :0.5300
## 4:18 Mean :0.5176
## 5:18 3rd Qu.:0.7200
## Max. :0.9700attach(data3) ## The following objects are masked from data:
##
## block, ndvidata3## fungicide race block year ndvi
## 1 A 1 1 1 0.22
## 2 A 2 1 1 0.52
## 3 A 3 1 1 0.62
## 4 A 4 1 1 0.92
## 5 A 5 1 1 0.42
## 6 B 1 1 1 0.22
## 7 B 2 1 1 0.42
## 8 B 3 1 1 0.62
## 9 B 4 1 1 0.83
## 10 B 5 1 1 0.90
## 11 C 1 1 1 0.22
## 12 C 2 1 1 0.72
## 13 C 3 1 1 0.62
## 14 C 4 1 1 0.72
## 15 C 5 1 1 0.52
## 16 A 1 2 1 0.22
## 17 A 2 2 1 0.62
## 18 A 3 2 1 0.82
## 19 A 4 2 1 0.97
## 20 A 5 2 1 0.72
## 21 B 1 2 1 0.12
## 22 B 2 2 1 0.22
## 23 B 3 2 1 0.82
## 24 B 4 2 1 0.62
## 25 B 5 2 1 0.92
## 26 C 1 2 1 0.32
## 27 C 2 2 1 0.52
## 28 C 3 2 1 0.72
## 29 C 4 2 1 0.82
## 30 C 5 2 1 0.42
## 31 A 1 3 1 0.32
## 32 A 2 3 1 0.52
## 33 A 3 3 1 0.72
## 34 A 4 3 1 0.93
## 35 A 5 3 1 0.52
## 36 B 1 3 1 0.12
## 37 B 2 3 1 0.22
## 38 B 3 3 1 0.42
## 39 B 4 3 1 0.52
## 40 B 5 3 1 0.82
## 41 C 1 3 1 0.02
## 42 C 2 3 1 0.32
## 43 C 3 3 1 0.72
## 44 C 4 3 1 0.72
## 45 C 5 3 1 0.62
## 46 A 1 1 2 0.13
## 47 A 2 1 2 0.43
## 48 A 3 1 2 0.53
## 49 A 4 1 2 0.93
## 50 A 5 1 2 0.33
## 51 B 1 1 2 0.13
## 52 B 2 1 2 0.33
## 53 B 3 1 2 0.53
## 54 B 4 1 2 0.74
## 55 B 5 1 2 0.92
## 56 C 1 1 2 0.13
## 57 C 2 1 2 0.63
## 58 C 3 1 2 0.53
## 59 C 4 1 2 0.63
## 60 C 5 1 2 0.43
## 61 A 1 2 2 0.15
## 62 A 2 2 2 0.53
## 63 A 3 2 2 0.73
## 64 A 4 2 2 0.94
## 65 A 5 2 2 0.63
## 66 B 1 2 2 0.10
## 67 B 2 2 2 0.13
## 68 B 3 2 2 0.73
## 69 B 4 2 2 0.53
## 70 B 5 2 2 0.93
## 71 C 1 2 2 0.23
## 72 C 2 2 2 0.43
## 73 C 3 2 2 0.63
## 74 C 4 2 2 0.73
## 75 C 5 2 2 0.33
## 76 A 1 3 2 0.23
## 77 A 2 3 2 0.43
## 78 A 3 3 2 0.63
## 79 A 4 3 2 0.96
## 80 A 5 3 2 0.43
## 81 B 1 3 2 0.09
## 82 B 2 3 2 0.13
## 83 B 3 3 2 0.33
## 84 B 4 3 2 0.43
## 85 B 5 3 2 0.87
## 86 C 1 3 2 0.08
## 87 C 2 3 2 0.23
## 88 C 3 3 2 0.63
## 89 C 4 3 2 0.63
## 90 C 5 3 2 0.53Including histogram and boxplot
hist(data3$ndvi)
boxplot(data3$ndvi~data3$fungicide)
boxplot(data3$ndvi~data3$race)
###Anova without transform the data
library(agricolae)
outANOVA<-aov(ndvi~block+year+race+fungicide+race*fungicide+year*race*fungicide, data = data3)##wrong way to do it because i am assuming the data was colected from the same experimental unit
anova(outANOVA)## Analysis of Variance Table
##
## Response: ndvi
## Df Sum Sq Mean Sq F value Pr(>F)
## block 2 0.1058 0.05288 4.5870 0.014144 *
## year 1 0.1082 0.10816 9.3813 0.003321 **
## race 4 3.8412 0.96029 83.2913 < 2.2e-16 ***
## fungicide 2 0.1192 0.05961 5.1707 0.008582 **
## race:fungicide 8 1.1793 0.14742 12.7865 2.148e-10 ***
## year:race 4 0.0066 0.00164 0.1421 0.965789
## year:fungicide 2 0.0018 0.00091 0.0789 0.924204
## year:race:fungicide 8 0.0221 0.00277 0.2400 0.981470
## Residuals 58 0.6687 0.01153
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1plot(outANOVA)
model <- aov(ndvi~block+fungicide*race*year+Error(block:race:fungicide/year),data=data3)##correct way, year is a split plot## Warning in aov(ndvi ~ block + fungicide * race * year +
## Error(block:race:fungicide/year), : Error() model is singularsummary(model)##
## Error: block:race:fungicide
## Df Sum Sq Mean Sq F value Pr(>F)
## block 2 0.106 0.0529 2.249 0.124175
## fungicide 2 0.119 0.0596 2.536 0.097242 .
## race 4 3.841 0.9603 40.847 2.67e-11 ***
## fungicide:race 8 1.179 0.1474 6.271 0.000115 ***
## Residuals 28 0.658 0.0235
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Error: block:race:fungicide:year
