Chi Square and Odds Ratio Researchers were interested in examining whether a his
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Question
Chi Square and Odds Ratio
Researchers were interested in examining whether a history of diabetes influenced where patients recovering from Coronary Artery Bypass Graft surgery completed their cardiac rehab. (5 points)
Crosstabs
diabetes2 * Post-event rehabilitation Crosstabulation
Post-event rehabilitation
Short hospital care
Extended care
unit
Outpatient care
Combination
Total
Diabetes
Yes
Count
16
12
20
8
56
Expected Count
22.3
12.9
15.9
4.8
56.0
Std. Residual
-1.3
-.2
1.0
1.4
No
Count
298
169
204
60
731
Expected Count
291.7
168.1
208.1
63.2
731.0
Std. Residual
.4
.1
-.3
-.4
Total
Count
314
181
224
68
787
Expected Count
314.0
181.0
224.0
68.0
787
Answer the following questions using the table above.
What are the total number of diabetics in this study?
What was the expected count and actual count of diabetics in outpatient care?
What was the overall sample size?
What percent of the sample size is not diabetic (this will require a calculation)?
What percent of nondiabetics were in an extended care unit?
Chi-Square Tests
Value
df
Asymp. Sig. (2-sided)
Pearson Chi-Square
5.341a
3
.148
Likelihood Ratio
5.123
3
.163
Linear-by-Linear Association
5.237
1
.022
N of Valid Cases
787
a. 1 cells (12.5%) have expected count less than 5. The minimum expected count is 4.84.
Identify the independent and dependent variable.
What is the null and alternate hypothesis?
What is the test statistic value?
Interpret the results in terms of the original research hypothesis. Assume alpha = .05.
Researchers were interested in whether patients with a history of angina are more likely to take anticoagulant drugs. (5 points)
angina2 * Taking anticoagulant drugs Crosstabulation
Taking anticoagulant drugs
Total
Yes
No
Angina
Yes
Count
311
25
336
Expected Count
177.3
158.7
336.0
Std. Residual
10.0
-10.6
No
Count
242
470
712
Expected Count
375.7
336.3
712.0
Std. Residual
-6.9
7.3
Total
Count
553
495
1048
Expected Count
553.0
495.0
1048.0
Value
df
Asymp. Sig. (2-sided)
Exact Sig. (2-sided)
Exact Sig. (1-sided)
Pearson Chi-Square
314.204
1
.000
Continuity Correctionb
311.859
1
.000
Likelihood Ratio
358.893
1
.000
Fisher's Exact Test
.000
.000
Linear-by-Linear Association
313.904
1
.000
N of Valid Cases
1048
Value
95% Confidence Interval
Lower
Upper
Odds Ratio for angina2 (Yes / No)
24.160
15.623
37.363
For cohort Taking anticoagulant drugs = Yes
2.723
2.447
3.030
For cohort Taking anticoagulant drugs = No
.113
.077
.165
N of Valid Cases
1048
Identify the null and alternate hypothesis.
Interpret test statistic and state conclusion based on original hypothesis. Assume alpha = .05
Interpret the odds ratio based on original research hypothesis.
Interpret the relative risk for those patients who take anticoagulant medications.
diabetes2 * Post-event rehabilitation Crosstabulation
Post-event rehabilitation
Short hospital care
Extended care
unit
Outpatient care
Combination
Total
Diabetes
Yes
Count
16
12
20
8
56
Expected Count
22.3
12.9
15.9
4.8
56.0
Std. Residual
-1.3
-.2
1.0
1.4
No
Count
298
169
204
60
731
Expected Count
291.7
168.1
208.1
63.2
731.0
Std. Residual
.4
.1
-.3
-.4
Total
Count
314
181
224
68
787
Expected Count
314.0
181.0
224.0
68.0
787
Explanation / Answer
1.
a) the total number of diabetics in this study is 56
b) the expected count and actual count of diabetics in outpatient care are 15.9 and 20 repectively
c) Tthe overall sample size is 787
d) The percent of the sample size is not diabetic is 731/787 = 0.9288 =93%
e) The percent of nondiabetics were in an extended care unit is 169/787 = 0.2147 =21.47%
f) Post-event rehabilitation is independent variables and Diabetics is dependent variable.
h) H0: Post-event rehabilitation and Diabetics are independent variables
H1: Post-event rehabilitation and Diabetics are not independent variables
i) Test Statistic, chisquare (X^2) = 5.3410
j) The Critical X^2: 7.814736 P-Value: 0.1485
Here chisquare = 5.3410 < Chisquare critical value and P value > 0.05 alpha
Hence, We accept H0. i.e.Post-event rehabilitation and Diabetics are independent variables
2)
i) H0: angina2 and Taking anticoagulant drugs are independent
H1: angina2 and Taking anticoagulant drugs are not independent
ii) Test statistic value is 314.204 and P - value = 0
Here P value < alpha 0.05, we reject H0
i.e.angina2 and Taking anticoagulant drugs are not independent
iii) The Odds Ratio for angina2 is lies between 15.623 and 37.363 at 95% confidence
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