Samples of Statistical Work

Design and Experiment AnalysisDealing with Residuals and Hypothesis Testing

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")

Statistics: Survival Analysis Tests and Analysis

#### 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_crabs(t_12)>t_crabs(t_13)>t_crabs(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)

Linear Regression Analysis Sample Work

Time Series Analysis and Forecasting