## Df Sum Sq Mean Sq F value Pr(>F)
## year 1 0.10816 0.10816 311.003 < 2e-16 ***
## fungicide:year 2 0.00182 0.00091 2.617 0.08965 .
## race:year 4 0.00655 0.00164 4.709 0.00454 **
## fungicide:race:year 8 0.02214 0.00277 7.956 1.08e-05 ***
## Residuals 30 0.01043 0.00035
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Test LSD with non-transformed data
outtestLSD<-LSD.test(outANOVA, c ("race","fungicide","year"), main = "ndvi~block+year+race+fungicide+race*fungicide+year*race*fungicide", console=TRUE)##
## Study: ndvi~block+year+race+fungicide+race*fungicide+year*race*fungicide
##
## LSD t Test for ndvi
##
## Mean Square Error: 0.01152927
##
## race:fungicide:year, means and individual ( 95 %) CI
##
## ndvi std r LCL UCL Min Max
## 1:A:1 0.2533333 0.05773503 3 0.12924153 0.3774251 0.22 0.32
## 1:A:2 0.1700000 0.05291503 3 0.04590820 0.2940918 0.13 0.23
## 1:B:1 0.1533333 0.05773503 3 0.02924153 0.2774251 0.12 0.22
## 1:B:2 0.1066667 0.02081666 3 -0.01742514 0.2307585 0.09 0.13
## 1:C:1 0.1866667 0.15275252 3 0.06257486 0.3107585 0.02 0.32
## 1:C:2 0.1466667 0.07637626 3 0.02257486 0.2707585 0.08 0.23
## 2:A:1 0.5533333 0.05773503 3 0.42924153 0.6774251 0.52 0.62
## 2:A:2 0.4633333 0.05773503 3 0.33924153 0.5874251 0.43 0.53
## 2:B:1 0.2866667 0.11547005 3 0.16257486 0.4107585 0.22 0.42
## 2:B:2 0.1966667 0.11547005 3 0.07257486 0.3207585 0.13 0.33
## 2:C:1 0.5200000 0.20000000 3 0.39590820 0.6440918 0.32 0.72
## 2:C:2 0.4300000 0.20000000 3 0.30590820 0.5540918 0.23 0.63
## 3:A:1 0.7200000 0.10000000 3 0.59590820 0.8440918 0.62 0.82
## 3:A:2 0.6300000 0.10000000 3 0.50590820 0.7540918 0.53 0.73
## 3:B:1 0.6200000 0.20000000 3 0.49590820 0.7440918 0.42 0.82
## 3:B:2 0.5300000 0.20000000 3 0.40590820 0.6540918 0.33 0.73
## 3:C:1 0.6866667 0.05773503 3 0.56257486 0.8107585 0.62 0.72
## 3:C:2 0.5966667 0.05773503 3 0.47257486 0.7207585 0.53 0.63
## 4:A:1 0.9400000 0.02645751 3 0.81590820 1.0640918 0.92 0.97
## 4:A:2 0.9433333 0.01527525 3 0.81924153 1.0674251 0.93 0.96
## 4:B:1 0.6566667 0.15821926 3 0.53257486 0.7807585 0.52 0.83
## 4:B:2 0.5666667 0.15821926 3 0.44257486 0.6907585 0.43 0.74
## 4:C:1 0.7533333 0.05773503 3 0.62924153 0.8774251 0.72 0.82
## 4:C:2 0.6633333 0.05773503 3 0.53924153 0.7874251 0.63 0.73
## 5:A:1 0.5533333 0.15275252 3 0.42924153 0.6774251 0.42 0.72
## 5:A:2 0.4633333 0.15275252 3 0.33924153 0.5874251 0.33 0.63
## 5:B:1 0.8800000 0.05291503 3 0.75590820 1.0040918 0.82 0.92
## 5:B:2 0.9066667 0.03214550 3 0.78257486 1.0307585 0.87 0.93
## 5:C:1 0.5200000 0.10000000 3 0.39590820 0.6440918 0.42 0.62
## 5:C:2 0.4300000 0.10000000 3 0.30590820 0.5540918 0.33 0.53
##
## Alpha: 0.05 ; DF Error: 58
## Critical Value of t: 2.001717
##
## least Significant Difference: 0.1754923
##
## Treatments with the same letter are not significantly different.
##
## ndvi groups
## 4:A:2 0.9433333 a
## 4:A:1 0.9400000 a
## 5:B:2 0.9066667 ab
## 5:B:1 0.8800000 abc
## 4:C:1 0.7533333 bcd
## 3:A:1 0.7200000 cde
## 3:C:1 0.6866667 def
## 4:C:2 0.6633333 def
## 4:B:1 0.6566667 def
## 3:A:2 0.6300000 defg
## 3:B:1 0.6200000 defg
## 3:C:2 0.5966667 defgh
## 4:B:2 0.5666667 efgh
## 2:A:1 0.5533333 efgh
## 5:A:1 0.5533333 efgh
## 3:B:2 0.5300000 fgh
## 2:C:1 0.5200000 fgh
## 5:C:1 0.5200000 fgh
## 2:A:2 0.4633333 gh
## 5:A:2 0.4633333 gh
## 2:C:2 0.4300000 hi
## 5:C:2 0.4300000 hi
## 2:B:1 0.2866667 ij
## 1:A:1 0.2533333 jk
## 2:B:2 0.1966667 jk
## 1:C:1 0.1866667 jk
## 1:A:2 0.1700000 jk
## 1:B:1 0.1533333 jk
## 1:C:2 0.1466667 jk
## 1:B:2 0.1066667 kouttestLSD## $statistics
## MSerror Df Mean CV t.value LSD
## 0.01152927 58 0.5175556 20.74646 2.001717 0.1754923
##
## $parameters
## test p.ajusted name.t ntr alpha
## Fisher-LSD