Suppose a researcher is interested in comparing the effects of three drugs on ag

Question

Suppose a researcher is interested in comparing the effects of three drugs on aggressiveness in monkeys. There is a possible order effect in administering the drugs to the monkeys along with the usual subject effect. There are 3 subjects available for this experiment.

1. Give an appropriate design for this experiment.

2. Outline an ANOVA table for your design choice by listing all sources of variation (indicating whether each is fixed or random) and listing the degrees of freedom.

3. List any potential problems with your chosen design and the analysis along with possible solutions.

Explanation / Answer

We can use here CRD means Completely Randomized Bloch Design, it;s a one way variation Table for testing of equality of three means draen from three Normal Populaions. Let Xij ( J = 1,2,3...., ni; i = 1,2,3) be three independent random samples from 3 normal populations with means µ1,µ2 and µ3 respectively and with a common variance 2. We may like to test the null hypothesis

H0 : µ1=µ2 =µ3 = µ and 12 =  22 = 32 = 2

Against the null hypothesis H1: µi 's are not equal, and 12 =  22 = 32 = 2

We have to prepare the ANOVA table as

Subjects Means SS df MS    F-Statistic

A X1 SSA n1 -1 MSA=SSA/(n1 -1) MSA/MSE

B X2 SSB   n2 -1 MSB=SSB/(n2 -1) MSB/MSE

C   X3 SSC n3 -1 MSC=SSC/n3 -1 MSC/MSE

E X SSE   n1 + n2+n3 -3 MSE = SSE / n1 + n2+n3 -3

If the calculated value of F at the desired level of p-value say 5% or 1% at given degrees of freedom is less than the tabulated value, we shall accept the hypothesis or we reject.

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