Statistics Final Year Topic: Sensitivity of a Chi-Square Goodness-of-Fit Test to Category Grouping

This Statistics final year project uses multinomial samples from declared null and alternative probability distributions to investigate a specific question in distribution assessment. 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 goodness-of-fit bins an explicit, reproducible comparison. Working with multinomial samples from declared null and alternative probability distributions lets you separate the target quantity from its estimate and explain when a statistical conclusion depends on assumptions.

How does category grouping affect the rejection behaviour of a chi-square goodness-of-fit test?

Agree the scenario ranges, sample sizes and reporting measures for goodness-of-fit bins before running the study.

Proposed project objectives

01Specify the data-generating conditions for multinomial samples from declared null and alternative probability distributions.
02Implement a reproducible analysis of goodness-of-fit bins with documented software settings.
03Evaluate the estimates and uncertainty relevant to this question: How does category grouping affect the rejection behaviour of a chi-square goodness-of-fit test?

A suggested research approach

Specify bins before looking at simulated results and examine expected-count adequacy. Compare plausible grouping rules while correctly accounting for probabilities estimated from the same sample. 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 multinomial samples from declared null and alternative probability distributions
Statistical software supporting distribution assessment and reproducible scripts
A supervisor-agreed range of scenarios and computational budget

Keep your project scope clear

Choosing bins after inspecting a favourable result changes the testing procedure and can invalidate nominal error claims.

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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