2x2 Chi square test of association

Question 1

Is there a relationship between smoking (S) and drinking (D) in students? Based on the 2x2 chi-square test, what do we aim to find out?

Answer 1

1) The observed counts in the D/S and ND/NS cells are higher than expected if there were no association

2) The observed counts in the ND/S & D/NS cells are lower than expected

Question 2

What is 2x2 chi-square test used for?

Answer 2

Assess whether there is a relationship between 2 categorical variables

Question 3

DoF for 2x2 chi-square test is…?

Answer 3

(Number of rows in category - 1) x (Number of columns in the category - 1)

Question 4

A researcher wants to test the hypothesis that there is an association between taking exercise and depressive episodes in people with a history of depression such that taking exercise reduces the tendency for depressive episodes. For a sample of 100 people she asks 2 questions:

1. Have you taken regular exercise in the last 6 months? (yes/no)
2. Have you had a depressive episode in the last 6 months? (yes/no)

The frequency data for this experiment are:

Observed:
Non exercise & Non Depressed- 18
Non exercise & Depressed- 36
Exercise & Non Depressed- 25
Exercise & Depressed- 21
Total exercise - 46
Total non-exercise - 54
Total depressed - 57
Total non-depressed - 43

Under the null hypothesis that taking exercise and depressive episode occurrence are independent what number of participants would be expect in:

a) Cell 1: associated with a ‘no’ response to exercise and a ‘no’ response to depressive episode

b) Cell 2: associated with a ‘no’ response to exercise and a ‘yes’ response to depressive episode

c) Cell 3: associated with a ‘yes’ response to exercise and a ‘no’ response to depressive episode

d) Cell 4: associated with a ‘yes’ response to exercise and a ‘yes’ response to depressive episode

Using the expected (E) values from parts a) to d) and the observed (O) values in the table above:

e) the quantity (E-O)^2/E for Cell 1 is:

f) The quantity (E-O)^2/E for Cell 2 is:

g) The quantity (E-O)^2/E for Cell 3 is:

h) The quantity (E-O)^2/E for Cell 4 is:

i) The chi-square statistic is:

j) Based on this chi-square value should the researcher reject the null hypothesis?

Answer 4

a) 23.22
b) 30.78
c) 19.78
d) 26.22
e) 1.17
f) 0.89
g) 1.38
h) 1.04
i) 4.48
j) Yes