Statistics Final Year Topic: Robustness of Levene and Brown–Forsythe Tests to Skewed Observations

This Statistics final year project uses grouped simulations with specified scale and shape parameters to investigate a specific question in robust inference. The analysis is designed around known generating conditions so that the behaviour of competing statistical procedures can be checked.

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Why choose this project topic?

This study makes variance tests an explicit, reproducible comparison. Working with grouped simulations with specified scale and shape parameters lets you separate the target quantity from its estimate and explain when a statistical conclusion depends on assumptions.

How do mean-centred and median-centred variance tests behave when the underlying groups are skewed?

Agree the scenario ranges, sample sizes and reporting measures for variance tests before running the study.

Proposed project objectives

01Specify the data-generating conditions for grouped simulations with specified scale and shape parameters.
02Implement a reproducible analysis of variance tests with documented software settings.
03Evaluate the estimates and uncertainty relevant to this question: How do mean-centred and median-centred variance tests behave when the underlying groups are skewed?

A suggested research approach

Define equal-variance and unequal-variance scenarios explicitly. Compare rejection rates using fixed group sizes and then examine imbalance, recording which centring method each implementation uses. Write the analysis before inspecting favourable runs, record random seeds where simulation is used, and keep generated study data distinct from observed field data.

What you will need

A written design for grouped simulations with specified scale and shape parameters
Statistical software supporting robust inference and reproducible scripts
A supervisor-agreed range of scenarios and computational budget

Keep your project scope clear

Changing distribution shape can alter more than variance, so interpretation must follow the actual simulated population properties.

Statistics project chapter outline

Use this outline as a starting point. You can edit the chapter titles to match your department’s format during setup.

Chapter 1Introduction
Chapter 2Literature Review
Chapter 3Theory and Methodology
Chapter 4Results and Applications
Chapter 5Summary, Conclusion and Recommendations

Turn this topic into your own final year project.

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