Question 1: Identify each of the variables in the above table either as nominal, ordinal, discrete or continuous.
Question 2: Fill up the following table using appropriate summary statistics for each of the listed variables. Discuss whether dyslipidaemia is related to HbA1c, diastolic BP, insulin status and patients’ age.
Question 3: Graphically determine the relationship between dyslipidaemia and each of the following variables: duration of diabetes group, BMI group and occupation type. Present each of the above variables on an appropriate graph and discuss.
Question 4: For the following questions show the detailed calculations, most marks will be allocated for correct calculations.
(a) The lifetime of a battery is normally distributed with a mean life of 40 hours and a standard deviation of 1.2 hours. Find the probability that a randomly selected battery lasts longer than 42 hours.
(b) At a hospital, the ages of all new employees hired during the last 5 years are normally distributed. Within this curve, 95% of the ages, centered about the mean, are between 24.6 and 37.4 years. Find the mean age and the standard deviation of the data.
(c) Given that the scores on a medical test follow a normal distribution with a mean of 460 and a standard deviation of 100. If all students in a class of 41 attend the test what is the probability that the given class will obtain a mean score of above 589.93?
Question 5: Consider that the distribution of systolic blood pressure in the population is positively skewed. What will be the shape of the sampling distribution of the sample mean of systolic blood pressure in large samples?
Question 6: Briefly discuss the difference between:
 Randomized clinical trial (RCT) and prospective cohort study,
 Casecontrol study and historical (retrospective) cohort study,
 Prospective cohort study and historical cohort study
Identifying Variables in the Cohort Study
Variables 
Classification 
Value labels 
ID Number 
Ordinal 
NA 
Age (in years) 
Discrete 
NA 
Age Group 
Nominal 
1: < 40 years, 2: 40  49 years, 3: 50 – 59 years and 4: >= 60 years 
Gender 
Nominal 
1: Male; 2: Female 
Occupation Type 
Nominal 
1: Sedentary worker; 2: Moderate worker; 3: Heavy physical worker 
Physical Activity Level 
Nominal 
0: Sufficient PA; 1: Insufficient PA 
Weight (in Kg) 
Continuous 
NA 
Height (in meter) 
Continuous 
NA 
BMI (in Kg/m^{2}) 
Continuous 
NA 
BMI Group 
Nominal 
0: Normal; 1: Overweight; 2: Obese 
Diastolic BP 
Discrete 
NA 
Systolic BP 
Discrete 
NA 
Hypertension 
Nominal 
0: Normotensive; 1: Hypertensive 
Duration of Diabetes 
Discrete 
NA 
Duration of Diabetes Group 
Nominal 
1: < 5 years; 2: 5 < 10 years; 3: >= 10 years 
HbA1c 
Continuous 
NA 
HbA1c Group 
Nominal 
0: <7 years; 1: >= 7 years 
Takes insulin 
Nominal 
0: No; 1: Yes 
Duration of Insulin (years) 
Discrete 
NA 
Total Cholesterol 
Discrete 
NA 
Total Cholesterol Group 
Nominal 
0: <200; 1: >= 200 
Triglyceride 
Discrete 
NA 
Triglyceride Group 
Nominal 
0: <150; 1: >= 150 
HDL Cholesterol 
Discrete 
NA 
HDL Cholesterol Group 
Nominal 
0: Normal; 1: Low 
LDL Cholesterol 
Discrete 
NA 
LDL Cholesterol Group 
Nominal 
0: <100; 1: >= 100 
Serum Creatinine 
Continuous 
NA 
Serum Creatinine Group 
Nominal 
0: < 100; 1: >= 100 
TC_HDL ratio 
Continuous 
NA 
LDL_HDL ratio 
Continuous 
NA 
Dyslipidemia 
Nominal 
0: No Dyslipidemia; 1: Yes Dyslipidemia 
Variable 
Dyslipidemia (% or median & IQR or mean & SD) 

Yes 
No 

Hb1Ac 
84.43 
15.57 
BP diastolic 
84.43 
15.57 
Insulin status: 

Yes 
31.97 
5.74 
No 
52.46 
9.84 
Age group: 

