MATH20811 Practical Statistics: Coursework 2
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Coursework 2 – Discrete Data Analysis
MATH20811 Practical Statistics: Coursework 2
(Nov - Dec 2022)
The marks awarded for this coursework constitute 30% of the total assessment for the module.
Your solution to the coursework should be reasonably concise - a maximum of about 10 pages with tables, plots, and code, but there is no penalty if you do exceed this. It should take, on average, about 15 hours to complete all the work.
Please read all the instructions and advice given below carefully. The submission deadline is 10:00 am on Monday 12 December 2022 .
Late Submission of Work: Any student’s work that is submitted after the given deadline will be classed as late, unless an extension has already been agreed via mitigating circumstances or a DASS extension.
The following rules for the application of penalties for late submission are quoted from the
latest University guidance on late submission document, version 1.4 (dated November 2020): ”Any work submitted at any time within the first 24 hours following the published submission deadline will receive a penalty of 10% of the maximum amount of marks available. Any work submitted at any time between 24 hours and up to 48 hours late will receive a deduction of 20% of the marks available, and so on, at the rate of an additional 10% of available marks deducted per 24 hours, until the assignment is submitted or no marks remain.”
Your submitted solutions should all be in one pdf document which must be prepared using LaTeX. For each part of the project you should provide explanations as to how you completed what is required, show your workings and also comment on computational results, where applicable.
When you include a plot, be sure to give it a title and label the axes correctly.
When you have written or used R code to answer any of the parts, then you should list this R code after the particular written answer to which it applies. This may be the R code for a function you have written and/or code you have used to produce numerical results, plots and tables. R code should be clearly annotated. Use the verbatim environment in LaTeX.
Do not use screenshots of R plots, or output in your report. You have seen earlier in the course how to include graphics in LaTeX.
Your file should be submitted through the Turnitin assessment called ”PS CW2 2022”in the folder ”MATH20811 CW2” under Assessment & Feedback on Blackboard and by the above time and date. Work will be marked anonymously on Blackboard so please ensure that your filename is clear but that it does not contain your name and student id number. Similarly, do not include your name and id number in the document itself.
There is a basic LaTeX template file on Blackboard which you may choose to use for typing-up your solutions. The file is called CW2_submitted_work .tex.
Turnitin will generate a similarity report for your submitted document and indicate matches to other sources, including billions of internet documents (both live and archived), a subscription repository of periodicals, journals and publications, as well as submissions from other students. Please ensure that the document you upload represents your own work and is written in your own words. The Turnitin report will be available for you to see shortly after the due date.
This coursework should hopefully help to reinforce some of the methodology you have been study- ing, as well as the skills in R you have been developing in the module. Correct interpretation and meaningful discussion of the results (i.e. attempt to put the results into context) are important in order to achieve a high mark for the coursework.
The following table gives the numbers of road casualties in Greater London during 2013, cat- egorised as being either ”fatal”, ”serious” or ”slight” and grouped by five modes of transport.
Casualty Severity Fatal Serious Slight Sum
Mode of Transport Pedestrian 65 773 4343 5181
Pedal Cycle 14 475 4134 4623
Powered 2 Wheeler 22 488 3992 4502
Car 25 310 9850 10185
Other Vehicles 6 146 2556 2708 Sum 132 2192 24875 27199
The question of interest is whether the five modes of transport differ in their respective prob- abilities of different casualty severity. You should regard the row sums as being fixed quantities here.
1. Given the description of the data, write down a suitable probability model for this matrix of counts.
[2 marks]
2. Read the data as a matrix into R and label the two dimensions appropriately. Print out your resulting data matrix.
Then calculate appropriate proportions and comment informally on the question of interest given above.
[5 marks]
3. Present the proportions data graphically and comment on the resulting plot.
[5 marks]
4. State the relevant statistical hypotheses and then:
— explain how the expected frequencies are calculated under the assumption that your
H0 is true and obtain their values for these data;
— test H0 vs Hl using a significance level α = 0.05 and a critical value from the asymptotic
null distribution of your test statistic. (You should clearly state what this distribution is.) State your conclusions.
[3 marks]
5. Print out some appropriate sets of residuals and comment on their values in the light of the conclusions you made in part (iv).
[3 marks]
6. Write a function in R to obtain B = 5000 values of the test statistic, each one calculated using a set of data simulated under the assumption that the null hypothesis is true. You should aim to efficiently make use of for loops in doing this.
Produce a histogram of these simulated values, superimpose the plot of the asymptotic null distribution and comment informally on the goodness-of-fit.
[6 marks]
7. Construct approximate 95% confidence intervals for (a) the difference between the proba- bility that a pedestrian is seriously injured and the probability that a car driver is seriously injured and (b) for cyclists only, the difference between the probabilities of a serious injury and a slight injury.
[6 marks] [Total marks = 30]
2022-12-03
Discrete Data Analysis