Question

8) Correctional services were interested in evaluating a cognitive-behavioural based intervention designed to reduce violence and offending. A group of researchers assigned nine offenders on parole into a control group for one year and recorded the number of violent incidents perpetrated by the offenders. Then, these offenders were given the intervention for one year and the number of violent incidents perpetrated by the offenders was recorded following the treatment. The researchers are interested in testing whether the treatment had any effect on the outcome. Control 4 7 4 6 8 5 9 7 4 Treatment 3 5 2 7 5 5 6 4 2

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?

f) What is the estimated effect size using Cohen’s d?

g) What is the 95% confidence interval around the difference population mean?

h) Did the intervention have an effect on the outcome?

Answer 1

(a)

The population is a t distribution with Degrees of Freedom = 9 - 1 = 8

(b)

H0: Null Hypothesis: 0 ( The intervention did not have an effect on the outcome )

HA: Alternative Hypothesis: 0 ( The intervention had an effect on the outcome ) (Claim)

(c)

= 0.05

df = 9 - 1 = 8

From Table, critical value of t = 1.86

(d)

From the data, values of d = Control - Treatment are calculated as follows:

d = Control - Treatment = 1, 2, 2, - 1, 3, 0, 3, 3, 2

From d values, the following statistics are calculated:

n = 9

= 1.667

s_d = 1.414

Test Statistic is given by:

(e)

Since calculated value of t = 3.536 is greater than critical value of t = 1.86, the difference is significant. Reject null hypothesis.

Conclusion:
The data support the claim that the intervention had an effect on the outcome.

(f)

The estimated effect size using Cohen’s d is given by:

(g)

= 0.05

df = 8

From Table, critical values of t = 2.3060

Confidence Interval:

So,

Answer is:

(0.5801, 2.7538)

(h)

The data support the claim that the intervention had an effect on the outcome.