install.packages("ggplot2")	
library(ggplot2)	
#================================================
# 1. One Sample T-test
bu<-c(1283,1102,1149,1473,1263,1082,976,1154,1217, 1344)

Ho: U=1200
Ha: U#1200

alpha=0.05 (conf.level=1-0.05)

t.test(x=bu,y=NULL,alternative="two.sided",mu=1200, conf.level=0.95)

#===============================================================
# 2. Paired T-Test

x<-c(247, 231, 246, 216, 242, 253, 254, 233, 253, 244)
y<-c(331, 369, 366, 358, 353, 341, 341, 380, 356, 409)

Ho: Ux-Yy=0 (Pre and post trx average CD4 T cells are the same)
Ha: Ux-Uy#0  (Pre and post trx average CD4 T cells are not the same)

#ploting data

 
 is.factor(Time)
 Time<-as.factor(Time)
 Patient<-c(as.factor(1:10),as.factor(1:10))
 Cd4<-c(x,y)
 dat2<-data.frame(Patient,Time,Cd4)
 dim(dat2)
 head(dat2)
 
 pair<-ggplot(dat2, aes(x =Time, y =Cd4)) +geom_line(aes(group=Patient, size=0.10,color=factor(Patient)))+
   scale_x_discrete(limits=rev(levels((dat2$Time))))+ylab("CD4+ T Cell Counts")
 pair+theme(legend.position="none")#removing title
 #Save the Graph
 
# getwd() #check your current working directory
#setwd("C:/Users/musie/Courses/Biostat1") #change the working directory
# pdf('pairt.pdf', width=8, height=12) # save the plot as pdf
 
 #Testing data 
 t.test(x,y,alternative="two.sided",mu=0,paired=TRUE, conf.level=0.95)
 
 
 #############################################################################
 3. Two Sample T-test
 # CD4+ T-cell counts data 
z1<-c(631, 508, 435, 578, 618, 557, 611, 568, 537, 656)
z2<-c(435, 552, 616, 507, 553, 741, 656, 555, 501, 493)
 
Ho: Uz1=Uz2 (Average CD4 T cells are the same in both groups)
Ha: Uz1#Uz2 (Average CD4 T cells are not  the same in both groups)

# Plot the data
 Group<-c(rep("Standard",10),rep("Experimental",10))
 cd4<-c(z1,z2)
 dat<-data.frame(cd4,Group)
 dim(dat)
 head(dat)
 t.2<-ggplot(dat, aes(x=Group, y=cd4,color=Group))+geom_boxplot(aes(fill=Group,color=Group),size=3,width=0.4, alpha=1)+
   scale_color_manual(values=c("orange","purple"))+scale_fill_manual(values=c("orange", "purple"))+xlab("")+
   ylab("CD4+ T Cell Counts")
  t.2+theme(legend.position="none")
  
 # Testing
  t.test(z1,z2,alternative="two.sided",mu=0,paired=FALSE, var.equal=TRUE, conf.level=0.95)
 
  ########################################################################
  # Anova
  #Plotting data in tabl12.1
  JH<-c(3.23,3.47,1.86,2.47,3.01,1.69,2.10,2.81,3.28,3.36,2.61,2.91,1.98,
        2.57,2.08,2.47,2.47,2.74,2.88,2.63,2.53)
  RLA<-c(3.22,2.88,1.71,2.89,3.77,3.29,3.39,3.86,2.64,2.71,2.71,3.41,2.87,
         2.61,3.39,3.17)
  SL<-c(2.79,3.22,2.25,2.98,2.47,2.77,2.95,3.56,2.88,2.63,3.38,3.07,2.81,
        3.17,2.23,2.19,4.06,1.98,2.81,2.85,2.43,3.20,3.53)
  
  Ho: The means in the three groups are the sample
  Ha: The means in the three groups are not the sample
  
  # Plot Data 
  Volume<-c(JH,RLA,SL)
  Centers<-c(rep("JH",21), rep("RLA",16), rep("SL",23))
  Table12.1Data<-data.frame(Volume, Centers)
  head(Table12.1Data)
  
  
  q<-ggplot(Table12.1Data, aes(x=Centers, y=Volume,color=Centers))+geom_boxplot(aes(fill=Centers, color=Centers),size=1, width = 0.3)+geom_jitter(position = position_jitter(width =0),size=3)+scale_color_manual(values=c("orange", "purple", "green"))+scale_fill_manual(values=c("orange", "purple", "green"))+xlab("Center")+ylab("Forced Expiratory Volume")+geom_boxplot(aes(fill=Centers, color=Centers),size=3, width = 0.4)
  q+theme(legend.position="none")
  
  #Test 
  anova.test<-aov(Volume~Centers, data=Table12.1Data)
  summary(anova.test)
 
  
  ####################################################
  #anova
  #Another Example
  A<-c(6.9,5.4,5.8,4.6,4.0)
  B<-c(8.3,6.8,7.8,9.2,6.5)
   C<-c(8,10.5,8.1,6.9,9.3)
# Create a vector with all the distances from the three groups
  
  Distance<-c(A,B,C)
# Create a vector with a list of 5 A's, 5 B's  \& 5 C's
	Teams<-c(rep("A",5),rep("B",5), rep("C",5))

	# Create a data frame with  distance \& team information
	
	 dat<-data.frame(Distance, Teams)
	head(dat)
	
	# Plot data 
	q<-ggplot(dat, aes(x=Teams, y=Distance,color=Teams))+geom_boxplot(aes(fill=Teams, color=Teams),size=1, width = 0.3)+geom_jitter(position = position_jitter(width =0),size=3)+scale_color_manual(values=c("orange", "purple", "green"))+scale_fill_manual(values=c("orange", "purple", "green"))+xlab("Teams")+ylab("Distance")+geom_boxplot(aes(fill=Teams, color=Teams),size=3, width = 0.4)
	q+theme(legend.position="none")
	
	# Test hypotheses
	
	results<-aov(Distance~Teams, data=dat)
 summary(results)
  
 # where is the difference coming from?
 
 # Adj for multiple test
 pairwise.t.test(Distance, Teams, p.adjust="bonferroni")