none race:fungicide:year 30 0.05
##
## $means
## ndvi std r LCL UCL Min Max Q25 Q50
## 1:A:1 0.2533333 0.05773503 3 0.12924153 0.3774251 0.22 0.32 0.220 0.22
## 1:A:2 0.1700000 0.05291503 3 0.04590820 0.2940918 0.13 0.23 0.140 0.15
## 1:B:1 0.1533333 0.05773503 3 0.02924153 0.2774251 0.12 0.22 0.120 0.12
## 1:B:2 0.1066667 0.02081666 3 -0.01742514 0.2307585 0.09 0.13 0.095 0.10
## 1:C:1 0.1866667 0.15275252 3 0.06257486 0.3107585 0.02 0.32 0.120 0.22
## 1:C:2 0.1466667 0.07637626 3 0.02257486 0.2707585 0.08 0.23 0.105 0.13
## 2:A:1 0.5533333 0.05773503 3 0.42924153 0.6774251 0.52 0.62 0.520 0.52
## 2:A:2 0.4633333 0.05773503 3 0.33924153 0.5874251 0.43 0.53 0.430 0.43
## 2:B:1 0.2866667 0.11547005 3 0.16257486 0.4107585 0.22 0.42 0.220 0.22
## 2:B:2 0.1966667 0.11547005 3 0.07257486 0.3207585 0.13 0.33 0.130 0.13
## 2:C:1 0.5200000 0.20000000 3 0.39590820 0.6440918 0.32 0.72 0.420 0.52
## 2:C:2 0.4300000 0.20000000 3 0.30590820 0.5540918 0.23 0.63 0.330 0.43
## 3:A:1 0.7200000 0.10000000 3 0.59590820 0.8440918 0.62 0.82 0.670 0.72
## 3:A:2 0.6300000 0.10000000 3 0.50590820 0.7540918 0.53 0.73 0.580 0.63
## 3:B:1 0.6200000 0.20000000 3 0.49590820 0.7440918 0.42 0.82 0.520 0.62
## 3:B:2 0.5300000 0.20000000 3 0.40590820 0.6540918 0.33 0.73 0.430 0.53
## 3:C:1 0.6866667 0.05773503 3 0.56257486 0.8107585 0.62 0.72 0.670 0.72
## 3:C:2 0.5966667 0.05773503 3 0.47257486 0.7207585 0.53 0.63 0.580 0.63
## 4:A:1 0.9400000 0.02645751 3 0.81590820 1.0640918 0.92 0.97 0.925 0.93
## 4:A:2 0.9433333 0.01527525 3 0.81924153 1.0674251 0.93 0.96 0.935 0.94
## 4:B:1 0.6566667 0.15821926 3 0.53257486 0.7807585 0.52 0.83 0.570 0.62
## 4:B:2 0.5666667 0.15821926 3 0.44257486 0.6907585 0.43 0.74 0.480 0.53
## 4:C:1 0.7533333 0.05773503 3 0.62924153 0.8774251 0.72 0.82 0.720 0.72
## 4:C:2 0.6633333 0.05773503 3 0.53924153 0.7874251 0.63 0.73 0.630 0.63
## 5:A:1 0.5533333 0.15275252 3 0.42924153 0.6774251 0.42 0.72 0.470 0.52
## 5:A:2 0.4633333 0.15275252 3 0.33924153 0.5874251 0.33 0.63 0.380 0.43
## 5:B:1 0.8800000 0.05291503 3 0.75590820 1.0040918 0.82 0.92 0.860 0.90
## 5:B:2 0.9066667 0.03214550 3 0.78257486 1.0307585 0.87 0.93 0.895 0.92
## 5:C:1 0.5200000 0.10000000 3 0.39590820 0.6440918 0.42 0.62 0.470 0.52
## 5:C:2 0.4300000 0.10000000 3 0.30590820 0.5540918 0.33 0.53 0.380 0.43
## Q75
## 1:A:1 0.270
## 1:A:2 0.190
## 1:B:1 0.170
## 1:B:2 0.115
## 1:C:1 0.270
## 1:C:2 0.180
## 2:A:1 0.570
## 2:A:2 0.480
## 2:B:1 0.320
## 2:B:2 0.230
## 2:C:1 0.620
## 2:C:2 0.530
## 3:A:1 0.770
## 3:A:2 0.680
## 3:B:1 0.720
## 3:B:2 0.630
## 3:C:1 0.720
## 3:C:2 0.630
## 4:A:1 0.950
## 4:A:2 0.950
## 4:B:1 0.725
## 4:B:2 0.635
## 4:C:1 0.770
## 4:C:2 0.680
## 5:A:1 0.620
## 5:A:2 0.530
## 5:B:1 0.910
## 5:B:2 0.925
## 5:C:1 0.570
## 5:C:2 0.480
##
## $comparison
## NULL
##
## $groups
## ndvi groups
## 4:A:2 0.9433333 a
## 4:A:1 0.9400000 a
## 5:B:2 0.9066667 ab
## 5:B:1 0.8800000 abc
## 4:C:1 0.7533333 bcd
## 3:A:1 0.7200000 cde
## 3:C:1 0.6866667 def
## 4:C:2 0.6633333 def
## 4:B:1 0.6566667 def
## 3:A:2 0.6300000 defg
## 3:B:1 0.6200000 defg
## 3:C:2 0.5966667 defgh
## 4:B:2 0.5666667 efgh
## 2:A:1 0.5533333 efgh
## 5:A:1 0.5533333 efgh
## 3:B:2 0.5300000 fgh
## 2:C:1 0.5200000 fgh
## 5:C:1 0.5200000 fgh
## 2:A:2 0.4633333 gh
## 5:A:2 0.4633333 gh
## 2:C:2 0.4300000 hi
## 5:C:2 0.4300000 hi
## 2:B:1 0.2866667 ij
## 1:A:1 0.2533333 jk
## 2:B:2 0.1966667 jk
## 1:C:1 0.1866667 jk
## 1:A:2 0.1700000 jk
## 1:B:1 0.1533333 jk
## 1:C:2 0.1466667 jk
## 1:B:2 0.1066667 k
##
## attr(,"class")
## [1] "group"Test Tukey’s HSD
outtestHSD<-HSD.test(outANOVA, c ("race","fungicide","year"), main = "ndvi~block+year+race+fungicide+race*fungicide+year*race*fungicide", console=TRUE)##
