Module Specification
The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module.
1. Module Title Introduction to Statistics using R
2. Module Code MATH163
3. Year Session 2023-24
4. Originating Department Mathematical Sciences
5. Faculty Fac of Science & Engineering
6. Semester Second Semester
7. CATS Level Level One
8. CATS Value 15
9. Member of staff with responsibility for the module
Dr L Yuan Mathematical Sciences Linglong.Yuan@liverpool.ac.uk
10. Module Moderator
11. Other Contributing Departments  
12. Other Staff Teaching on this Module
Dr DJ Haw Mathematical Sciences D.Haw@liverpool.ac.uk
13. Board of Studies
14. Mode of Delivery
15. Location Main Liverpool City Campus
    Lectures Seminars Tutorials Lab Practicals Fieldwork Placement Other TOTAL
16. Study Hours 24

   12

     12

 48
17.

Private Study

 102
18.

TOTAL HOURS

 150
 
    Lectures Seminars Tutorials Lab Practicals Fieldwork Placement Other
19. Timetable (if known)            
 
20. Pre-requisites before taking this module (other modules and/or general educational/academic requirements):

 
21. Modules for which this module is a pre-requisite:

 
22. Co-requisite modules:

 
23. Linked Modules:

 
24. Programme(s) (including Year of Study) to which this module is available on a mandatory basis:
25. Programme(s) (including Year of Study) to which this module is available on a required basis:
26. Programme(s) (including Year of Study) to which this module is available on an optional basis:
27. Aims
 

1. Use software R to display and analyse data, perform tests and demonstrate basic statistical concepts.

2. Describe statistical data and display it using variety of plots and diagrams.

3. Understand basic laws of probability: law of total probability, independence, Bayes’ rule.

4. Be able to estimate mean and variance.

5. Be familiar with properties of some probability distributions and relations between them: Binomial, Poisson, Normal, t, Chi-squared.

6. To perform simple statistical tests: goodness-of-fit test, z-test, t-test.

7. To understand and be able to interpret p-values.

8. To be able to report finding of statistical outcomes to non-specialist audience.

9. Group work will help students to develop transferable skills such as communication, the ability to coordinate and prioritise tasks, time management and teamwork.
 
28. Learning Outcomes
 

(LO1) An ability to apply statistical concepts and methods covered in the module's syllabus to well defined contexts and interpret results.
 

(LO2) An ability to understand, communicate, and solve straightforward problems related to the theory and derivation of statistical methods covered in the module's syllabus.
 

(LO3) An ability to understand, communicate, and solve straightforward theoretical and applied problems related to probability theory covered in the syllabus.
 

(LO4) Use the R programming language fluently in well-defined contexts. Students should be able to understand and correct given code; select appropriate code to solve given problems; select appropriate packages to solve given problems; and independently write small amounts of code.
 
29. Teaching and Learning Strategies
 

Material is presented during lectures (2 hours per week). Tutorials (1 hour per week) are used for consolidation and practice, and for help with individual questions. Computer labs (1 hour per week) are used for practice of the language R.
 
30. Syllabus
   

Introduction and description of data: graphical summaries, shape, location and spread of data.

Elements of Probability Theory:
• intuitive meaning of probability
• events and compound events
• conditional probability and Bayes' rule
• independence

Discrete and continuous random variables:
• probability mass function, probability density function and distribution function
• generating random variables
• expectation, variance and covariance
• Binomial and Poisson distributions
• Normal distribution, t-distribution
• approximations
• Central Limit Theorem

Statistical Inference:
• principles of hypothesis testing and interpretation of p-values; type I and type II errors
• Chi-squared test of goodness of fit and chi-squared test of association
• distrib ution of sample mean and sample variance
• Normal confidence intervals and z-test for mean
• One-sample t-test
 
31. Recommended Texts
  Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module.
 

Assessment
32. EXAM Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
  written exam 90 60
33. CONTINUOUS Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
  Homework 1 0 20
  Homework 2 0 20