This document contains code for conducting statistical analysis on a dataset. It generates sample data with factors for operator, order, and method. It performs exploratory data analysis including plots. It then conducts an ANOVA and Fisher's LSD test to analyze differences between groups.

1. Samples of Statistical Work

5. Operator=as.factor(c(rep("Operator 1", 4), rep("Operator 2", 4), rep("Operator 3", 4), rep("Operator 4", 4))) ####
COLUMN EFFECT ####
Order=as.factor(c(rep(1:4, 4)))
Method=as.factor(c("C", "B", "A", "D", "D", "C", "B", "A", "A", "D", "C", "B", "B", "A", "D", "C"))
Time=c(10, 7, 5, 10, 14, 18, 10, 10, 7, 11, 11, 12, 8, 8, 9, 14)
tv.data=data.frame(Operator, Order, Method, Time)
tv.data
#### SOME EXPLORATORY PLOTS ####
plot.design(tv.data, main="Generated by Plot Design")
boxplot(split(Time, Method), main="Observations vs Method")
boxplot(split(Time, Operator), main="Observations vs Operator")
boxplot(split(Time, Order), main="Observations vs Order of Assembly")

11. #### ANOVA ####
milk.aov=aov(Obs ~ Solution + Days, data=milk.data)
summary(milk.aov)
anova(milk.aov)
#### SOME PLOTS ####
par(mfrow=c(2,2))
plot(milk.aov)
#### Fisher LSD ####
y.bar<-tapply(Obs, Solution, mean)
MSE<-anova(milk.aov)$Mean[3]
(t_cr<-qt(0.025,6,lower.tail=F))
(t_12<-(y.bar[1] - y.bar[2])/sqrt(MSE*2/4))
(t_13<-(y.bar[1] - y.bar[3])/sqrt(MSE*2/4))
(t_23<-(y.bar[2] - y.bar[3])/sqrt(MSE*2/4))
# We reject H0 if |t| > t_cr
abs(t_12)>t_cr
abs(t_13)>t_cr
abs(t_23)>t_cr
# Or we can compute P-value:
2*pt(abs(t_12), 6,lower.tail=F)
2*pt(abs(t_13), 6,lower.tail=F)
2*pt(abs(t_23), 6,lower.tail=F)