## Study: ndvi~block+year+race+fungicide+race*fungicide+year*race*fungicide
##
## HSD Test for ndvi
##
## Mean Square Error: 0.01152927
##
## race:fungicide:year, means
##
## ndvi std r Min Max
## 1:A:1 0.2533333 0.05773503 3 0.22 0.32
## 1:A:2 0.1700000 0.05291503 3 0.13 0.23
## 1:B:1 0.1533333 0.05773503 3 0.12 0.22
## 1:B:2 0.1066667 0.02081666 3 0.09 0.13
## 1:C:1 0.1866667 0.15275252 3 0.02 0.32
## 1:C:2 0.1466667 0.07637626 3 0.08 0.23
## 2:A:1 0.5533333 0.05773503 3 0.52 0.62
## 2:A:2 0.4633333 0.05773503 3 0.43 0.53
## 2:B:1 0.2866667 0.11547005 3 0.22 0.42
## 2:B:2 0.1966667 0.11547005 3 0.13 0.33
## 2:C:1 0.5200000 0.20000000 3 0.32 0.72
## 2:C:2 0.4300000 0.20000000 3 0.23 0.63
## 3:A:1 0.7200000 0.10000000 3 0.62 0.82
## 3:A:2 0.6300000 0.10000000 3 0.53 0.73
## 3:B:1 0.6200000 0.20000000 3 0.42 0.82
## 3:B:2 0.5300000 0.20000000 3 0.33 0.73
## 3:C:1 0.6866667 0.05773503 3 0.62 0.72
## 3:C:2 0.5966667 0.05773503 3 0.53 0.63
## 4:A:1 0.9400000 0.02645751 3 0.92 0.97
## 4:A:2 0.9433333 0.01527525 3 0.93 0.96
## 4:B:1 0.6566667 0.15821926 3 0.52 0.83
## 4:B:2 0.5666667 0.15821926 3 0.43 0.74
## 4:C:1 0.7533333 0.05773503 3 0.72 0.82
## 4:C:2 0.6633333 0.05773503 3 0.63 0.73
## 5:A:1 0.5533333 0.15275252 3 0.42 0.72
## 5:A:2 0.4633333 0.15275252 3 0.33 0.63
## 5:B:1 0.8800000 0.05291503 3 0.82 0.92
## 5:B:2 0.9066667 0.03214550 3 0.87 0.93
## 5:C:1 0.5200000 0.10000000 3 0.42 0.62
## 5:C:2 0.4300000 0.10000000 3 0.33 0.53
##
## Alpha: 0.05 ; DF Error: 58
## Critical Value of Studentized Range: 5.575498
##
## Minimun Significant Difference: 0.34564
##
## Treatments with the same letter are not significantly different.
##
## ndvi groups
## 4:A:2 0.9433333 a
## 4:A:1 0.9400000 ab
## 5:B:2 0.9066667 abc
## 5:B:1 0.8800000 abcd
## 4:C:1 0.7533333 abcde
## 3:A:1 0.7200000 abcde
## 3:C:1 0.6866667 abcde
## 4:C:2 0.6633333 abcde
## 4:B:1 0.6566667 abcde
## 3:A:2 0.6300000 abcdef
## 3:B:1 0.6200000 abcdef
## 3:C:2 0.5966667 bcdefg
## 4:B:2 0.5666667 cdefg
## 2:A:1 0.5533333 defg
## 5:A:1 0.5533333 defg
## 3:B:2 0.5300000 efgh
## 2:C:1 0.5200000 efgh
## 5:C:1 0.5200000 efgh
## 2:A:2 0.4633333 efghi
## 5:A:2 0.4633333 efghi
## 2:C:2 0.4300000 efghij
## 5:C:2 0.4300000 efghij
## 2:B:1 0.2866667 fghij
## 1:A:1 0.2533333 ghij
## 2:B:2 0.1966667 hij
## 1:C:1 0.1866667 hij
## 1:A:2 0.1700000 ij
## 1:B:1 0.1533333 ij
## 1:C:2 0.1466667 ij
## 1:B:2 0.1066667 jouttestHSD## $statistics
## MSerror Df Mean CV MSD
## 0.01152927 58 0.5175556 20.74646 0.34564
##
## $parameters
## test name.t ntr StudentizedRange alpha
## Tukey race:fungicide:year 30 5.575498 0.05
##
## $means
## ndvi std r Min Max Q25 Q50 Q75
## 1:A:1 0.2533333 0.05773503 3 0.22 0.32 0.220 0.22 0.270
## 1:A:2 0.1700000 0.05291503 3 0.13 0.23 0.140 0.15 0.190
## 1:B:1 0.1533333 0.05773503 3 0.12 0.22 0.120 0.12 0.170
## 1:B:2 0.1066667 0.02081666 3 0.09 0.13 0.095 0.10 0.115
## 1:C:1 0.1866667 0.15275252 3 0.02 0.32 0.120 0.22 0.270
## 1:C:2 0.1466667 0.07637626 3 0.08 0.23 0.105 0.13 0.180
## 2:A:1 0.5533333 0.05773503 3 0.52 0.62 0.520 0.52 0.570
## 2:A:2 0.4633333 0.05773503 3 0.43 0.53 0.430 0.43 0.480
## 2:B:1 0.2866667 0.11547005 3 0.22 0.42 0.220 0.22 0.320
## 2:B:2 0.1966667 0.11547005 3 0.13 0.33 0.130 0.13 0.230
## 2:C:1 0.5200000 0.20000000 3 0.32 0.72 0.420 0.52 0.620
## 2:C:2 0.4300000 0.20000000 3 0.23 0.63 0.330 0.43 0.530
## 3:A:1 0.7200000 0.10000000 3 0.62 0.82 0.670 0.72 0.770
## 3:A:2 0.6300000 0.10000000 3 0.53 0.73 0.580 0.63 0.680
## 3:B:1 0.6200000 0.20000000 3 0.42 0.82 0.520 0.62 0.720
## 3:B:2 0.5300000 0.20000000 3 0.33 0.73 0.430 0.53 0.630
## 3:C:1 0.6866667 0.05773503 3 0.62 0.72 0.670 0.72 0.720
## 3:C:2 0.5966667 0.05773503 3 0.53 0.63 0.580 0.63 0.630
## 4:A:1 0.9400000 0.02645751 3 0.92 0.97 0.925 0.93 0.950
## 4:A:2 0.9433333 0.01527525 3 0.93 0.96 0.935 0.94 0.950
## 4:B:1 0.6566667 0.15821926 3 0.52 0.83 0.570 0.62 0.725
## 4:B:2 0.5666667 0.15821926 3 0.43 0.74 0.480 0.53 0.635
## 4:C:1 0.7533333 0.05773503 3 0.72 0.82 0.720 0.72 0.770
## 4:C:2 0.6633333 0.05773503 3 0.63 0.73 0.630 0.63 0.680
## 5:A:1 0.5533333 0.15275252 3 0.42 0.72 0.470 0.52 0.620
## 5:A:2 0.4633333 0.15275252 3 0.33 0.63 0.380 0.43 0.530
## 5:B:1 0.8800000 0.05291503 3 0.82 0.92 0.860 0.90 0.910
## 5:B:2 0.9066667 0.03214550 3 0.87 0.93 0.895 0.92 0.925
## 5:C:1 0.5200000 0.10000000 3 0.42 0.62 0.470 0.52 0.570
## 5:C:2 0.4300000 0.10000000 3 0.33 0.53 0.380 0.43 0.480
##
## $comparison
## NULL
##
## $groups
## ndvi groups
## 4:A:2 0.9433333 a
## 4:A:1 0.9400000 ab
## 5:B:2 0.9066667 abc
## 5:B:1 0.8800000 abcd
## 4:C:1 0.7533333 abcde
## 3:A:1 0.7200000 abcde
## 3:C:1 0.6866667 abcde
## 4:C:2 0.6633333 abcde
## 4:B:1 0.6566667 abcde
## 3:A:2 0.6300000 abcdef
## 3:B:1 0.6200000 abcdef
## 3:C:2 0.5966667 bcdefg
## 4:B:2 0.5666667 cdefg
## 2:A:1 0.5533333 defg
## 5:A:1 0.5533333 defg
## 3:B:2 0.5300000 efgh
## 2:C:1 0.5200000 efgh
## 5:C:1 0.5200000 efgh
## 2:A:2 0.4633333 efghi
## 5:A:2 0.4633333 efghi
## 2:C:2 0.4300000 efghij
## 5:C:2 0.4300000 efghij
## 2:B:1 0.2866667 fghij
## 1:A:1 0.2533333 ghij
## 2:B:2 0.1966667 hij
## 1:C:1 0.1866667 hij
## 1:A:2 0.1700000 ij
## 1:B:1 0.1533333 ij
## 1:C:2 0.1466667 ij
## 1:B:2 0.1066667 j
##
## attr(,"class")
## [1] "group"Question 4
setwd("C:/Users/clemendeoliveira/Desktop/Homework3")
data4=read.csv("quest4.csv",header = T,check.names = F,na.strings = -9,sep = ",")
str(data4)## 'data.frame': 48 obs. of 6 variables:
