The theory and methods of Statistics play an important role in all walks of life, society, medicine and industry. They enable important understanding to be gained and informed decisions to be made, about a population by examining only a small random sample of the members of that population. For example, to decide whether a new drug improves the symptoms of a disease in all those diagnosed as having the condition (the population), a clinical trial might be undertaken in which a sample of people who receive the new drug is compared with a sample receiving no active treatment. Such statistical inferences about a population are subject to uncertainty - what we observe in our particular sample (or samples) may not hold for the whole population. Probability theory and statistical distributions are needed to quantify this uncertainty, and assess the accuracy of our inference about the population. This module aims to lay foundations in probability and distribution theory, data analysis and the use of a statistical software package, which will be built upon in later modules.
The module begins by introducing statistical data analysis by using the freely available R package, https://cran.r-project.org/. Statistical analysis and report writing are discussed along with the use of the R software package for summarising and interpreting data.
It then formally defines probability and studies the key properties. The concepts of random variables as outcomes of random experiments are introduced and the key properties of the commonly used standard univariate random variables are studied. Emphasis is placed on learning the theories by proving key properties of each distribution.
Basic ideas of statistical inference, including techniques of point and interval estimation and hypothesis testing, are introduced and illustrated with practical examples.
One of the pre-requisites for MATH2010, MATH2011, MATH2013, MATH2040
Aims and Objectives
Having successfully completed this module you will be able to:
- A good understanding of elementary probability theory and its application
- A good understanding of exploratory data analysis.
- Ability to write a short-report describing a simple statistical data set.
- A good understanding of the concept of a statistical distribution
- A good understanding of the standard univariate distributions and their properties
- A good understanding of the basic concepts of statistical inference
- A good understanding of the Central Limit Theorem and its application
- A good understanding of the laws of probability and the use of Bayes theorem
Exploratory data analysis: measures of location and spread; symmetry and skewness.
Introduction to the R package for exploratory data analysis using graphics
Presentation and interpretation of data and report writing.
Probability: Sample space, events, outcome, and axioms of probability. Addition and multiplication rules. The law of total probability, conditional probability, independence, Bayes Theorem. Practical applications.
Random variables: Discrete and continuous random variables. Probability mass function, probability density function and cumulative distribution function. Expectation, variance and moments.
Discrete probability distributions: Bernoulli trials, binomial, geometric, hyper-geometric, Poisson.
Continuous probability distributions: uniform, exponential, normal, and log-normal.
Joint probability distribution, covariance, correlation, independence.
Sample and population : Sampling distributions. The Central Limit Theorem.
Statistical modelling and Inference: Point and interval estimation, Hypothesis testing and P-value; various one sample and two sample t-tests. . Collection of data and design of experiments.
Learning and Teaching
Teaching and learning methods
Lectures, small group tutorials, computer laboratories, report writing.
|Total study time||150|
Resources & Reading list
MOORE, D.S. and MCCABE, G.P.. Introduction to the Practice of Statistics. Freeman.
MAINDONALD, J. and BRAUN, J. Data analysis and graphics using R : an example-based approach. Cambridge.
RAWLEY, M.J.. Statistics: An Introduction using R. Wiley.
ROSS, S.A.. First Course in Probability. Pearson.
HOGG, R.V. and TANIS, E.. Probability and Statistical Inference. Pearson.
DALGAARD, P.. Introductory Statistics with R. Springer.
DEGROOT, M.H. and SCHERVISH, M.J.. Probability and Statistics. Pearson.
This is how we’ll formally assess what you have learned in this module.
This is how we’ll assess you if you don’t meet the criteria to pass this module.
Repeat type: Internal & External