Complete randomized experimental design

1. Complete Randomized Experimental
Design using R script
Dr. D. Dutta Roy
Psychology Research Unit
Indian Statistical Institute

2. Hypothetical data
• a1=1:10
• a2=5:14
• a3=10:19
• a4=data.frame(a1=1:5,a2=5:14,a3=10:19)
• a4
• summary(a4)
• a5=stack(a4)
• a5
• boxplot(a4, main="Systematic variation across three training
groups", ylab="Score",xlab="Training groups",col=c(2:4))
• colnames(a4)=c("Theory","Practical","Theory and practical")

3. • a6=aov(a5$values~a5$ind)
• summary(a6)
• tapply(a5$values,a5$ind,mean)
• tapply(a5$values,a5$ind,sd)

4. Fitted data and residual
• paste(a5$values)
• paste(a6$fitted.values)
• paste(a6$residuals)

5. Multiple Range test
• TukeyHSD(a6)
• plot(TukeyHSD(a6))
• kruskal.test(a5$values~a5$ind)
• barplot(tapply(a5$values,a5$ind,mean))

6. Assumptions
• dependent variable should be measured at the continuous level
(i.e., they are interval or ratio variables).
• two independent variables should each consist of two or more
categorical, independent groups.
• You should have independence of observations, which means that
there is no relationship between the observations in each group or
between the groups themselves.
• There should be no significant outliers.
• Your dependent variable should be approximately normally
distributed for each combination of the groups of the two
independent variables.
• There needs to be homogeneity of variances for each combination
of the groups of the two independent variables.