- You are a nurse working in a Diabetes Education Center (DEC) in Guelph, Ontario. You are interested in studying the relationship between weight (kg) and HbA1c levels (%) in children. You collected data on a random selection of 10-year boys in the clinic that were recently diagnosed with type II diabetes mellitus (T2DM). The table below provides the data that you collected on 15 boys. Assuming HbA1c levels are normally-distributed and α=0.05, use these data to answer the questions below the table.
a. Provide an appropriate plot of the data to show the relationship between weight and HbA1c levels. Comment on the relationship between the two variables. [1 Mark]
b. You decide to explore whether weight is predictive of HbA1c levels. You run a simple linear regression in SPSS to assess this. Provide the regression equation that expresses the relationship between the two variables, and provide the interpretation from one measure in the output that indicates the utility (goodness) of the regression equation. Provide the SPSS output to support your work. [2 Marks]
c. What is the Pearson’s Correlation Coefficient expressing the relationship between weight and HbA1c levels? Show your work. [1 Mark]
d. What is the HbA1c level that you would predict for a weight of 35.2kg? What is the model error for this weight? Show all calculations. [2 Marks]
- A randomized controlled trial (RCT) was undertaken involving 481 type I (insulin-dependent) patients with diabetes who had little or no evidence of retinopathy at baseline. Retinopathies are abnormalities of the retina that sometimes occur among patients with diabetes and can result in advanced stages in substantial losses of vision. Patients were randomized to either Sorbinil, an aldose-reductase inhibitor, or placebo and were seen in 1 year and every month up to 48 months after randomization. The primary endpoint of the RCT was based on change in retinopathy severity level from baseline to the final visit at 48 months (i.e., severity level at 48 months less severity level at baseline). An ordinal grading scale was used to evaluate change: 2+ levels better, 1 level better, no change, 1 level worse., 5+ levels worse. The outcome data (number of people for each change in retinopathy severity level) for the treatment group2 are given in the table below. Use these data to answer the questions below the data table.
GROUP Better Worse
TOTAL
2+ Levels 1 Level No Change 1 Level 2 Levels 3 Levels 4 Levels 5+ Levels
Placebo 5 17 84 59 37 18 9 14 243
Sorbinil 4 21 97 50 22 16 14 14 238
TOTAL 9 38 181 109 59 34 23 28 481
a. You conduct the appropriate statistical test at a 95% confidence level to determine if there is an association between treatment group and change in retinopathy severity level. What do you conclude from this test? Show all calculations. (2 Marks)
b. The primary outcome for the study was worsening by 2 or more levels. Conduct the appropriate statistical test at a 95% confidence level to determine whether the proportion of participants that worsened by 2 or more levels was lower in the treatment group (Sorinil group) compared to the control group (Placebo group). What do you conclude from your test? Show all calculations. [2 Marks]
- A clinical trial was conducted in which three competing treatments for joint pain were compared in terms of their mean time to pain relief in patients with osteoarthritis. Because investigators hypothesize that there may be a difference in time to pain relief in men versus women, they randomly assign 15 participating men to one of the three competing treatments and randomly assign 15 participating women to one of the three competing treatments (i.e., stratified randomization). Participating men and women do not know to which treatment they are assigned. They are instructed to take the assigned medication when they experience joint pain and to record the time, in minutes, until the pain subsides. The data (time in minutes to pain relief) are shown below and are organized by the assigned treatment and sex of the participant. Use these data to answer the questions below the data table. Assume α=0.05.
Treatment Male Female
A 12 21
15 19
16 18
17 24
14 25
B 14 21
17 20
19 23
20 27
17 25
C 25 37
27 34
29 36
24 26
22 29
a. Create box & whisker plots to compare the time until pain subsides in males and females across the three treatment groups. Comment on the patterns you see for time until pain subsides across groups for both sexes. [2 Marks]
b. Run the appropriate statistical test to determine if there is a significant difference in the time until pain subsides in males across the three treatment groups. What do you conclude from running this test? Provide the calculation and/or SPSS output to support your answer. [1 Mark]
c. Run the appropriate statistical test to determine if there is a significant difference in the time until pain subsides in females across the three treatment groups. What do you conclude from running this test? Provide the calculation and/or SPSS output to support your answer. [1 Mark]
d. You decide to conduct post-hoc tests to follow up on the results for males. Choose an appropriate post-hoc test and discuss the results in terms of where specific group differences lie. Show all work. [2 Marks]
- A RCT is conducted involving 13 surgical patients to test the time taken (in minutes) for blood to clot. The patients are randomly assigned to two different drug groups (A, B) and the time taken for blood to clot in the two groups is recorded. The data are provided in the table below. Use these data to answer the questions below the table.
