You read a newspaper article that describes a study of whether stress management
ID: 3371331 • Letter: Y
Question
You read a newspaper article that describes a study of whether stress management can help reduce heart attacks. The 107 subjects all had reduced blood flow to the heart and so were at risk of a heart attack. They were assigned at random to three groups. The article goes on to say:
One group took a four-month stress management program, another underwent a four-month exercise program and the thirst received usual heart care from their personal physicians. In the next three years, only three of the 33 people in the stress management group suffered “cardiac events”, defined as a fatal or non-fatal heart attack or a surgical procedure such as a bypass or angioplasty. In the same period, seven of the 34 people in the exercise group and 12 out of the 40 patients in usual care suffered such events.
a. Use the information in the news article to make a two-way table that describes the study results.
b. What are the success rates of the three treatments in preventing cardiac events?
c. Find the expected cell counts under the null hypothesis that there is no difference among the treatments. Verify that the expected counts meet the guidelines for use of the chi-square test.
d. Is there a significant difference among the success rates for the three treatments?
e. Write a brief summary that includes the test results and also percentages that compare the success of the two treatments.
Explanation / Answer
Result:
you read a newspaper article that describes a study of whether stress management can help reduce heart attacks. The 107 subjects all had reduced blood flow to the heart and so were at risk of a heart attack. They were assigned at random to three groups. The article goes on to say:
One group took a four-month stress management program, another underwent a four-month exercise program and the thirst received usual heart care from their personal physicians. In the next three years, only three of the 33 people in the stress management group suffered “cardiac events”, defined as a fatal or non-fatal heart attack or a surgical procedure such as a bypass or angioplasty. In the same period, seven of the 34 people in the exercise group and 12 out of the 40 patients in usual care suffered such events.
a. Use the information in the news article to make a two-way table that describes the study results.
stress management
Exercise
usual care
Total
cardiac events
3
7
12
22
No cardiac events
30
27
28
85
Total
33
34
40
107
b. What are the success rates of the three treatments in preventing cardiac events?
success rates in stress management = 30/33 =0.909
success rates in Exercise= 27/34=0.7941
success rates in usual care= 28/40 =0.70
c. Find the expected cell counts under the null hypothesis that there is no difference among the treatments. Verify that the expected counts meet the guidelines for use of the chi-square test.
Expected Frequencies
Column variable
stress management
Exercise
usual care
Total
cardiac events
6.785
6.991
8.224
22
No cardiac events
26.215
27.009
31.776
85
Total
33
34
40
107
All the expected values are >5. There fore the expected counts meet the guidelines for use of the chi-square test.
d. Is there a significant difference among the success rates for the three treatments?
Calculations
fo-fe
-3.7850
0.0093
3.7757
3.7850
-0.0093
-3.7757
(fo-fe)^2/fe
2.1115
0.0000
1.7334
0.5465
0.0000
0.4486
Data
Level of Significance
0.05
Number of Rows
2
Number of Columns
3
Degrees of Freedom
2
Results
Critical Value
5.991
Chi-Square Test Statistic
4.8400
p-Value
0.0889
Do not reject the null hypothesis
Calculated chi square 4.84 is < critical chi square value 5.991 at 5% level of significance.
There is no significant difference among the success rates for the three treatments.
e. Write a brief summary that includes the test results and also percentages that compare the success of the two treatments.
The success rate in stress management group is 0.909, success rate in Exercise group is 0.7941 and success rate in usual care group is 0.70. There is no significant difference among the success rates for the three treatments, chi square =4.84, P> 0.05.
stress management
Exercise
usual care
Total
cardiac events
3
7
12
22
No cardiac events
30
27
28
85
Total
33
34
40
107
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