## $ Block : int 1 1 1 1 1 1 1 1 1 1 ...
## $ wplot : int 1 1 1 1 2 2 2 2 3 3 ...
## $ splot : int 1 2 3 4 1 2 3 4 1 2 ...
## $ Herbicide: Factor w/ 4 levels "A","B","C","D": 1 1 1 1 2 2 2 2 3 3 ...
## $ Variety : int 1 2 3 4 1 2 3 4 1 2 ...
## $ Humidity : num 10.9 11.5 13 14.3 9 10 12.1 16 9.6 10.2 ...data4$Block=as.factor(data4$Block)
data4$wplot=as.factor(data4$wplot)
data4$splot=as.factor(data4$splot)
data4$Herbicide=as.factor(data4$Herbicide)
data4$Variety = as.factor(data4$Variety)
summary(data4)## Block wplot splot Herbicide Variety Humidity
## 1:16 1:12 1:12 A:12 1:12 Min. : 6.60
## 2:16 2:12 2:12 B:12 2:12 1st Qu.:10.97
## 3:16 3:12 3:12 C:12 3:12 Median :12.85
## 4:12 4:12 D:12 4:12 Mean :13.13
## 3rd Qu.:15.53
## Max. :18.40attach(data4)
data4## Block wplot splot Herbicide Variety Humidity
## 1 1 1 1 A 1 10.9
## 2 1 1 2 A 2 11.5
## 3 1 1 3 A 3 13.0
## 4 1 1 4 A 4 14.3
## 5 1 2 1 B 1 9.0
## 6 1 2 2 B 2 10.0
## 7 1 2 3 B 3 12.1
## 8 1 2 4 B 4 16.0
## 9 1 3 1 C 1 9.6
## 10 1 3 2 C 2 10.2
## 11 1 3 3 C 3 11.7
## 12 1 3 4 C 4 13.0
## 13 1 4 1 D 1 6.6
## 14 1 4 2 D 2 8.7
## 15 1 4 3 D 3 10.8
## 16 1 4 4 D 4 14.7
## 17 2 1 1 A 1 12.3
## 18 2 1 2 A 2 11.4
## 19 2 1 3 A 3 15.4
## 20 2 1 4 A 4 17.2
## 21 2 2 1 B 1 10.3
## 22 2 2 2 B 2 12.5
## 23 2 2 3 B 3 16.1
## 24 2 2 4 B 4 16.5
## 25 2 3 1 C 1 11.0
## 26 2 3 2 C 2 10.1
## 27 2 3 3 C 3 14.1
## 28 2 3 4 C 4 15.9
## 29 2 4 1 D 1 9.0
## 30 2 4 2 D 2 11.2
## 31 2 4 3 D 3 14.8
## 32 2 4 4 D 4 15.2
## 33 3 1 1 A 1 14.3
## 34 3 1 2 A 2 13.3
## 35 3 1 3 A 3 18.1
## 36 3 1 4 A 4 16.5
## 37 3 2 1 B 1 12.1
## 38 3 2 2 B 2 12.7
## 39 3 2 3 B 3 17.3
## 40 3 2 4 B 4 18.4
## 41 3 3 1 C 1 13.0
## 42 3 3 2 C 2 12.0
## 43 3 3 3 C 3 16.8
## 44 3 3 4 C 4 15.2
## 45 3 4 1 D 1 10.8
## 46 3 4 2 D 2 11.4
## 47 3 4 3 D 3 16.0
## 48 3 4 4 D 4 17.1Including histogram and boxplot
hist(data4$Humidity)
boxplot(data4$Humidity~data4$Herbicide)
boxplot(data4$Humidity~data4$Variety)
###Anova without transform the data
splitplot4 <- aov(Humidity~Block+Herbicide*Variety+Error(Block/wplot/splot),data = data4)
summary(splitplot4)##
## Error: Block
## Df Sum Sq Mean Sq
## Block 2 88.28 44.14
##
## Error: Block:wplot
## Df Sum Sq Mean Sq F value Pr(>F)
## Herbicide 3 24.516 8.172 65.27 5.69e-05 ***
## Residuals 6 0.751 0.125
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Error: Block:wplot:splot
## Df Sum Sq Mean Sq F value Pr(>F)
## Variety 3 227.51 75.84 85.558 5.91e-13 ***
## Herbicide:Variety 9 15.61 1.73 1.956 0.0915 .
## Residuals 24 21.27 0.89
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1splitplotwrongway <- aov(Humidity~Block+Herbicide+Block*Herbicide+Variety+Herbicide*Variety,data = data4)
summary(splitplotwrongway)## Df Sum Sq Mean Sq F value Pr(>F)
## Block 2 88.28 44.14 49.795 2.88e-09 ***
## Herbicide 3 24.52 8.17 9.219 0.000308 ***
## Variety 3 227.51 75.84 85.558 5.91e-13 ***
## Block:Herbicide 6 0.75 0.13 0.141 0.989110
## Herbicide:Variety 9 15.61 1.73 1.956 0.091525 .
## Residuals 24 21.27 0.89
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1library(agricolae)
model_1=with(data4,sp.plot(Block,Herbicide,Variety,Humidity))##
## ANALYSIS SPLIT PLOT: Humidity
## Class level information
##
## Herbicide : A B C D
## Variety : 1 2 3 4
## Block : 1 2 3
##
## Number of observations: 48
##
## Analysis of Variance Table
##
## Response: Humidity
## Df Sum Sq Mean Sq F value Pr(>F)
## Block 2 88.275 44.138 352.5141 6.009e-07 ***
## Herbicide 3 24.516 8.172 65.2662 5.685e-05 ***
## Ea 6 0.751 0.125
## Variety 3 227.512 75.837 85.5577 5.909e-13 ***
## Herbicide:Variety 9 15.607 1.734 1.9564 0.09152 .
## Eb 24 21.273 0.886
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## cv(a) = 2.7 %, cv(b) = 7.2 %, Mean = 13.12708gla= model_1$gl.a