Drug Patient 1 Patient 2 Patient 3 Patient 4 Patient 5 Patient 6 Patient 7
A 8.8 8.4 7.9 8.7 9.1 9.6
B 9.9 9.0 11.1 9.6 8.7 10.4 9.5
a. Conduct the appropriate statistical test to determine whether the time taken for blood to clot in the two drug groups is the same. Assume that time taken for blood to clot is normally distributed with equal variance in the patient population, and α = 0.05. Show all calculations. [2 Marks]
b. What would you conclude for the hypothesis tested in question a if you assumed that α=0.01? (continue to assume that time is normally distributed with equal variance in the patient population). Explain. [1 Mark]
c. Calculate the 95% confidence interval for the mean difference between the drugs for the time until blood clots. Show your calculation. [1 Mark]
- It is fairly-well known that perception of weight by adolescents does not always agree with their actual weight. What is less clear is whether actual weight differs by gender. For this purpose, a study was performed among students in a local high school (143 boys, 143 girls), where students provided their actual weight by self-report. The students were classified as underweight if their body mass index (BMI, kg/m2) ) was less than 18.0 , as normal if BMI was ≥ 18.0 and < 25.0, and overweight if their BMI was ≥ 25.0. Based on these criteria, 17 of the girls were underweight, 113 were or normal weight, and 13 were overweight. For the boys, 7 were underweight, 115 were normal weight, and 21 were overweight. Use these data to answer the questions below.
a. Conduct the appropriate statistical test to determine if there is an association between gender and weight classification, assuming α=0.05. What do you conclude based on the test results? Show all calculations. [2 Marks]
b. What is the p-value for the test you calculated in question a? Does this p-value support the conclusion you reached in question a? Explain. [1 Mark]
- An important hypothesis in hypertension research is that sodium restriction may lower blood pressure. However, it is difficult to achieve sodium restriction over the long term, and dietary counseling in a group setting is sometimes used to achieve this goal. The data on urinary sodium (mEq/8hr) in the table below were obtained from 36 older adults who had received 8 weeks of prior dietary counselling and 32 older adults who received no dietary counselling. Previous research has shown that sodium is not normally-distributed in the older adult population. Use these data to answer the questions below the table.
Patient No Counseling Received
Counselling Patient No Counseling Received Counselling
1 27.85 30.50 19 19.76 34.52
2 12.03 9.59 20 19.08 23.01
3 21.84 4.55 21 34.57 15.67
4 13.94 20.78 22 19.66 13.28
5 16.68 11.69 23 36.81 26.87
6 41.78 32.51 24 40.34 24.37
7 14.97 5.46 25 32.51 30.00
8 22.07 12.95 26 37.54 23.11
9 17.65 16.50 27 30.78 19.81
10 20.56 11.63 28 19.57 20.92
11 14.82 15.89 29 37.83 32.67
12 33.18 24.68 30 39.63 7.88
13 14.96 9.64 31 43.87 33.45
14 28.97 18.93 32 17.65 26.75
15 40.08 19.45 33 21.00
16 36.76 30.78 34 16.89
17 36.11 22.46 35 26.79
18 31.58 25.87 36 22.01
a. Select an appropriate plot to compare urinary sodium levels in the two groups. Based on the plot, develop a one-sided question that could be answered by a hypothesis test of the difference in mean sodium levels between the 2 groups. [2 Marks]
b. Conduct the appropriate statistical test to answer the one-sided question you developed in question (a) above. What is the answer to your question? Show all calculations. Assume α=0.05. [2 Marks]
c. What is the p-value for the test statistic you calculated in question (b) above. Show your calculation. [1 Mark]
- You are a RN working in the cardiac outpatient clinic of a large teaching hospital. You are interested in the predictors of high blood pressure in cardiac patients. You have access to a data set of 1,267 clinic patients that contains data on age (AGE, years), sex (MALE, 1=Yes, 2=No), dystolic blood pressure (DBP, mmHg ), systolic blood pressure (SBP, mmHg) and body mass index (BMI). Previous research has shown that DBP and SBP are approximately normally distributed. The excel data set containing the data on these patients is available in the ‘Data Sets’ folder under the Contents tab in A2L. The data set is called DBP_SBP.xlsx. Use these data to answer the questions below.
