Statistics Final Year Topic: Comparison of Pearson and Fisher Tests in Sparse Two-by-Two Tables

This Statistics final year project uses simulated contingency tables under documented sampling schemes to investigate a specific question in categorical 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 sparse tables an explicit, reproducible comparison. Working with simulated contingency tables under documented sampling schemes lets you separate the target quantity from its estimate and explain when a statistical conclusion depends on assumptions.

How do margin structure and sample size affect rejection rates for Pearson and Fisher tests in two-by-two tables?

Agree the scenario ranges, sample sizes and reporting measures for sparse tables before running the study.

Proposed project objectives

01Specify the data-generating conditions for simulated contingency tables under documented sampling schemes.
02Implement a reproducible analysis of sparse tables with documented software settings.
03Evaluate the estimates and uncertainty relevant to this question: How do margin structure and sample size affect rejection rates for Pearson and Fisher tests in two-by-two tables?

A suggested research approach

Distinguish fixed-margin from product-binomial generation where relevant. Compare null rejection rates and chosen alternatives, stating the exact two-sided definition used by the software. 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 contingency tables under documented sampling schemes
Statistical software supporting categorical inference and reproducible scripts
A supervisor-agreed range of scenarios and computational budget

Keep your project scope clear

Different sampling schemes and two-sided definitions can change the comparison and must be reported explicitly.

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

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