STAT2401: Assignment 2

• This ASSIGNMENT IS ASSESSED. It carries weight 15% towards your final mark

for the STAT2401 unit.

• Your work for this assignment must be submitted by 3:00pm on Friday 14th May

2021.

• You are only required to submit your answer sheet in PDF with the following layout

and order:

Page 1 Questions 1, 2 (a) & 2 (b)

Page 2 Questions 2 (c) & 2 (d)

Page 3 Questions 2 (e)

Page 4 Questions 2 (f), 2 (g), 3 (a) & 3 (b)

Page 5 Questions 3 (c) & 3 (d)

Page 6 Questions 3 (e)

Page 7 Questions 3 (f) & 3 (g)

Page 8 Questions 4 (a), 4 (b), 4 (c) & 5

and use the font type Times New Roman with size 12. You will not gain any mark

if you don’t follow the layout and order. Only electronic submission is acceptable. More

than 8 pages submission would not be accepted. Let me know if you have any difficulty.

– The submission of your answer should be done via LMS over the Assignment 1

Upload Point under the Assignments and Tests folder. Only 1 single PDF

document would be accepted. The PDF file should be save as "your student

ID [Your name].pdf", fail to meet this requirement would not be accepted. Lastly,

no any other format, including any photo format, would be accepted except PDF

format.

– It is preferred that your submission typed. Your name and student ID should be on

every page and pages should be numbered.

• Please ensure that you write your name and student number on your work.

• Unless special considerations were granted, any student failing to submit work by the

deadline will receive a penalty for late submission (5% per day late, 0 marks after 7 days).

The number of days late by is a whole number rounded up from the time after 3:00pm

on the due date.

• Plagiarism: The work that you submit must be your sole effort (i.e. not copied from

someone else). If you are found guilty of plagiarism, you will be subjected to disciplinary

action. You are reminded of the University ‘Policy on Plagiarism’:

https://www.governance.uwa.edu.au/procedures/policies/

policies-and-procedures?method=document&id=UP07%2F21

STAT2401: Assignment 2

An Airway Experiment

This assignment aims to analyze a dataset. An experiment was carried out to examine differ-

ences in airway responses of individuals depending on the condition of the individual.

This experiment involved the taking of samples from deceased individuals lungs. Each individual

was categorised as either a control (group 1) subject (patient), a fatal asthma (group 2)

subject (patient), or a non-fatal asthma (group 3) subject (patient). 5 random samples per

subject (patient) were taken. The figure below illsurates the data structure

group control fatal non-fatal

patient 240 244 249 ... ... 234 237 250 ... ... 238 239 242 ... ...

replicate

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The aim of the experiment was to compare the three groupings with respect to the response

measurement the perimeter of the airway basement membrane (peri-inter) (pbm). This experi-

ment is a nested design.

The data for this experiment can be found on the STAT2401 webpages and be read into R by

using the following commands:

dat = read.csv("ass2_data.csv",header=T)

Contact the lecturer immediately if you have difficulty accessing this data set.

We would like in this assignment for you to analyse this data under the nested design (with

transformation and without transformation on pbm). Find the instructions below and answer

all the questions.

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Instructions & Questions:

1. This is a nested design. Determine the random factor(s), the fixed factor(s), and the

response.

[3 Marks]

2. Analyze the orginal data, take the response to be pbm

(a) Give the boxplot of pbm against group.

[2 Marks]

(b) Comment on the boxplot given in question (a).

[2 Marks]

(c) The model for fitting the data is given by

Yijk︸ ︷︷ ︸

bpm

= µ︸ ︷︷ ︸

Overall

Mean

+ αi︸ ︷︷ ︸

Effect of

group i

+ βij︸ ︷︷ ︸

Random Error

patient within group

+ ijk︸ ︷︷ ︸

Random Error

for i = 1, . . . , 3, j = 1, . . . , 30, k = 1, . . . , 5. The µ and αi are fixed mean parameters.

βij and ijk are all independent, Normal random variables with mean 0 and variances

σ2β, and σ

2 respectively. Write down the R-code for fitting this ANOVA model.

[2 Marks]

(d) Fit the model in part (c) to the data and report the ANOVA table.

[2 Marks]

(e) To check the assumptions, we rather than fitting the model with a single error term

(One-way ANOVA model) and obtain the Overall Residual. Plot the followings

i. ”Overall” Residuals vs Fitted Values

ii. Standardized ”Overall” Residuals vs Fitted Values

iii. Q-Q plot for the Standardized ”Overall” Residuals

[3 Marks]

(f) Comment on the plots in part (e).

[2 Marks]

(g) Based on the ANOVA table presented in part (d), is the group factor significant?

[2 Marks]

3. Analyze the data with transformation, take the response be natural logarithm of perimeter

of the airway basement membrane, (log(pbm)), and repeat part 2(a)-2(g).

[15 Marks]

4. Following Question 3, answer the following questions

(a) What is the standard error of difference (SED) of Y¯1.. − Y¯2..?

[2 Marks]

(b) What is the least significant difference (LSD) of Y¯1.. − Y¯2..?

[2 Marks]

(c) Construct 95% C.I.s (use LSD without any adjustment) for the differences of all

group means (µ + α1) − (µ + α2), (µ + α1) − (µ + α3), and (µ + α2) − (µ + α3) in

this particular order.

[2 Marks]

5. Do all the groups have the same pbm? If not, which groups have the highest and lowest

pbm?

[2 Marks]

[Total: 41 Marks]

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