Question

A researcher is interested in determining if the attitude about homosexual marriages is dependent on region. In order to do the Chi-Square association test, she ran analysis with Minitab and came up with the contingency table that summarizes the actual observations and the expected observations. α=0.05.

	Agree	Disagree	Neutral
East	78	136	16
Midwest	63	183	16
South	74	23	16
West	50	138	7

Report your test statistic and your conclusion .

Round your test statistic to the nearest decimal. Report your conclusion as D (dependent) or I (independent)

Answer 1

Chi-square test of independence

Solution:

Here, we have to use chi square test for independence of two categorical variables.

Null hypothesis: H₀: The attitude about homosexual marriages is independent on region.

Alternative hypothesis: H_a: The attitude about homosexual marriages is dependent on region.

We are given level of significance = α = 0.05

Test statistic formula is given as below:

Chi square = ∑[(O – E)^2/E]

Where, O is observed frequencies and E is expected frequencies.

E = row total * column total / Grand total

We are given

Number of rows = r = 4

Number of columns = c = 3

Degrees of freedom = df = (r – 1)*(c – 1) = 3*2 = 6

α = 0.05

Critical value = 12.59159

(by using Minitab)

Calculation tables for test statistic are given as below:

Observed Frequencies
	Column variable
Row variable	Agree	Disagree	Neutral	Total
East	78	136	16	230
Midwest	63	183	16	262
South	74	23	16	113
West	50	138	7	195
Total	265	480	55	800

Expected Frequencies
	Column variable
Row variable	Agree	Disagree	Neutral	Total
East	76.1875	138	15.8125	230
Midwest	86.7875	157.2	18.0125	262
South	37.43125	67.8	7.76875	113
West	64.59375	117	13.40625	195
Total	265	480	55	800

Calculations
(O - E)
1.8125	-2	0.1875
-23.7875	25.8	-2.0125
36.56875	-44.8	8.23125
-14.5938	21	-6.40625

(O - E)^2/E
0.043119	0.028986	0.002223
6.519892	4.234351	0.224853
35.72612	29.60236	8.721284
3.297185	3.769231	3.061262

Chi square = ∑[(O – E)^2/E] = 95.23087

P-value = 2.48E-18 = 0.00

(By using Minitab)

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that the attitude about homosexual marriages is dependent on region.

Conclusion: D