Question

10) Correctional services were interested in further evaluating a cognitive-behavioural based intervention. The same group of researchers randomly assigned 15 offenders into a low intensity, medium intensity, or high intensity intervention program. The researchers then gathered data on the number of violent incidents perpetrated by offenders over the five years after their release. They were interested in whether the intensity of the intervention program had any effect on the outcome.

Low :9 8 6 8 7

Medium:8 7 5 6 8

High: 5 6 7 4 3

a) What is the appropriate model of the population(s)?

b) What are the appropriate hypotheses for this analysis?

c) What is/are the critical value(s) for this test using an alpha of 0.05?

d) What is the observed value of the appropriate test statistic?

e) What is your decision regarding the stated hypotheses?

Answer 1

Excel output for ANOVA is attached below

######## ANSWERS:

a] assuming parent populations are normally distributed

Here we will use One way ANOVA for equality of means.

b] Null & Alternative hypotheses are

H0: μ1=μ2=μ3 ( intensity of intervention has no effect on the outcome)

H1: μ1,μ2,μ3 not all are equal( intensity of intervention has effect on the outcome)

c]critical value = Fcrit =3.8853 at 5% significance level

d] observed bvalue Fobt = 4.8364

e] decision rule is Reject H0 if Fobt > Fcrit

So we reject H0 at 5% significance level

#Conclusion: there is sufficient evidence that the intensity has significant effect on the outcome.