Statistics Final Year Topic: False Discovery and Power Trade-Offs in Two Multiple-Testing Procedures

This Statistics final year project uses simulated families of tests with declared null and non-null effects to investigate a specific question in multiple comparisons. 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 multiple testing an explicit, reproducible comparison. Working with simulated families of tests with declared null and non-null effects lets you separate the target quantity from its estimate and explain when a statistical conclusion depends on assumptions.

How do Bonferroni and Benjamini–Hochberg procedures differ in rejection behaviour under selected proportions of true null hypotheses?

Agree the scenario ranges, sample sizes and reporting measures for multiple testing before running the study.

Proposed project objectives

01Specify the data-generating conditions for simulated families of tests with declared null and non-null effects.
02Implement a reproducible analysis of multiple testing with documented software settings.
03Evaluate the estimates and uncertainty relevant to this question: How do Bonferroni and Benjamini–Hochberg procedures differ in rejection behaviour under selected proportions of true null hypotheses?

A suggested research approach

Separate independent and explicitly correlated test scenarios. Track family-wise error, false discovery proportion and true discoveries with clearly defined treatment of runs that contain no rejections. 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 families of tests with declared null and non-null effects
Statistical software supporting multiple comparisons and reproducible scripts
A supervisor-agreed range of scenarios and computational budget

Keep your project scope clear

The two procedures target different error criteria; a higher discovery count does not by itself establish superiority.

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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