Question

n Merced, California, a random sample of 400 adults were chosen to study the strength of

the relationship between being religious and participating in the presidential election. The results can be seen below. Calculate Cramer’s

V for this data.

Religious

Non-Religious

Voted

145

75

Didn’t vote

115

65

Answer 1

applying chi square test:

Expected	Ei=row total*column total/grand total	voted	did not vote	Total
	religious	143.00	117.00	260
	non religious	77.00	63.00	140
	total	220	180	400
chi square    χ2	=(Oi-Ei)2/Ei	voted	did not vote	Total
	religious	0.0280	0.0342	0.062
	non religious	0.0519	0.0635	0.115
	total	0.080	0.098	0.178

here test statistic X² =0.178

Cramer;s V =sqrt(X²/(n*(k-1)) ; where k is minimum of row and column categories ; which is 2 here,

hence Cramer;s V =sqrt(0.178/400)=0.0211