glb= model_1$gl.b
Ea= model_1$Ea
Eb= model_1$Eb
out1= with(data4,HSD.test(Humidity, Herbicide, gla, Ea, console=TRUE))##
## Study: Humidity ~ Herbicide
##
## HSD Test for Humidity
##
## Mean Square Error: 0.1252083
##
## Herbicide, means
##
## Humidity std r Min Max
## A 14.01667 2.382448 12 10.9 18.1
## B 13.58333 3.143199 12 9.0 18.4
## C 12.71667 2.382448 12 9.6 16.8
## D 12.19167 3.301090 12 6.6 17.1
##
## Alpha: 0.05 ; DF Error: 6
## Critical Value of Studentized Range: 4.895599
##
## Minimun Significant Difference: 0.5000712
##
## Treatments with the same letter are not significantly different.
##
## Humidity groups
## A 14.01667 a
## B 13.58333 a
## C 12.71667 b
## D 12.19167 cout2= with(data4,HSD.test(Humidity, Variety, glb, Eb, console=TRUE))##
## Study: Humidity ~ Variety
##
## HSD Test for Humidity
##
## Mean Square Error: 0.8863889
##
## Variety, means
##
## Humidity std r Min Max
## 1 10.74167 2.063738 12 6.6 14.3
## 2 11.25000 1.315295 12 8.7 13.3
## 3 14.68333 2.356744 12 10.8 18.1
## 4 15.83333 1.459971 12 13.0 18.4
##
## Alpha: 0.05 ; DF Error: 24
## Critical Value of Studentized Range: 3.901262
##
## Minimun Significant Difference: 1.060295
##
## Treatments with the same letter are not significantly different.
##
## Humidity groups
## 4 15.83333 a
## 3 14.68333 b
## 2 11.25000 c
## 1 10.74167 cout3= with(data4,HSD.test(Humidity, Herbicide:Variety, glb, Eb, console=TRUE))##
## Study: Humidity ~ Herbicide:Variety
##
## HSD Test for Humidity
##
## Mean Square Error: 0.8863889
##
## Herbicide:Variety, means
##
## Humidity std r Min Max
## A:1 12.50000 1.708801 3 10.9 14.3
## A:2 12.06667 1.069268 3 11.4 13.3
## A:3 15.50000 2.551470 3 13.0 18.1
## A:4 16.00000 1.513275 3 14.3 17.2
## B:1 10.46667 1.556706 3 9.0 12.1
## B:2 11.73333 1.504438 3 10.0 12.7
## B:3 15.16667 2.722744 3 12.1 17.3
## B:4 16.96667 1.266228 3 16.0 18.4
## C:1 11.20000 1.708801 3 9.6 13.0
## C:2 10.76667 1.069268 3 10.1 12.0
## C:3 14.20000 2.551470 3 11.7 16.8
## C:4 14.70000 1.513275 3 13.0 15.9
## D:1 8.80000 2.107131 3 6.6 10.8
## D:2 10.43333 1.504438 3 8.7 11.4
## D:3 13.86667 2.722744 3 10.8 16.0
## D:4 15.66667 1.266228 3 14.7 17.1
##
## Alpha: 0.05 ; DF Error: 24
## Critical Value of Studentized Range: 5.381037
##
## Minimun Significant Difference: 2.924944
##
## Treatments with the same letter are not significantly different.
##
## Humidity groups
## B:4 16.96667 a
## A:4 16.00000 ab
## D:4 15.66667 ab
## A:3 15.50000 ab
## B:3 15.16667 abc
## C:4 14.70000 abcd
## C:3 14.20000 abcde
## D:3 13.86667 bcdef
## A:1 12.50000 cdefg
## A:2 12.06667 defg
## B:2 11.73333 efg
## C:1 11.20000 fgh
## C:2 10.76667 gh
## B:1 10.46667 gh
## D:2 10.43333 gh
## D:1 8.80000 hlibrary(lsmeans)
meanseparation<-lsmeans(splitplotwrongway, ~Herbicide, adjust='Tukey')## NOTE: Results may be misleading due to involvement in interactionsmeanseparation<-summary(meanseparation)
HSD.test(splitplotwrongway,c("Herbicide"),console=TRUE)##
## Study: splitplotwrongway ~ c("Herbicide")
##
## HSD Test for Humidity
##
## Mean Square Error: 0.8863889
##
## Herbicide, means
##
## Humidity std r Min Max
## A 14.01667 2.382448 12 10.9 18.1
## B 13.58333 3.143199 12 9.0 18.4
## C 12.71667 2.382448 12 9.6 16.8
## D 12.19167 3.301090 12 6.6 17.1
##
## Alpha: 0.05 ; DF Error: 24
## Critical Value of Studentized Range: 3.901262
##
## Minimun Significant Difference: 1.060295
##
## Treatments with the same letter are not significantly different.
##
## Humidity groups
## A 14.01667 a
## B 13.58333 ab
## C 12.71667 bc
## D 12.19167 clibrary(lsmeans)
meanseparation2<-lsmeans(splitplotwrongway, ~Variety, adjust='Tukey')## NOTE: Results may be misleading due to involvement in interactionsmeanseparation2<-summary(meanseparation2)
HSD.test(splitplotwrongway,c("Variety"),console=TRUE)##
## Study: splitplotwrongway ~ c("Variety")
##
## HSD Test for Humidity
##
## Mean Square Error: 0.8863889
##
## Variety, means
##
## Humidity std r Min Max
## 1 10.74167 2.063738 12 6.6 14.3
## 2 11.25000 1.315295 12 8.7 13.3
## 3 14.68333 2.356744 12 10.8 18.1
## 4 15.83333 1.459971 12 13.0 18.4
##
## Alpha: 0.05 ; DF Error: 24
## Critical Value of Studentized Range: 3.901262
##
## Minimun Significant Difference: 1.060295
##
## Treatments with the same letter are not significantly different.
##
## Humidity groups
## 4 15.83333 a
## 3 14.68333 b
## 2 11.25000 c
## 1 10.74167 cComputing graph bar for Herbicide
library(ggplot2)
graph<-lsmeans(splitplot4, ~Herbicide, adjust='Tukey')## Note: re-fitting model with sum-to-zero contrasts## NOTE: Results may be misleading due to involvement in interactionsgraph<-summary(graph)
graph$Herbicide <- factor(graph$Herbicide, levels = c( "A","B","C","D"))
ggplot(graph, aes(x=Herbicide, y=lsmean, fill=Herbicide)) +
geom_bar(position=position_dodge(0.9), stat="identity",
colour="black", # Use black outlines
size=.3) + scale_fill_brewer() +
geom_errorbar(aes(ymin=lsmean-SE, ymax=lsmean+SE),
size=.5, # Thinner lines
colour="black",
width=.2,
position=position_dodge(.9)) +
xlab("Herbicide") +
ylab("Humidity") +
ggtitle("Humidity Question 4 - Herbicide") +
annotate("text",x=1,y=16,label="a", size=10)+
annotate("text",x=2,y=16,label="ab", size=10)+
annotate("text",x=3,y=16,label="bc", size=10)+
annotate("text",x=4,y=16,label="c", size=10)+
theme_bw() +
theme(axis.text.x = element_text(angle = 45, hjust = 1))+
theme(axis.title=element_text( size = rel(2.1) , color="black")) +
theme(axis.text = element_text(colour = "black", size="20")) +
theme(legend.title = element_text(size = "14"))+
theme(legend.position = "none")+
theme(plot.title = element_text(size = rel(2)))## Warning: Removed 4 rows containing missing values (geom_errorbar).
###Computing graph bar for Variety
library(ggplot2)
graph<-lsmeans(splitplot4, ~Variety, adjust='Tukey')## Note: re-fitting model with sum-to-zero contrasts## NOTE: Results may be misleading due to involvement in interactionsgraph<-summary(graph)
graph$Variety <- factor(graph$Variety, levels = c( "1","2","3","4"))
ggplot(graph, aes(x=Variety, y=lsmean, fill=Variety)) +
geom_bar(position=position_dodge(0.9), stat="identity",
colour="black", # Use black outlines
size=.3) + scale_fill_brewer() +
geom_errorbar(aes(ymin=lsmean-SE, ymax=lsmean+SE),
size=.5, # Thinner lines
colour="black",
width=.2,
position=position_dodge(.9)) +
xlab("Variety") +
ylab("Humidity") +
ggtitle("Humidity Question 4 - Variety") +
annotate("text",x=1,y=16,label="a", size=10)+
annotate("text",x=2,y=16,label="b", size=10)+
annotate("text",x=3,y=18,label="c", size=10)+
annotate("text",x=4,y=19,label="c", size=10)+
theme_bw() +
theme(axis.text.x = element_text(angle = 45, hjust = 1))+
theme(axis.title=element_text( size = rel(2.1) , color="black")) +
theme(axis.text = element_text(colour = "black", size="20")) +
theme(legend.title = element_text(size = "14"))+
theme(legend.position = "none")+
theme(plot.title = element_text(size = rel(2)))## Warning: Removed 4 rows containing missing values (geom_errorbar).
