# KC5001 - Applied Statistical Methods

## What will I learn on this module?

The aim of the module is to enhance your hands-on statistical modelling expertise. The module considers important continuous probability distributions leading on to parameter estimation and goodness of fit. Hypothesis testing for both parametric and non-parametric situations are introduced for each of one and two – possibly paired – samples. This is extended to design, and analysis, of experiments. You will also study residual analysis for model assessment and goodness-of-fit with examples based on the classic simple linear regression model.

The module will cover topics such as:
Probability distributions including standard continuous distributions.
Central Limit Theorem.
Mean and variance of a linear combination of random variables.
Principles of estimation and estimation via the method of moments.
Maximum likelihood estimation. Goodness-of-fit test and contingency tables.
Tests for variances and proportions. Test and confidence intervals using F- and chi-squared distributions.

Nonparametric statistics
Sign test; Wilcoxon signed rank test; Mann-Whitney U-test; Wald-Wolfowitz runs test; Spearman’s rank correlation coefficient.

Regression Analysis
(Pearson’s) correlation coefficient; simple linear regression. Transformations of variables. Residual Analysis.

Design and Analysis of Experiments
Completely randomised, randomised block, Latin square and missing values.

### How will I learn on this module?

You will learn on this module via a combination of lectures and laboratory sessions involving the use of appropriate statistical software. Classes will be scheduled in our modern computer laboratories enabling you to apply the techniques presented in the lecture part of the session and, in this way, gain an understanding of the material and use software as appropriate to solve problems. The bespoke laboratory sessions will take place broadly every other week.

Assessment involves an assignment and a laboratory examination. You will receive both written and oral feedback from the assignment. Oral feedback will be given concurrently during the laboratory sessions. Further to this, you will also receive exam feedback after the end of semester exam, particularly relevant if you are considering further statistical modules at Level 6.

Your ability to solve problems based on case studies using appropriate statistical techniques will be assessed via an individual assignment with individualised data, and your ability to construct logical multistep solutions and to critically evaluate your findings for a range of problems will be tested in a laboratory exam at the end of the module.

In addition, we operate an open-door policy where you can meet with your module tutor to seek further advice or help if required.

### How will I be supported academically on this module?

You will be supported academically chiefly through participation in the hands-on laboratory sessions, where you will be analysing data with appropriate software. This provides you with the opportunity to receive support on both the theory and technical components of the module simultaneously as well as offering experience of conditions representative of the final assessment.

You can engender further feedback and discussion with the teaching team at any time through our open-door policy. In addition, all teaching materials and supplementary material (such as interesting articles) are available through the e-learning portal.

### What will I be expected to read on this module?

All modules at Northumbria include a range of reading materials that students are expected to engage with. The reading list for this module can be found at: http://readinglists.northumbria.ac.uk

### What will I be expected to achieve?

Knowledge & Understanding:
1. Demonstrate knowledge and understanding of parametric estimation procedures and goodness of fit using analytical and numerical techniques
2. Apply modern statistical software to problem solving

Intellectual / Professional skills & abilities:

3. Use appropriate statistical methodology in simple linear regression, residual analysis and experimental design and interpret your findings
4. Select and apply the appropriate statistical process to carry out both parametric and nonparametric hypothesis tests

Personal Values Attributes (Global / Cultural awareness, Ethics, Curiosity) (PVA):

5. Critically evaluate statistical models based on given or sourced data from real-life situations.

### How will I be assessed?

You will be formally assessed by a piece of mid-term coursework and a laboratory exam at the end of semester.

SUMMATIVE
1. Coursework (30%) – 1, 2, 4, 5
2. Laboratory examination (70%) – 1, 3, 4

FORMATIVE
Formative assessment will be available on a broadly fortnightly basis in the laboratory sessions via typical lecturer-student interactions, allowing them to extend, consolidate and evaluate their knowledge.

Formative feedback will be provided on your work, and errors in understanding will be addressed reactively using one-to-one or small group discussions. Solutions for laboratory tasks will be provided after you have attempted the questions, allowing you to receive feedback on the correctness of their solutions and to seek help if matters are still not clear.
The module learning outcomes are addressed on the weekly seminar question sheets, which the students attempt during the timetabled laboratory sessions.

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### Module abstract

This module showcases the applied nature of statistics and will enhance your hands-on statistical modelling expertise. The central limit theorem is introduced along with several important continuous probability distributions. Estimation of parameters is demonstrated by both maximum likelihood and the method of moments. Hypothesis tests for proportions and non-parametric samples are introduced and the module concludes with the design and analysis of experiments. Modern statistical software will be used throughout the module. Assessment of the module is by one individual assignment (30%) and one formal laboratory examination (70%). The module is designed to provide students with a grounding in an applied statistical environment and experience of statistical software.

### Course info

UCAS Code G100

Credits 20

Mode of Study 3 years Full Time or 4 years with a placement (sandwich)/study abroad

Department Mathematics, Physics and Electrical Engineering

Location City Campus, Northumbria University

City Newcastle

Start September 2024 or September 2025

## Mathematics BSc (Hons)

All information is accurate at the time of sharing.

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