Statistics Final Year Topic: Performance of Classical and Welch ANOVA under Heterogeneous Group Variances

This Statistics final year project uses multi-group simulations with controlled means, variances and allocations to investigate a specific question in experimental analysis. 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 unequal anova an explicit, reproducible comparison. Working with multi-group simulations with controlled means, variances and allocations lets you separate the target quantity from its estimate and explain when a statistical conclusion depends on assumptions.

How do variance heterogeneity and unequal group sizes influence classical and Welch ANOVA rejection rates?

Agree the scenario ranges, sample sizes and reporting measures for unequal anova before running the study.

Proposed project objectives

01Specify the data-generating conditions for multi-group simulations with controlled means, variances and allocations.
02Implement a reproducible analysis of unequal anova with documented software settings.
03Evaluate the estimates and uncertainty relevant to this question: How do variance heterogeneity and unequal group sizes influence classical and Welch ANOVA rejection rates?

A suggested research approach

Run null scenarios before selected alternative mean patterns. Keep the number of groups manageable, compare empirical error and power, and quantify Monte Carlo uncertainty for each design. 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 multi-group simulations with controlled means, variances and allocations
Statistical software supporting experimental analysis and reproducible scripts
A supervisor-agreed range of scenarios and computational budget

Keep your project scope clear

An omnibus rejection does not identify which group means differ or justify an unplanned series of pairwise tests.

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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