Cocaine produces short-term feelings of physical and mental well-being. But to m
ID: 3179457 • Letter: C
Question
Cocaine produces short-term feelings of physical and mental well-being. But to maintain the effects, the drug has been taken more frequently and at higher doses. This can lead to addiction. After stopping the drug, users feel fatigued and depressed. A study compared rehabilitation rates of 74 cocaine addicted subjects for 3 treatments: antidepressant () standard (lithium) placebo (sugar pill) The number of individuals receiving each treatment who relapsed back into regular use was counted. The results are given in the 2x2 Chi-square table below. a. First, calculate the marginal and conditional probabilities from the raw data. Make 2 bar charts based on the conditional probabilities: one for the percent of individuals within each treatment group who relapsed, and one for the percent of individuals within each treatment group who did not relapse. b. Second, calculate the expected counts in each cell of the table, and then calculate a Chi-square value. Using the Chi Square Table from class, get a bounded P value for getting a Chi-square value that high or higher by chance alone. State the null and alternate hypotheses and your conclusions given the Chi-square test of hypotheses. c. Finally, enter the data into SPSS following the same structure as for the smoking example from class. Conduct the Chi-square test using the Crosstabs procedure as we did in class. State the results of the test.Explanation / Answer
Result:
b).
Ho: There is no association between relapse and treatment.
H1: There is a association between relapse and treatment.
Chi-Square Test
Observed Frequencies
Column variable
Calculations
Row variable
C1
C2
Total
fo-fe
R1
15
10
25
6.2162
-6.2162
R2
7
19
26
-2.1351
2.1351
R3
4
19
23
-4.0811
4.0811
Total
26
48
74
Expected Frequencies
Column variable
Row variable
C1
C2
Total
(fo-fe)^2/fe
R1
8.7838
16.2162
25
4.3992
2.3829
R2
9.1351
16.8649
26
0.4990
0.2703
R3
8.0811
14.9189
23
2.0610
1.1164
Total
26
48
74
Data
Level of Significance
0.05
Number of Rows
3
Number of Columns
2
Degrees of Freedom
2
Results
Critical Value
5.991
Chi-Square Test Statistic
10.7288
P value = 0.0047
Calculated chi square = 10.7288, P=0.0047 which is < 0.05 level.
Ho is rejected.
We conclude that there is association between relapse and treatment.
c).
Ho: There is no association between relapse and treatment.
H1: There is a association between relapse and treatment.
treatment * relapse Crosstabulation
Count
relapse
Total
No
Yes
treatment
1
15
10
25
2
7
19
26
3
4
19
23
Total
26
48
74
Chi-Square Tests
Value
df
Asymptotic Significance (2-sided)
Pearson Chi-Square
10.729a
2
.005
Likelihood Ratio
10.751
2
.005
Linear-by-Linear Association
9.573
1
.002
N of Valid Cases
74
a. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 8.08.
Calculated chi square = 10.729, P=0.005 which is < 0.05 level.
Ho is rejected.
We conclude that there is association between relapse and treatment.
Chi-Square Test
Observed Frequencies
Column variable
Calculations
Row variable
C1
C2
Total
fo-fe
R1
15
10
25
6.2162
-6.2162
R2
7
19
26
-2.1351
2.1351
R3
4
19
23
-4.0811
4.0811
Total
26
48
74
Expected Frequencies
Column variable
Row variable
C1
C2
Total
(fo-fe)^2/fe
R1
8.7838
16.2162
25
4.3992
2.3829
R2
9.1351
16.8649
26
0.4990
0.2703
R3
8.0811
14.9189
23
2.0610
1.1164
Total
26
48
74
Data
Level of Significance
0.05
Number of Rows
3
Number of Columns
2
Degrees of Freedom
2
Results
Critical Value
5.991
Chi-Square Test Statistic
10.7288
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