Statistics Final Year Topic: Type-I Error of Welch and Pooled t-Tests with Unequal Variances and Sample Sizes

This Statistics final year project uses two-group simulations under a known equal-mean null hypothesis to investigate a specific question in hypothesis testing. 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 welch test balance an explicit, reproducible comparison. Working with two-group simulations under a known equal-mean null hypothesis lets you separate the target quantity from its estimate and explain when a statistical conclusion depends on assumptions.

How do variance ratios and group-size imbalance affect the false-positive rates of Welch and pooled two-sample t-tests?

Agree the scenario ranges, sample sizes and reporting measures for welch test balance before running the study.

Proposed project objectives

01Specify the data-generating conditions for two-group simulations under a known equal-mean null hypothesis.
02Implement a reproducible analysis of welch test balance with documented software settings.
03Evaluate the estimates and uncertainty relevant to this question: How do variance ratios and group-size imbalance affect the false-positive rates of Welch and pooled two-sample t-tests?

A suggested research approach

Cross a small set of variance ratios with sample-size allocations while keeping distributional choices explicit. Estimate rejection rates with Monte Carlo uncertainty before exploring power separately. 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 two-group simulations under a known equal-mean null hypothesis
Statistical software supporting hypothesis testing and reproducible scripts
A supervisor-agreed range of scenarios and computational budget

Keep your project scope clear

Null rejection rates and power answer different questions and must not be combined into a single accuracy claim.

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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