Assignment 2
t-Test & Diagnostic Tests
Question 1
In a pre-test post-test experimental design, a researcher is interested to test the effect of a new
cholesterol-lowering drug as an alternative to statins. Data collected from a sample of 20 patients, as
follow:
Test the hypothesis that the new drug is effective to lower the cholesterol level at 0.01 level of
significance.
[3.5 Marks]
a. State the appropriate null and alternative hypotheses;
b. Calculate the test statistic;
c. Determine the critical value;
d. What would be your decision and conclusion. Justify your answer;
e. Is it appropriate to calculate and interpret the 99% CI?
f. Calculate and interpret two appropriate measures of effect size;
g. Run the analysis through SPSS and answer the part ‘d’ and ‘f’ by using the SPSS output.
Respondent
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Pre-test
5.16
5.25
4.89
4.90
4.77
5.61
5.64
4.63
5.01
6.41
5.66
5.56
5.27
5.84
6.04
5.43
5.71
6.41
5.83
6.06
Post-test
4.70
4.68
4.65
4.21
4.16
5.35
4.65
4.59
4.80
5.05
5.09
4.47
5.03
5.35
5.69
4.70
5.01
5.25
5.26
5.61
Question 2
Data on systolic blood pressure for male and female students are presented in the following Table. Test
the significance of difference in systolic blood pressure level between the two groups at 0.05 level of
significance.
[3.5 Marks]
a. State the appropriate null and alternative hypotheses;
b. Calculate the test statistic;
c. Determine the critical value;
d. What would be your decision and conclusion. Justify your answer.
e. Calculate and interpret eta-squared;
f. Calculate and interpret the 95% CI;
g. Run the analysis through SPSS and answer the part ‘d’ and ‘e’ by using the SPSS output.
Respondent
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Male
128.00
110.00
118.00
138.00
130.00
140.00
128.00
110.00
152.00
120.00
112.00
180.00
108.00
120.00
120.00
155.00
128.00
110.00
120.00
136.00
Female
110.00
100.00
120.00
142.00
120.00
102.00
116.00
118.00
106.00
120.00
102.00
120.00
86.00
138.00
140.00
110.00
100.00
110.00
160.00
100.00
Question 3
Consider a new diagnostic test’s developed for diabetes which uses biomarkers in the patients’ saliva
to assess diabetic status; if the test returns a positive result then the patient is presumed to have the
disease. The true diagnosis is whether the patient truly has diabetes or not. This can be assessed with
what is termed a “gold standard”, the conclusive test such as a blood test. The following Table is the
summary of a randomly selected sample whom tested by using the newly developed test and also
confirmed using the blood test as the gold standard. Report the validity of newly developed diagnostic
test (the performance of the diagnostic test relative to the gold standard) by calculating and
interpreting the following parameters:
[3 Marks]
a. Sensitivity;
b. Specificity;
c. Accuracy;
d. Apply the Bayes Theorem to calculate the Positive Predictive Value (PPV) and Negative Predictive
Value (NPV);
Test Results
Positive
Negative
Diabetic
620
230
850
True Diagnosis
Not Diabetic
530
1870
2400
Total
1150
2100
3250