Question

Ten randomly selected mental institutions were examined to determine the effects of three different antipsychotic drugs on patients with the same type of symptoms. Each institution used one and only one of the three drugs exclusively for one year period. The proportion of treated patients in each institution who were discharged after one year of treatment were given below

Drug1 0.1 0.12 0.08 0.14

Drug2 0.12 0.14 0.19

Drug3 0.2 0.25 0.15

a. Identify the outcome variable, factor, treatment, and experimental unit.

b.Write a linear statistical model for this study, and explain the model components.

c.What is general objective of one way ANOVA?Write the assumptions necessary for an analysis of variance of the data

Answer 1

#Que a

Outcome variable= effect of antipsychotic drugs on patients

Treatment= Three different types of drugs

Experimental unit = patients in mental instituation

#Que b

Yij = µ + ti + eij

Yij =effect of ith drug on jth mental institution

µ=general mean effect

ti =effect of ith drug

eij=random error

µ_estimated=mean(0.1,0.12,0.8,014,0.12,0.14,0.19,0.2,0.25,0.15)= 0.221

t1_estimated=0.29; t2_estimated=0.15; t3_estimated=0.2

hence model is Yij_estimated = 0.221 + ti_estimated

where Yij_estimated = estimated effect of ith drug on jth mental institution

#Que c

General objective in onev way anova is to check whether all three drugs are equally effective or significantly differ from one another

i.e H0: t1=t2=t3 vs H1: ti≠tj for at least one pair (i,j) and i≠j

Assumption of one way ANOVA

• Normality – That each sample is taken from a normally distributed population.
• Sample independence – that each sample has been drawn independently of the other samples.
• Variance Equality – That the variance of data in the different groups should be the same.