###bONUS
setwd("C:/Users/clemendeoliveira/Desktop/Homework3")
data5=read.table("quest5.txt",header = T,check.names = F)
str(data5)## 'data.frame': 48 obs. of 8 variables:
## $ Block : int 1 1 1 1 1 1 1 1 1 1 ...
## $ wplot : int 1 1 1 1 1 1 2 2 2 2 ...
## $ subplot : int 1 1 1 2 2 2 1 1 1 2 ...
## $ subsubplot: int 1 2 3 1 2 3 1 2 3 1 ...
## $ Soil : Factor w/ 2 levels "Conventional",..: 1 1 1 1 1 1 2 2 2 2 ...
## $ Cultivar : Factor w/ 2 levels "Susceptible",..: 2 2 2 1 1 1 2 2 2 1 ...
## $ Nitrogen : Factor w/ 3 levels "High","Low","Medium": 2 3 1 2 3 1 2 3 1 2 ...
## $ Yield : int 140 145 150 136 140 145 142 146 148 132 ...data5$Block=as.factor(data5$Block)
data5$wplot=as.factor(data5$wplot)
data5$subplot=as.factor(data5$subplot)
data5$subsubplot=as.factor(data5$subsubplot)
data5$Soil=as.factor(data5$Soil)
data5$Cultivar = as.factor(data5$Cultivar)
data5$Nitrogen=as.factor(data5$Nitrogen)
summary(data5)## Block wplot subplot subsubplot Soil Cultivar
## 1:12 1:24 1:24 1:16 Conventional:24 Susceptible:24
## 2:12 2:24 2:24 2:16 Non_Till :24 Tolerant :24
## 3:12 3:16
## 4:12
##
##
## Nitrogen Yield
## High :16 Min. :130.0
## Low :16 1st Qu.:136.0
## Medium:16 Median :140.0
## Mean :139.5
## 3rd Qu.:142.0
## Max. :150.0attach(data5) ## The following objects are masked from data4:
##
## Block, wplotdata5## Block wplot subplot subsubplot Soil Cultivar Nitrogen Yield
## 1 1 1 1 1 Conventional Tolerant Low 140
## 2 1 1 1 2 Conventional Tolerant Medium 145
## 3 1 1 1 3 Conventional Tolerant High 150
## 4 1 1 2 1 Conventional Susceptible Low 136
## 5 1 1 2 2 Conventional Susceptible Medium 140
## 6 1 1 2 3 Conventional Susceptible High 145
## 7 1 2 1 1 Non_Till Tolerant Low 142
## 8 1 2 1 2 Non_Till Tolerant Medium 146
## 9 1 2 1 3 Non_Till Tolerant High 148
## 10 1 2 2 1 Non_Till Susceptible Low 132
## 11 1 2 2 2 Non_Till Susceptible Medium 138
## 12 1 2 2 3 Non_Till Susceptible High 140
## 13 2 1 1 1 Conventional Tolerant Low 138
## 14 2 1 1 2 Conventional Tolerant Medium 146
## 15 2 1 1 3 Conventional Tolerant High 149
## 16 2 1 2 1 Conventional Susceptible Low 136
## 17 2 1 2 2 Conventional Susceptible Medium 134
## 18 2 1 2 3 Conventional Susceptible High 138
## 19 2 2 1 1 Non_Till Tolerant Low 135
## 20 2 2 1 2 Non_Till Tolerant Medium 136
## 21 2 2 1 3 Non_Till Tolerant High 140
## 22 2 2 2 1 Non_Till Susceptible Low 130
## 23 2 2 2 2 Non_Till Susceptible Medium 132
## 24 2 2 2 3 Non_Till Susceptible High 134
## 25 3 1 1 1 Conventional Tolerant Low 142
## 26 3 1 1 2 Conventional Tolerant Medium 150
## 27 3 1 1 3 Conventional Tolerant High 146
## 28 3 1 2 1 Conventional Susceptible Low 134
## 29 3 1 2 2 Conventional Susceptible Medium 136
## 30 3 1 2 3 Conventional Susceptible High 138
## 31 3 2 1 1 Non_Till Tolerant Low 137
## 32 3 2 1 2 Non_Till Tolerant Medium 140
## 33 3 2 1 3 Non_Till Tolerant High 142
## 34 3 2 2 1 Non_Till Susceptible Low 136
## 35 3 2 2 2 Non_Till Susceptible Medium 130
## 36 3 2 2 3 Non_Till Susceptible High 130
## 37 4 1 1 1 Conventional Tolerant Low 142
## 38 4 1 1 2 Conventional Tolerant Medium 147
## 39 4 1 1 3 Conventional Tolerant High 150
## 40 4 1 2 1 Conventional Susceptible Low 139
## 41 4 1 2 2 Conventional Susceptible Medium 140
## 42 4 1 2 3 Conventional Susceptible High 142
## 43 4 2 1 1 Non_Till Tolerant Low 140
## 44 4 2 1 2 Non_Till Tolerant Medium 141
## 45 4 2 1 3 Non_Till Tolerant High 140
## 46 4 2 2 1 Non_Till Susceptible Low 134
## 47 4 2 2 2 Non_Till Susceptible Medium 132
## 48 4 2 2 3 Non_Till Susceptible High 136hist(data5$Yield)
boxplot(data5$Yield~data5$Soil)
boxplot(data5$Yield~data5$Cultivar)
boxplot(data5$Yield~data5$Nitrogen)
splitplot5 <- aov(Yield~Block+Soil*Cultivar*Nitrogen+Error(Block/wplot/subplot/subsubplot),data = data5)
summary(splitplot5)##
## Error: Block
## Df Sum Sq Mean Sq
## Block 3 142.4 47.47
##
## Error: Block:wplot
## Df Sum Sq Mean Sq F value Pr(>F)
## Soil 1 261.3 261.3 20.91 0.0196 *
## Residuals 3 37.5 12.5
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Error: Block:wplot:subplot
## Df Sum Sq Mean Sq F value Pr(>F)
## Cultivar 1 602.1 602.1 97.856 6.16e-05 ***
## Soil:Cultivar 1 0.3 0.3 0.054 0.824
## Residuals 6 36.9 6.2
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Error: Block:wplot:subplot:subsubplot
