Word limit: 3,500 words maximum, excluding the R script
Deadline: Monday, April 22, 2024, 12pm
When completing the assignment, please remember that
• you should answer all of the questions and all the parts of each question;
• your assignment submission must include a complete log of your R session, including
your R script with the commands and any graphical outputs produced. The log and the
plots don’t count towards the word limit;
• you do not need to write a lot in response to each question, but you should present your
results, etc., in a neat, orderly, and professional manner, as if you were including them
in a formal paper (e.g., a report or a dissertation). That is, do not just dump raw R
outputs into the main text of your assignment;
• the word-limit for this assignment is a maximum upper limit only. You must be thorough
and precise to do well, but you need not “pad out” your assignment to get anywhere
close to this limit;
• adhere to APA formatting style for reporting your findings. See here for information:
https://apastyle.apa.org/instructional-aids/numbers-statistics-guide.pdf
Question One
The file undergrads.csv (available on Moodle) contains information regarding two groups of
universities in the UK: the Russell Group and the Cathedrals Group. The information relates
to the academic year 2020-2021 (source: Higher Education Statistics Agency, HESA).
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The four variables included in the data set are:
• ukpc– the percentage of registered undergraduates who are domiciled in the UK
• eupc– the percentage of registered undergraduates who are domiciled in EU countries
• noneupc– the percentage of registered undergraduates who are domiciled in non-EU
countries (other than the UK)
• fempc– the percentage of registered undergraduates who are female
The group to which each university belongs is coded as either russ or cath in the additional
variable group.
Conduct a statistical comparison of the two groups of universities in relation to
each of the four variables. Write a very brief report on what kinds of analyses
you conducted and what you discovered. Remember to justify your choice of
method(s) for the data analysis.
Question Two
Table 1 contains information about the results of random mandatory drug testing in English
prisons (source: HMPPS Annual Digest 2019-2020). It shows the numbers of positive tests for
different types of drugs in the years ending March 2018 and March 2020 respectively.
Table 1: Table 1. Positive drug tests for years ending March 2018 and March 2020
Drug 2018 2020
Amphetamines 62 122
Barbiturates 2 3
Benzodiazepines 320 217
Buprenorphine 1063 779
Cannabis 3067 3082
Cocaine 259 259
Methadone 325 375
Opiates 1257 1110
Psychoactive Substances 6636 2203
Complete a statistical analysis to test whether the distributions of positive tests
are different between the two years. Write a very brief report on what kinds of
analyses you undertook and what you discovered. Ensure that you justify your
choice of method(s) for the data analysis. If you find a statistically significant
difference, comment on the size of – and the main contributors to – the overall
effect.
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Question Three
The data set usrelig.csv, available on Moodle, contains a number of social indicators, for
the years 2008-2009, relating to the 50 states of the USA, plus the District of Columbia
(Source: US Census Bureau, Statistical Abstracts of the United States). Data concerning the
proportion of women smokers in each state are also included (source: Behavioral Risk Factor
Surveillance System, 2009), as are two estimates of religiosity and religious affiliation (source:
Pew Research Center, 2014; data for 2008-2009 were not available).
The following variables are included in the file:
• vrelig – the percentage of people in the state who described themselves as “highly
religious”
• cathpc – the estimated percentage of Roman Catholics in the state’s population
• abort – the abortion rate for the state (per thousand women)
• femsmoke – the estimated proportion of female smokers in the state (as a percentage of
the state’s female population)
• pov – the percentage of individuals in the state who live below the poverty level
• hsch – the percentage of the state’s population who have graduated from high school
• univ – the percentage of graduates in the state’s population (i.e. those with at least a
bachelor’s degree)
• urban – the percentage of the state’s population which lives in urban (as opposed to
rural) areas
Read the data set into R and use an appropriate method (or methods) to investigate a possible relationship between the percentage of “highly religious” people (as
your outcome variable) and the percentage of graduates in the state’s population
(as your predictor variable).
In your report, make sure that you describe clearly what kinds of analyses you undertook and
what you found out. Ensure that you justify fully your choice of method(s) for the data analysis.
When performing any regression analyses, ensure that you also undertake and report all of
the necessary diagnostics. Where appropriate, make sure that you also plot your regression
model(s) and write down the model(s) in the form of an equation that we could potentially
use to make predictions manually.
Question Four
Table 2 shows the sizes of the male and female prison populations in England in two corresponding weeks of 2021 and 2022 (source: HMPPS weekly reports).
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Table 2: Table 2. English prisons: numbers of prisoners by gender in corresponding weeks of
2020 and 2022
Reported Gender 28-Feb-2020 25-Feb-2022
Female 3721 3202
Male 80147 76522
Undertake a statistical analysis to test whether there is any association between
year and prisoner gender. Write a very brief report on what kinds of analyses
you undertook and what you found out. Ensure that you justify your choice of
method(s) for the data analysis. If you do find a statistically significant association,
ensure that you also comment on the effect size
