ANOVA (Example)

A researcher wishes to try three different techniques to lower the blood pressure of individuals diagnosed with high blood pressure. The subjects are randomly assigned to three groups: the first group takes medication, and the second group exercise, and the third group follows a special diet. After four weeks, the reduction in each person’s blood pressure is recorded. At α=0.05, test the claim that there is no difference among the means.

The data follows:

Solution:

STEP 1 State the hypothesis and identify the claim.

      H0: µ1 = µ2 = µ3 (claim)

      H1 = At least one mean is different from the others

STEP 2 Find the critical value, since k=3 and N=15,

      d.f.N. = k-1= 3-1 =2

      d.f.D. = N-k= 15-3 =12

The critical value is 3.89, obtained from table H in Appendix C with α = 0.05.

STEP 3 Compute the test value.

            

c. Find the between group variance.

d. Find the within group variance.

e. Find the F test value.

STEP 4 Make the decision. 

             The decision is to reject the null   hypothesis since 9.17>3.89.

STEP 5 Summarize the results. 

There is enough evidence to reject the claim and conclude that at least one mean is different from the other. 

By: Andrea Beatrice Pechueco