ST1PS: Probability and Statistics

Module code: ST1PS

Module provider: Mathematics and Statistics; School of Mathematical, Physical and Computational Sciences

Credits: 20

Level: Level 1 (Certificate)

When you'll be taught: Semester 2

Module convenor: Dr Karen Poulter, email: k.l.poulter@reading.ac.uk

Pre-requisite module(s): Before taking this module, you must have at least a grade B in A-Level Mathematics, or equivalent. (Open)

Co-requisite module(s):

Pre-requisite or Co-requisite module(s):

Module(s) excluded:

Placement information: NA

Academic year: 2024/5

Available to visiting students: Yes

Talis reading list: Yes

Last updated: 21 May 2024

Overview

Module aims and purpose

The aim of this module is to provide an introduction to probability and probability distributions, and to fundamental results and techniques for statistical inference and data science, with a focus on regression and hypothesis testing. The module will include a revision of probability topics that students have already met, and will describe various discrete and continuous probability distributions. The module will also include estimation of confidence intervals and hypothesis testing for means, variances and proportions, and statistical modelling of data from observational studies. Some simple models will be described and their role in data analysis illustrated. Students will benefit from seeing some applications of probability and statistics in medical statistics and forensics, and from learning how to analyse data using software packages.

Module learning outcomes

By the end of the module, it is expected that students will be able to:

1. Calculate probabilities in simple problems, and make use of a range of discrete and continuous probability distributions
2. Identify and apply appropriate methods for statistical inference for one and two sample problems
3. Fit simple statistical models to data and use them to make inferences about the population
4. Analyse data using statistical software, interpret the results and communicate them clearly

Module content

• Revision of probability concepts: definitions of sample spaces, outcomes and events; calculating probabilities for problems with equally likely outcomes; the axioms of probability.
• Conditional probability and independence; the law of total probability and Bayes' theorem.
• An introduction to discrete random variables and their properties, including Bernoulli, binomial, negative binomial, geometric, hypergeometric and Poisson random variables.
• An introduction to continuous random variables and their properties, including the uniform exponential, normal, beta and gamma distributions.
• Bivariate distributions, including the bivariate Normal distribution.
• Summary statistics, transformations and the graphical display of data.
• Sampling distributions.
• Confidence intervals for population means, variances and proportions in one and two samples.
• Hypothesis tests for population means, variances and proportions in one and two samples.
• Contingency tables; the chi-square test.
• The simple linear regression model; fitting a straight line; testing the significance of a regression relationship; analysis of variance.
• Statistics in epidemiology: case-control and cohort studies; relative risk and odds ratios; confounding and interaction.
• Use of statistical software packages: SAS and R.

Structure

Teaching and learning methods

The material is delivered via lectures and screencasts supported by tutorials which tackle non-assessed exercises, together with computer based practical work.  

Study hours

At least 52 hours of scheduled teaching and learning activities will be delivered in person, with the remaining hours for scheduled and self-scheduled teaching and learning activities delivered either in person or online. You will receive further details about how these hours will be delivered before the start of the module.

Please note the independent study hours above are notional numbers of hours; each student will approach studying in different ways. We would advise you to reflect on your learning and the number of hours you are allocating to these tasks.

Semester 1 The hours in this column may include hours during the Christmas holiday period.

Semester 2 The hours in this column may include hours during the Easter holiday period.

Summer The hours in this column will take place during the summer holidays and may be at the start and/or end of the module.

Assessment

Requirements for a pass

Students need to achieve an overall module mark of 40% to pass this module.

Summative assessment

Penalties for late submission of summative assessment

The Support Centres will apply the following penalties for work submitted late:

Assessments with numerical marks

• where the piece of work is submitted after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for that piece of work will be deducted from the mark for each working day (or part thereof) following the deadline up to a total of three working days;
• the mark awarded due to the imposition of the penalty shall not fall below the threshold pass mark, namely 40% in the case of modules at Levels 4-6 (i.e. undergraduate modules for Parts 1-3) and 50% in the case of Level 7 modules offered as part of an Integrated Masters or taught postgraduate degree programme;
• where the piece of work is awarded a mark below the threshold pass mark prior to any penalty being imposed, and is submitted up to three working days after the original deadline (or any formally agreed extension to the deadline), no penalty shall be imposed;
• where the piece of work is submitted more than three working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.

Assessments marked Pass/Fail

• where the piece of work is submitted within three working days of the deadline (or any formally agreed extension of the deadline): no penalty will be applied;
• where the piece of work is submitted more than three working days after the original deadline (or any formally agreed extension of the deadline): a grade of Fail will be awarded.

The University policy statement on penalties for late submission can be found at: /cqsd/-/media/project/functions/cqsd/documents/qap/penaltiesforlatesubmission.pdf

You are strongly advised to ensure that coursework is submitted by the relevant deadline. You should note that it is advisable to submit work in an unfinished state rather than to fail to submit any work.

Formative assessment

Formative assessment is any task or activity which creates feedback (or feedforward) for you about your learning, but which does not contribute towards your overall module mark.

Non-assessed problem sheets with solutions and generic feedback.  

Reassessment

Additional costs