## Df Sum Sq Mean Sq F value Pr(>F)
## Nitrogen 2 176.04 88.02 17.013 2.51e-05 ***
## Soil:Nitrogen 2 25.79 12.90 2.493 0.1039
## Cultivar:Nitrogen 2 30.79 15.40 2.976 0.0701 .
## Soil:Cultivar:Nitrogen 2 4.54 2.27 0.439 0.6498
## Residuals 24 124.17 5.17
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1model_2=with(data5,ssp.plot(Block,Soil,Cultivar,Nitrogen,Yield))##
## ANALYSIS SPLIT-SPLIT PLOT: Yield
## Class level information
##
## Soil : Conventional Non_Till
## Cultivar : Tolerant Susceptible
## Nitrogen : Low Medium High
## Block : 1 2 3 4
##
## Number of observations: 48
##
## Analysis of Variance Table
##
## Response: Yield
## Df Sum Sq Mean Sq F value Pr(>F)
## Block 3 142.42 47.47 3.7978 0.15103
## Soil 1 261.33 261.33 20.9067 0.01963 *
## Ea 3 37.50 12.50
## Cultivar 1 602.08 602.08 97.8555 6.161e-05 ***
## Soil:Cultivar 1 0.33 0.33 0.0542 0.82369
## Eb 6 36.92 6.15
## Nitrogen 2 176.04 88.02 17.0134 2.506e-05 ***
## Nitrogen:Soil 2 25.79 12.90 2.4926 0.10385
## Nitrogen:Cultivar 2 30.79 15.40 2.9758 0.07006 .
## Nitrogen:Soil:Cultivar 2 4.54 2.27 0.4389 0.64980
## Ec 24 124.17 5.17
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## cv(a) = 2.5 %, cv(b) = 1.8 %, cv(c) = 1.6 %, Mean = 139.4583gla= model_2$gl.a
glb= model_2$gl.b
glc= model_2$gl.c
Ea= model_2$Ea
Eb= model_2$Eb
Ec= model_2$Ec
out1= with(data5,HSD.test(Yield, Soil, gla, Ea, console=TRUE))##
## Study: Yield ~ Soil
##
## HSD Test for Yield
##
## Mean Square Error: 12.5
##
## Soil, means
##
## Yield std r Min Max
## Conventional 141.7917 5.191793 24 134 150
## Non_Till 137.1250 4.937104 24 130 148
##
## Alpha: 0.05 ; DF Error: 3
## Critical Value of Studentized Range: 4.500659
##
## Minimun Significant Difference: 3.248071
##
## Treatments with the same letter are not significantly different.
##
## Yield groups
## Conventional 141.7917 a
## Non_Till 137.1250 bout2= with(data5,HSD.test(Yield, Cultivar, glb, Eb, console=TRUE))##
## Study: Yield ~ Cultivar
##
## HSD Test for Yield
##
## Mean Square Error: 6.152778
##
## Cultivar, means
##
## Yield std r Min Max
## Susceptible 135.9167 3.944359 24 130 145
## Tolerant 143.0000 4.577829 24 135 150
##
## Alpha: 0.05 ; DF Error: 6
## Critical Value of Studentized Range: 3.460456
##
## Minimun Significant Difference: 1.752118
##
## Treatments with the same letter are not significantly different.
##
## Yield groups
## Tolerant 143.0000 a
## Susceptible 135.9167 bout3= with(data5,HSD.test(Yield, Nitrogen, glc, Ec, console=TRUE))##
## Study: Yield ~ Nitrogen
##
## HSD Test for Yield
##
## Mean Square Error: 5.173611
##
## Nitrogen, means
##
## Yield std r Min Max
## High 141.7500 5.916080 16 130 150
## Low 137.0625 3.623419 16 130 142
## Medium 139.5625 6.021835 16 130 150
##
## Alpha: 0.05 ; DF Error: 24
## Critical Value of Studentized Range: 3.531697
##
## Minimun Significant Difference: 2.008262
##
## Treatments with the same letter are not significantly different.
##
## Yield groups
## High 141.7500 a
## Medium 139.5625 b
## Low 137.0625 csplitplotwrongway5 <- aov(Yield~Block+Soil+Block*Soil+Cultivar+Soil*Cultivar+Nitrogen+Nitrogen*Cultivar*Soil,data = data5)
summary(splitplotwrongway5)## Df Sum Sq Mean Sq F value Pr(>F)
## Block 3 142.4 47.5 8.841 0.000237 ***
## Soil 1 261.3 261.3 48.670 9.45e-08 ***
## Cultivar 1 602.1 602.1 112.131 1.19e-11 ***
## Nitrogen 2 176.0 88.0 16.393 1.54e-05 ***
## Block:Soil 3 37.5 12.5 2.328 0.094517 .
## Soil:Cultivar 1 0.3 0.3 0.062 0.804937
## Cultivar:Nitrogen 2 30.8 15.4 2.867 0.072524 .
## Soil:Nitrogen 2 25.8 12.9 2.402 0.107768
## Soil:Cultivar:Nitrogen 2 4.5 2.3 0.423 0.658978
## Residuals 30 161.1 5.4
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1library(lsmeans)
meanseparation5<-lsmeans(splitplotwrongway5, ~Soil, adjust='Tukey')## NOTE: Results may be misleading due to involvement in interactionsmeanseparation2<-summary(meanseparation5)
HSD.test(splitplotwrongway5,c("Soil"),console=TRUE)##
## Study: splitplotwrongway5 ~ c("Soil")
##
## HSD Test for Yield
##
## Mean Square Error: 5.369444
##
## Soil, means
##
## Yield std r Min Max
## Conventional 141.7917 5.191793 24 134 150
## Non_Till 137.1250 4.937104 24 130 148
##
## Alpha: 0.05 ; DF Error: 30
## Critical Value of Studentized Range: 2.888209
##
## Minimun Significant Difference: 1.366116
##
## Treatments with the same letter are not significantly different.
##
## Yield groups
## Conventional 141.7917 a
## Non_Till 137.1250 blibrary(lsmeans)
meanseparation5.1<-lsmeans(splitplotwrongway5, ~Cultivar, adjust='Tukey')## NOTE: Results may be misleading due to involvement in interactionsmeanseparation5.1<-summary(meanseparation5.1)
HSD.test(splitplotwrongway5,c("Cultivar"),console=TRUE)##
## Study: splitplotwrongway5 ~ c("Cultivar")
##
## HSD Test for Yield
##
## Mean Square Error: 5.369444
##
## Cultivar, means
##
## Yield std r Min Max
## Susceptible 135.9167 3.944359 24 130 145
## Tolerant 143.0000 4.577829 24 135 150
##
## Alpha: 0.05 ; DF Error: 30
## Critical Value of Studentized Range: 2.888209
##
## Minimun Significant Difference: 1.366116
##
## Treatments with the same letter are not significantly different.
##
## Yield groups
## Tolerant 143.0000 a
## Susceptible 135.9167 blibrary(lsmeans)
meanseparation5.2<-lsmeans(splitplotwrongway5, ~Nitrogen, adjust='Tukey')## NOTE: Results may be misleading due to involvement in interactionsmeanseparation5.2<-summary(meanseparation5.2)
HSD.test(splitplotwrongway5,c("Nitrogen"),console=TRUE)##
## Study: splitplotwrongway5 ~ c("Nitrogen")
##
## HSD Test for Yield
##
## Mean Square Error: 5.369444
##
## Nitrogen, means
##
## Yield std r Min Max
## High 141.7500 5.916080 16 130 150
## Low 137.0625 3.623419 16 130 142
## Medium 139.5625 6.021835 16 130 150
##
## Alpha: 0.05 ; DF Error: 30
## Critical Value of Studentized Range: 3.48642
##
## Minimun Significant Difference: 2.019689
##
## Treatments with the same letter are not significantly different.
##
## Yield groups
## High 141.7500 a
## Medium 139.5625 b
## Low 137.0625 c