Statistics Final Year Topic: Coverage and Width of Confidence Intervals for a Small Binomial Proportion

This Statistics final year project uses binomial simulations across prespecified probabilities and sample sizes to investigate a specific question in statistical 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 binomial intervals an explicit, reproducible comparison. Working with binomial simulations across prespecified probabilities and sample sizes lets you separate the target quantity from its estimate and explain when a statistical conclusion depends on assumptions.

How do Wald, Wilson and exact binomial intervals behave near the boundaries of the probability scale?

Agree the scenario ranges, sample sizes and reporting measures for binomial intervals before running the study.

Proposed project objectives

01Specify the data-generating conditions for binomial simulations across prespecified probabilities and sample sizes.
02Implement a reproducible analysis of binomial intervals with documented software settings.
03Evaluate the estimates and uncertainty relevant to this question: How do Wald, Wilson and exact binomial intervals behave near the boundaries of the probability scale?

A suggested research approach

Include very low and very high probabilities as well as central cases. Compare coverage and width, record intervals outside the probability range and state the meaning of exact coverage conservatism. 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 binomial simulations across prespecified probabilities and sample sizes
Statistical software supporting statistical inference and reproducible scripts
A supervisor-agreed range of scenarios and computational budget

Keep your project scope clear

An interval's label does not guarantee the desired balance between coverage and precision in every finite sample.

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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