MATH1041 - Statistics for Life and Social Science Assignment - UNSW

Assignment Task

Data: Together with this document, you should have received your unique dataset in an e-mail sent to your official university email address. The data (that is, your dataset) are available in a text file with the name 5476958.csv. If you have not received your dataset (double check your UNSW email inbox and the spam folder), please contact your explanations about the assignment and typesetting.

Scenario

Parkinson’s disease (PD), or simply Parkinson’s, is a chronic degenerative disorder of the central nervous system in the brain that affects both the motor system and non-motor systems. The symptoms usually emerge slowly, and as the disease progresses, non-motor symptoms become more common. Early symptoms are tremor, rigidity, slowness of movement, and difficulty with walking, speaking or swallowing. Problems may also arise with cognition, behaviour, sleep, and sensory systems. a

The original dataset b analysed by J. Hlavnička et al. in 2017 c includes a random sample of 30 patients with early untreated Parkinson’s disease (PD), a second independent random sample of 50 patients with Rapid Eye Movement (REM) sleep behaviour disorder (RBD), which are at high risk of developing Parkinson’s disease; and a third independent random sample of 50 healthy controls (HC). All patients were scored clinically by a well-trained professional neurologist with experience in movement disorders. All subjects were also examined during a single session with a speech specialist. In the (first) column Code, an entry such as RBD01 would indicate that this is Patient 01 out of 50 in the REM sleep Behaviour Disorder group.

The data you received by email is a random sample extracted from the original data described above. A limited number of rows of your personal dataset is shown on the right. The variables considered here are: Age, Sex, Duration of pause intervals (ms) and RateSpeech timing (-/min) (acoustic information about the rhythmic organization of speech describing its quality), and FingerTaps (giving an ordered score in { 0 , 1 , 2 , 3 , 4 } to a finger tapping task, where 0 indicates “no problem” and 4 indicates “cannot or can only barely perform the task”). It is usually assumed that people with Parkinson’s disease tend to have, on average, a higher Duration of pause intervals and a lower Rate of speech timing.

The Analysis Tasks

The questions below follow a logical order that can be used for analysing real data. Also, working through these questions will help you better understand some concepts presented in the slides, which will be helpful for the final exam.

PART 1- Study Design

1. In this question, you will think about the research questions and aspects of study design. For all parts in Q1, your answers should be no more than one sentence long.

• Briefly, explain what is the research question that the stakeholders are interested in based on what is described in the Keep this in mind when you analyse the data in Parts II and III.
• What is the population that is of interest to researchers?
• What are the cases here? (We do not expect a list of all cases )
• Is it an observational study or is it an experiment? Provide a brief justification for your answer.

2. In this question, you will describe the organisation of the data. For each one of part a–c, your answer should be no more than two sentences.

• Your data is provided to you in a specific file What is the extension of the data file and what does the extension stand for?
• What is the sample size? (We expect a value )
• What are the IDs (labels)? Give only the ID of the first
• Complete the table below so that it lists all of the variables that are contained in the dataset and the type of each variable. You should add rows to the table as required. When describing the type of each variable, you should be more specific than just saying that the variable is categorical or quantitative,

i.e. you should specify what kind of categorical or quantitative variable it is.

PART 2 - Exploratory Data Analysis

3. Your second task, as any statistician would, is to explore your data with univariate analyses to gain a good understanding of each variable in the data set. This is always a good strategy to help you detect problems in a data set, and also to know enough about your data to better answer the research questions.

a. Let us deal with missing values first, if How many missing values are there in your dataset? You can determine this using the R function is.na(). (They are indicated by NA entries after importation into R, a code meaning “Non Available”.) Just state the number of missing values.

b. When doing initial data exploration, it is always good to consider the potential reasons for missing data and where they appear in the data One way to handle missing values is sometimes to replace all of them with a suitably chosen value. Other times, it is more appropriate to leave them as they are. Considering the scenario, and looking closely at your data, what is the appropriate strategy here? Justify your answer. Your answer should be no more than two sentences.

