Question

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 5 8 7 Medium: 6 6 5 7 8 High: 6 4 7 8 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

(a) The appropriate model of the population is:

Yij = μ + τi + ϵij,

where Yij represents the j-th observation (j=1,2,…,ni) on the i-th treatment (i=1,2,…,k levels). So, Y23 represents the third observation using level 2 of the factor. μ is the common effect for the whole experiment, τi represents the i-th treatment effect, and ϵij represents the random error present in the j-th observation on the i-th treatment.

(b) The hypothesis being tested is:

H₀: µ₁ = µ₂ = µ₃

H_a: Not all means are equal

(c) The critical value is 3.89.

(d) The observed value of the appropriate test statistic is 1.54.

(e) Since 1.54 < 3.89, we fail to reject the null hypothesis.

Therefore, we cannot conclude that the intensity of the intervention program had any effect on the outcome.

	Mean	n	Std. Dev
	7.4	5	1.52	Group 1
	6.4	5	1.14	Group 2
	5.6	5	2.07	Group 3
	6.5	15	1.68	Total
ANOVA table
Source	SS	df	MS	F	p-value
Treatment	8.13	2	4.067	1.54	.2530
Error	31.60	12	2.633
Total	39.73	14