Question

In a study of binge drinking among undergraduates at Ohio University, a researcher was interested in gender differences as related to binge drinking and to drinking-related arrests. She wanted to know two things: (a) Is there a significant relationship between gender and binge drinking (as defined by 5 or more drinks at one sitting), and (b) Is there a significant relationship between gender and drinking-related arrests? A random sample of males and females were asked about their experiences with binge drinking and with drinking-related arrests. Test for a relationship in the following data:

                              Binge Drinking?

  YES        NO

   Male                       36         21

   Female                   26         45


What is the calculated chi-squared value

Answer 1

Solution:

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

Null hypothesis: H0: There is no relationship in two variables.

Alternative hypothesis: Ha: There is a relationship in two variables.

We assume 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 = 2

Number of columns = c = 2

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

α = 0.05

Critical value = 3.841459

(by using Chi square table or excel)

Calculation tables for test statistic are given as below:

Observed Frequencies
	Binge Drinking?
Gender	Yes	No	Total
Male	36	21	57
Female	26	45	71
Total	62	66	128

Expected Frequencies
	Binge Drinking?
Gender	Yes	No	Total
Male	27.60938	29.39063	57
Female	34.39063	36.60938	71
Total	62	66	128

Calculations
(O - E)
8.390625	-8.39063
-8.39063	8.390625

(O - E)^2/E
2.549952	2.39541
2.047145	1.923075

Test Statistic = Chi square = ∑[(O – E)^2/E] = 8.915582

χ2 statistic = 8.915582

P-value = 0.002827

(By using Chi square table or excel)

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that there is a relationship in two variables.