Statistics Final Year Topic: Validity of a Permutation Test under Unequal Group Variances

This Statistics final year project uses simulated independent groups under known null and alternative scenarios to investigate a specific question in resampling 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 permutation exchangeability an explicit, reproducible comparison. Working with simulated independent groups under known null and alternative scenarios lets you separate the target quantity from its estimate and explain when a statistical conclusion depends on assumptions.

How do variance inequality and group-size imbalance affect a naive permutation test of a mean difference?

Agree the scenario ranges, sample sizes and reporting measures for permutation exchangeability before running the study.

Proposed project objectives

01Specify the data-generating conditions for simulated independent groups under known null and alternative scenarios.
02Implement a reproducible analysis of permutation exchangeability with documented software settings.
03Evaluate the estimates and uncertainty relevant to this question: How do variance inequality and group-size imbalance affect a naive permutation test of a mean difference?

A suggested research approach

Compare naive and explicitly studentised statistics using the same permutations. Track rejection rates across balanced and unbalanced designs and state the exchangeability assumptions of each procedure. 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 simulated independent groups under known null and alternative scenarios
Statistical software supporting resampling inference and reproducible scripts
A supervisor-agreed range of scenarios and computational budget

Keep your project scope clear

Permuting labels is not automatically valid for every null hypothesis or heteroskedastic data structure.

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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