c. We now move on to univariate graphical Create a boxplot of the variable Age. Include it in your submitted assignment properly labelled.

d. Comment on the presence or absence of outliers in the boxplot you produced in part c (in no more than one sentence).

e. Create an appropriate graphical summary for the variable FingerTaps (only for the subjects that are

NOT healthy controls). Include it in your submitted assignment properly labelled.

f. Comment in no more than one sentence on the trend that you see in the graphical summary in part e.

g. We now move on to univariate numerical Create an appropriate numerical summary for the variable Sex.

h. In no more than one sentence, comment on the result of part g.

i. Compute the five number summary of variable Duration for all subjects combined (healthy and non-healthy). (Do NOT use the fivenum() )

j. In no more than one sentence, comment on the result of part i.

4. i. We now want to study the relationship between the variables Duration and RateSpeech. What type of graphical summary is appropriate for this? Just state the name of the summary (no justification needed here).

ii. It is sometimes appropriate to add a least-squares line to graphical summaries of the kind referred to in part a. Is it the case here? Just answer yes or no for this part.

iii. Justify your answer to the part 4.b. Write no more than 3

iv. Now, produce the graphical summary referred to in part 4.a. Ensure that your plot is properly labelled and include it in your

v. Describe the nature of the relationship observed on the plot you produced in part d, using the four adjectives (or their antonyms) given in the lecture slides. Your answer should be no more than four sentences, but writing only one sentence should suffice. What else do you notice on this plot?

vi. What is an appropriate numerical summary to describe the relationship between the Duration and Rate of Speech? Just state the name of the numerical

vii. Compute the value of the numerical summary referred to in part 4.f. Give your answer to at least two decimal

viii. Comment on the value of the numerical summary you computed in part 4.g in no more than one

ix. Given the results you obtained in the previous parts, it is only necessary to study either Duration or Rate of Speech. (By the way, do you understand why?) We will now focus on Duration . Produce two (side-by-side) boxplots to compare the Duration of healthy controls to the other subjects. Ensure that your plot is properly labelled and include it in your

x. Comment on the trend you see in the plot you produced in part 4.i in no more than one

PART 3: Modeling and Inference

5. Now, we are going to do some modeling and statistical inference.

a. Let µ ₁ be the mean of variable Duration for healthy Let µ ₂ be the mean of variable Duration for non-healthy people. We want to compare µ ₁ to µ ₂ and we assume that µ ₁ is KNOWN (equal to 146) while µ ₂ is UNKNOWN . Recall the name of the hypothesis test strategy you can use here.

b. Perform an appropriate hypothesis test to compare the true means of Duration between healthy and non-healthy You must summarise all steps in your solution:

• state the null (give both H ₀ and H ₀ ) and alternative ( H _a ) hypotheses relevant to the research objectives stated in this scenario,
• an expression/formula for a suitable test statistic,
• its observed value in the sample,
• the null distribution for this statistic,
• the expression of the P-value,
• the numerical value of the P-value,
• your interpretation of the P-value and
• your conclusion in plain

c. Given what you know about the scenario, and by referring to the boxplot obtained in part II, and to any other calculation you can do, briefly discuss the validity of all the assumptions needed to safely apply this hypothesis test. What other graphs could you do here to verify some of these assumptions? (No need to include the graph in your assignment, just give the name of the graph and what it can be used )

6. i Produce a one-sided 95% confidence interval for the difference in means of Duration between healthy controls and non-healthy ones, still assuming that the mean for healthy people is known .

ii. Does this confidence interval include the value µ ₁ given in part a? Is your answer to this consistent with your conclusions from the hypothesis test in part 5.b?

iii. Referring back to the scenario, write a one-sentence plain-language interpretation of the confidence interval obtained

This MATH1041 - Mathematics has been solved by our PhD Experts at My Uni Paper.