< 40 years 
12.84 
3.01 
40 – 49 years 
30.33 
4.37 
50 – 59 years 
34.15 
7.38 
≥ 60 years 
7.10 
0.82 
The relationship between two categorical variables can be shown only with the help of clustered bar charts. This is the most appropriate chart to show the relationship between categorical variables. From figure 3.1, it is clear that dyslipdaemia is maximum in normal people and minimum in obese people.
Figure 3.1: Relationship between BMI group and dyslipdaemia
Again, from figure 3.2, it is clear that dyslipdaemia increases with the increase in age. Figure 3.3 shows the relationship between dyslipdaemia. It shows that dyslipdaemia is maximum in sedentary workers and is almost negligible in heavy physical workers.
Figure 3.2: Relationship between diabetes group and dyslipdaemia
Figure 3.3: Relationship between occupation type and dyslipdaemia
Let X be the lifetime of a battery. The lifetime of a battery is normally distributed. The mean life is given by 40 hours and the standard deviation is given by 1.2 hours. Therefore, the probability that a randomly selected bulb will last longer than 42 hours is P (X > 42) =
Let X be ages of all new employees hired during the last 5 years in a hospital. The ages are said to be distributed normally. The 95% confidence interval of the ages are given by (24.6, 37.4). Since the data is normally distributed, it can be said that the difference between the confidence interval can be distributed into four equal parts to determine the standard deviation. Thus the standard deviation can be given by ((37.4 – 24.6) / 4) = 3.2. By approaching two standard deviations towards the left of the distribution, the mean can be obtained. Thus, the mean is given by ((37.4 – (2 * 3.2)) = 31.
Let X be the scores of a medical test. The scores of a medical test is normally distributed. The mean score is given by 460 and the standard deviation is given by 100. Therefore, the probability that the given class will obtain a score higher than 589.93 is P (X > 589.93) =
The distribution of systolic blood pressure in the population is positively skewed. Thus, the shape of the sampling distribution will also be distributed normally. This can be said from the central limit theorem. The theorem states that when innumerable random samples are drawn from a population, then, the sample means of each of the samples will be equal to the population mean µ and the population standard deviation σ. The sample will also be normally distributed as the population. The sample will always follow a normal distribution if the sample size becomes large, whatever the size of the population may be.
Summary Statistics and Dyslipidaemia Relationships
In this case, it is known that the population is distributed normally. Thus, from the theorem, it can be clearly said that the sampling distribution of the blood pressure of the population is also normally distributed as the sampling distribution contains innumerable number of random samples from the population.
1.A randomized clinical trial is the type of study where the participants are assigned randomly to different groups which compare different treatments. The participants or the researchers are not allowed to choose in which group which participant is going to be in. It will always be selected randomly. This procedure will be able to make the different groups similar to each other and the treatments received by the participants can be compared in each of the groups objectively. The when the trial starts, the best treatment is not known. The patient gets full freedom to decide whether he wants to participate in the random trial. This is randomized clinical trial.
When a research is conducted over a long period of time on the group of some individuals possessing a lot of similar characteristics and differing in one certain characteristic (eg, smoker and nonsmoker female nurses) for comparison of them for a particular outcome (eg., lung cancer) is known as prospective cohort study
2.Case Control study is a study of comparison of two types of patients. One group possesses a particular disease of interest and the other group does not possess the disease. It also indicates the frequency of exposure to the disease or risk and determine the relationship between them.
Retrospective cohort study on the other hand, is the type of research study where, the records of medical history of the participants similar in many ways and different in a particular characteristic are compared for the outcome of interest. In this case, the data is always available and is not based on experiments.
3.In both prospective and retrospective and retrospective cohort study, the participants of interest are the same. They all possess similar characteristic and differ in one characteristic. The difference between the two types of study is that prospective cohort study is done on the basis of the samples selected and monitoring them over a period of time. Thus, the collection of data is time consuming. On the other hand, the retrospective study is done on the basis of medical history data of the individuals on the characteristic of interest. Thus, in prospective study, the sample is selected and then the data is collected by monitoring them, but in retrospective study, the data is obtained at first and then the sample is selected on the basis of the accepted data.
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