# MPH5041 Introductory Biostatistics

## Question:

Question 1: Identify all the variables in this table as either nominal, ordinal or discrete.

Question 2: Complete the following table by providing appropriate summary statistics on each of the variables.

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Discuss whether dyslipidemia is related to HbA1c and diastolic BP. Also, discuss insulin status and the patients’ age.

Question 3: Draw a graph to show the relationship between dyslipidemia, each of the following variables.

Give each of these variables a graph and discuss.

Question 4: These questions are about the details of calculations. The majority of marks will be used to calculate correctly.

(a) The average life span of a battery is 40 hours with a standard deviation at 1.2 hours.

Find the probability that a random battery will last more than 42 hours.

(b) The ages of all hospital employees hired within the last 5 years is normally distributed.

95% of these ages are between 24.6 to 37.4 years.

Find the standard deviation and the average age of the data.

(c) A normal distribution of scores from a medical exam has a mean score at 460 and an average deviation of 100.

How likely is it that all 41 students from a class receive a score greater than 589.93 if the test is taken by all?

Question 5 : Consider the fact that the distributions of systolic and diastolic blood pressures in the population are positively skewed.

What is the distribution of the sample mean of Systolic Blood Pressure in large samples?

Question 6: Describe the difference between

Randomized clinical trial (RCT), and prospective cohort study

Case-control study and retrospective cohort study.

Prospective cohort study or historical cohort study

Variables

Classification

Identification Number

Ordinal

Age (in years).

Age Group

Nominal

1: 40 Years, 2: 40 – 49 Years, 3: 50– 59 Years, and 4:>= 60 Year.

Nominal

1: Male, 2: Female

Type of occupation

Nominal

1: Sedentary work; 2: Moderate work; 3: Heavy physical labor

Physical Activity Level

Nominal

0: Sufficient AP;

1 Insufficient PA

Weight (in kg)

Height (in meters)

BMI (in kg/m2)

Nominal

Diastolic BBP

Nominal

Duration of diabetes

Diabetes Group: Duration

Nominal

1: 5 years; 2 : 5 –10 years; 3 : >=10 years

HbA1c group

Nominal

0: 7 year; 1: >=7 years

Insulin is required

Nominal

0: Not; 1: Yes

Insulin duration (years)

Total Cholesterol

Nominal

Nominal

Nominal

0: Normal; 1 = Low

Nominal

Nominal

Ratio of TC_HDL

LDL/HDL ratio

Nominal

Variable

Dyslipidemia (%; median & IQR, or mean &SD)

Yes

No

Insulin status

Yes

No

Age group

40 years

40-49 Years

50 – 59 Years

>= 60 Years

Clustered bars charts can only show the relationship between categorical variable.

This chart shows the relationship between categorical variables.

Figure 3.1 shows clearly that dyslipdaemia can be found in both normal and obese individuals.

Figure 3.1. Relationship between BMI and dyslipdaemia

Figure 3.2 shows that dyslipdaemia rises with age.

Figure 3.3 shows the relationship of dyslipdaemia.

It is evident that dyslipdaemia occurs most in sedentary workers but almost none in heavy physical workers.

Figure 3.2. Relationship between diabetes group & dyslipdaemia

Figure 3.3. Relationship between dyslipdaemia and occupation type

Let X be a measure of the life expectancy of a battery.

Normally, the battery’s lifetime is distributed.

The average life of a battery is 40 hours while the standard deviation is 1.2.

Thus, P (X> 42) is the probability that a randomly selected bulb lasts longer than 42 hours.

Let X represent the ages all new employees that were hired within the last five years at a hospital.

The ages will be distributed in a normal way.

(24.6, 37.5) gives the 95% confidence interval.

The data is normally distributed so the difference between confidence intervals can be broken down into four equal parts. This will give rise to the standard deviation.

So the standard deviation can be calculated as ((37.4-24.6) / 4. = 3.2.

You can find the mean by approaching two standard deviations in the left-hand corner of the distribution.

So, the mean is ((37.4-(2) * 3.2) = 31.

Let X be a score from a medical test.

Normally, the scores of a test are distributed.

The standard deviation is 100 and the mean score is 460.

Thus, P (X > 589.93 = Probability that given class will get a score greater than 589.93) =

Positively, the distributions of systolic and diastolic blood pressures in the population are distorted.

This means that the distribution of sampling is not normal.

This can be seen in the central limit theory.

This theorem says that if random samples are taken from a population, then their sample means will equal the population average u and standard deviation s.

The population will also have a normal distribution of the sample.

If the sample size is greater than the population, the distribution of the sample will follow the same pattern.

It is clear that the population is distributed normal in this example.

According to the theorem, the normal distribution of blood pressure in the population can also be seen as the sampling distribution includes an innumerable number random samples.

1.A randomized clinical trial is where participants are randomly assigned into different groups to compare different treatments.

Participants and researchers cannot choose which group they will be in.

It will always be chosen randomly.

This will allow the different groups to be similar and each participant can compare the treatment received.

The best treatment is unknown until the trial starts.

The patient is free to choose whether to take part in the random study.

This is a randomised clinical trial.

A prospective cohort study is a study that compares the outcomes of a group of individuals who share many of the same characteristics but differ in one characteristic (eg., female nurses who smoke and those who don’t) over a period of time.

2.Case Control Study is a study that compares two types of patients.

One group is affected by a disease, while the other doesn’t.

It also shows the likelihood of being exposed to that disease or risk, and helps determine the relationship between them.

A retrospective cohort study is, however, a type research study where the medical histories of participants, which are often similar, but differ in certain characteristics, are compared in order to find the outcome of particular interest.

The data in this case is available all the time and not dependent on experiments.

3.The participants of interest in prospective, retrospective and retrospective cohort studies are identical.

The participants of interest share the same characteristics, and each one is different.

The main difference between these two types of studies is that prospective cohort studies are based on the selection of samples and their monitoring over a time period.

This makes data collection time-consuming.

The retrospective study, on the other hand is based on the medical history of the subjects with the characteristic of interest.

In prospective study, the sample of interest is first selected, and then data is collected by monitoring them. Retrospective study, however, is done on the basis that the data is first obtained and then data is used to select the sample based on the accepted data.

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