Question

A psychologist studying addiction tests whether cravings for cocaine and relapse are independent. The following table lists the observed frequencies in the small sample of people who use drugs.

Obs. Freq. Relapse

Yes No

Cravings Yes    21 12 33

No 6 15 21

27 27 N = 54

(a) Conduct a chi-square test for independence at a 0.05 level of significance. (Round your answer to two decimal places.)

Decide whether to retain or reject the null hypothesis.

(b) Compute effect size using ϕ and Cramer's V. Hint: Both should give the same estimate of effect size. (If necessary, round your intermediate steps to two or more decimal places. Round your answers to two decimal places.)

ϕ =

V =

Answer 1

a)

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	Yes	No	Total
	Yes	16.5000	16.5000	33
	No	10.5000	10.5000	21
	total	27	27	54
chi square    χ2	=(Oi-Ei)2/Ei	Yes	No	Total
	Yes	1.227	1.227	2.4545
	No	1.929	1.929	3.8571
	total	3.1558	3.1558	6.3117
test statistic X2 =		6.3117
p value =		0.0120

from above: test statistic =6.31

since p value < 0.05 , we reject null hypothesis

b)

Phi cpefficieint =φ=√(X2/n)=

0.34

Cramer V=φc=√(X2/(n*(k-1)))=

0.34