The following table refers to a survey of senior high school students in Dayton,
ID: 3152444 • Letter: T
Question
The following table refers to a survey of senior high school students in Dayton, Ohio. Construct a row percentage table. That is, cigarette smoking is treated as the response variable, and alcohol is treated as the explanatory variable. Construct a column percentage table. The role of response and explanatory variable is now reversed. If there was no association, how many people would you expect in the four different groups? Do the two variables seem independent? Or associated (dependent)? Calculate appropriate measures of association.Explanation / Answer
Cigarette
Alcohol
Yes
No
Yes
1449
500
1949
No
46
281
327
1495
781
2276
Row percentage
74.35
25.65
100.00
14.07
85.93
100.00
65.69
34.31
100.00
Column percentage
96.92
64.02
85.63
3.08
35.98
14.37
100
100
100
Expected Frequencies
Cigarette
Alcohol
Yes
No
Total
Yes
1280.21
668.79
1949
No
214.79
112.21
327
Total
1495
781
2276
Calculations
fo-fe
168.7913
-168.791
-168.791
168.7913
(fo-fe)^2/fe
22.25458
42.59999
132.6427
253.9064
Chi square test statistic =451.4
Calculated chi square =451.4 > 3.841 the table value at 0.05 level.
There is association between cigarette smoking and alcohol use.
Phi coefficient = sqrt(451.4/(451.4+2276))
=0.445
Cigarette
Alcohol
Yes
No
Yes
1449
500
1949
No
46
281
327
1495
781
2276
Row percentage
74.35
25.65
100.00
14.07
85.93
100.00
65.69
34.31
100.00
Column percentage
96.92
64.02
85.63
3.08
35.98
14.37
100
100
100
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