a. Run a simple linear regression in SPSS to predict DBP from BMI. Using two measures from the SPSS output, comment on whether BMI is useful in predicting DBP. Provide the output to support your comments. [2 Marks]
b. Run a simple linear regression in SPSS to predict SBP from AGE. Using two measure from the SPSS output, comment on whether AGE is useful in predicting SBP. Provide the output to support your comments. [2 Marks]
c. Generate an appropriate plot showing the relationship between DBP and BMI. Comment on the pattern seen in this plot in relation to the results you obtained in question (a) above. [1 Mark]
- A study was conducted to examine whether protein concentration (mg/mL) impacts pancreatic function in cystic fibrosis patients. Pancreatic function was measured by trypsin secretion [U/(kg/hr)]. Prior research has shown that protein concentration in this patient population is approximately normally distributed. Protein concentrations levels were obtained for patients with three levels of trypsin secretion: 1) ≤ 50, 2) 51-1,000, and 3) >1,000. The data are provided in the table below. Use these data to answer the questions below the table. Assume α=0.05.
Trypsin Secretion
≤ 50 [U/(kg/hr) Trypsin Secretion
51-1,000 [U/(kg/hr) Trypsin Secretion
1,000 [U/(kg/hr)
Subject Number Protein Concentration (mg/mL) Subject Number Protein Concentration (mg/mL) Subject Number Protein Concentration (mg/mL)
1 1.7 1 1.4 1 2.9
2 2.0 2 2.4 2 3.8
3 2.0 3 2.4 3 4.4
4 2.2 4 3.3 4 4.7
5 4.0 5 4.4 5 5.0
6 4.0 6 4.7 6 5.6
7 5.0 7 6.7 7 7.4
8 6.7 8 7.6 8 9.4
9 7.8 9 9.5 9 10.3
10 11.7
a. You begin by plotting the data to see whether there is any evidence to suggest that protein concentration levels differ across the three trypsin secretion groups. Generate an appropriate plot of the data and comment on the pattern of protein concentration across the three trypsin secretion groups. [2 Marks]
b. Run the appropriate statistical test to determine if there is a significant difference in protein concentration across the three trypsin secretion groups. What do you conclude from running this test? Provide the calculation and/or SPSS output to support your answer. [1 Mark]
- A study was conducted that compared the time to awaken from a general anesthetic for
ten orthopedic patients that had two knee replacements done in two separate surgeries,
with the anesthetic differing for surgeries on the first knee and the second knee. The
anesthetic used for the first knee replacement was the same for all 10 patients, as was the case for the second knee replacement in the patients. All surgeries were performed by the same surgeon. The study was interested in determining whether there was a difference in the time to awaken following surgery for the two different anesthetics. The data for the
ten patients are provided in the table below. Use these data to answer the question below
the table.
Patient Anesthetic 1 (1st Knee)
Time to awaken (in min) Anesthetic 2 (2nd Knee)
Time to awaken (in min)
1 142 138
2 140 136
3 144 147
4 144 139
5 142 143
6 146 141
7 149 143
8 150 145
9 142 136
10 148 146
a. Conduct the appropriate statistical test to determine if there is a difference in the time to awaken from the anesthetics for the two different types of anesthetic. Assume α=0.05. Show all calculations. [2 Marks]
b. What is the p-value for the test you performed in question a above? Does this p-value support the conclusion you reached in question a? Explain. [2 Marks]
