Question

Students are classified according to religious preference (Buddhist, Jewish,

Protestant, Roman Catholic, or Other) and political affiliation (Democrat, Republican,

Independent, or Other).

RELIGIOUS PREFERENCE AND POLITICAL AFFILIATION

RELIGIOUS PREFERENCE

POLITICAL

AFFILIATION BUDDHIST JEWISH PROTESTANT ROM. CATH. OTHER TOTAL

Democrat 30 30 40 60 40 200

Republican 10 10 40 20 20 100

Independent 10 10 20 20 40 100

Other 0 0 0 0 100 100

Total 50 50 100 100 200 500

(a) Is anything suspicious about these observed frequencies?

(b) Using the .05 level of significance, test the null hypothesis that these two variables

are independent.

(c) If appropriate, estimate the effect size

Answer 1

(a)

Some observed frequencies are zero which is suspicious.

(b)

Hypotheses are:

H0: The two variables Political affiliation and religious preference are independent.

Ha: The two variables Political affiliation and religious preference are not independent.

Following is the output of chi square test statistics

Chi-square Contingency Table Test for Independence
			Buddhist	Jewish	Protestant	Rom. Cath.	Other	Total
	Democrat		30	30	40	60	40	200
	Republican		10	10	40	20	20	100
	Independent		10	10	20	20	40	100
	Other		0	0	0	0	100	100
	Total		50	50	100	100	200	500
			220.00	chi-square
			12	df
			2.37E-40	p-value
			.663	Phi coefficient
			.383	Cramér's V

The p-value of the test is;

p-value = 0.0000

Since p-value is less than 0.05 so we reject the null hypothesis.

That is we can not conclude that the two variables Political affiliation and religious preference are independent.

(c)

The effect size is: 0.663

It is large effect size.