STAT 3401/STAT

STAT 3401/STAT 4065
Assignment Two
Important: This assignment is assessed, and carries weight 20% towards your final mark for the
STAT3401/STAT 4065 unit. Your work for this assignment must be submitted to the unit lecturer by
5pm on Monday, 20 May 2019.
You may hand in your work during the lectures/computer labs of the STAT3401/STAT 4065 on 20 May,
or electronically at any time before the due date and time. Any student failing to submit work by the
deadline will receive a penalty for late submission (5% per day late) unless the unit lecturer is advised
as soon as possible of any extenuating circumstances. Please ensure that you include your name and
student number on your work.
Plagiarism: The work that you submit must be your sole effort (i.e. not copied from anyone else). If
you are found guilty of plagiarism you may be penalised.
The two assignment questions involve the analysis of some data. The data sets mentioned are available
from LMS. If you have difficulty accessing the data sets you should contact the lecturer immediately.
For these two assignments you should hand in a mini-report. The mini-report for each exercise should
be no longer than a single side of A4 paper (excluding any relevant Figures, Tables or computer output,
which can be attached as an appendix). You will be marked down for exceeding this page limit. The
aim of the mini-report is to convey the aims, methodology and results of your data analysis in a concise,
readable fashion. It is strongly recommended that you structure your report into sections, along the
following lines.
Introduction: Summarise the data and the aims of the analysis.
Methodology: Describe the statistical methods that you use (technical details not required).
Results: Describe the results of your analysis and their interpretations.
Discussion: Draw conclusions (based on your results) as necessary. Discuss any interesting issues
arising from your analysis.
Marks for each mini-report will be awarded (with a relative weighting of 2:3) for
Exposition: your mini-reports should be well organised. You should aim to write in a concise, yet
readable, manner.
Statistical content: marks will be awarded for the correct use of appropriate statistical techniques,
and for the correct interpretation of results from these techniques.
1
Question one
The file rats-ctt.csv contains data from a study of weight gain, where investigators randomly assigned
30 rats to three treatment groups: treatment 1 was a control (no additive); treatments 2 and 3 consisted
of two different additives (thiouracil and thyroxin respectively) to the rats drinking water. Weight was
measured at baseline (week 0) and at weeks 1, 2, 3, and 4.
The data are in “wide” format. Specifically, the meaning of the variable in the data set are:
Name Value
ID Identifier for the rat
Treat Treatment (1=Control, 2=Thiouracil, 3=Thyroxin)
Week0 Baseline weight
Week1 Weight at Week 1
Week2 Weight at Week 2
Week3 Weight at Week 3
Week4 Weight at Week 4
Aims of the analysis: To assess how the two additives affect the weight gain of the rats.
Note: Due to an accident at the beginning of the study, data on 3 rats from the thyroxin group are
unavailable.
2
Question two
In medical science, there has recently been increased interest in the therapeutic use of hormones. However,
such drastic therapies require detailed knowledge about their effect on the different aspects of
growth. An experiment has been set up to investigate the effect of the inhibition of the production of
testosterone in male Wistar rats on their craniofacial growth.
A total of 50 male Wistar rats have been randomized to either a control group or one of the two treatment
groups where treatment consisted of a low or high dose of the drug Decapeptyl, which is an inhibitor for
testosterone production in rats. The treatment started at the age of 45 days, and measurements were
taken every 10 days, with the first observation taken at the age of 50 days. The responses of interest are
distances (in pixels) between well-defined points on X-ray pictures of the skull of each rat, taken after
the rat has been anesthetized.
For the purpose of this assignment, we will consider one of the measurements which can be used to
characterize the height of the skull. Not all rats have measurements up to the age of 110 days. This is
due to the fact that many rats do not survive anaesthesia and therefore drop out before the end of the
study.
The file rats.txt contains the data from this study. Specifically, the following variables can be found
in that data set:
Name Value
obs observation number
treat treatment group: control (con), low dose (low) or high dose (hig)
rat rat identification number
age age of the rat at the moment the observation is made
response the response measured
Aims of the analysis: Of primary interest is the estimation of changes over time and testing whether
these changes are treatment dependent.
Note: Instead of using age directly, you may want to consider the transformation log(1+ (age-45)/10).
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