Statistics Final Year Topic: Bias in a Sample Mean when Response Probability Depends on an Observed Auxiliary Variable

This Statistics final year project uses synthetic survey populations with known outcomes and response probabilities to investigate a specific question in survey 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 selective nonresponse an explicit, reproducible comparison. Working with synthetic survey populations with known outcomes and response probabilities lets you separate the target quantity from its estimate and explain when a statistical conclusion depends on assumptions.

How does auxiliary-variable-dependent response affect an unweighted mean and a response-weighted estimate?

Agree the scenario ranges, sample sizes and reporting measures for selective nonresponse before running the study.

Proposed project objectives

01Specify the data-generating conditions for synthetic survey populations with known outcomes and response probabilities.
02Implement a reproducible analysis of selective nonresponse with documented software settings.
03Evaluate the estimates and uncertainty relevant to this question: How does auxiliary-variable-dependent response affect an unweighted mean and a response-weighted estimate?

A suggested research approach

Draw probability samples, generate response under a stated model and compare estimators against the population mean. Examine model misspecification, extreme weights and uncertainty estimation 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 synthetic survey populations with known outcomes and response probabilities
Statistical software supporting survey inference and reproducible scripts
A supervisor-agreed range of scenarios and computational budget

Keep your project scope clear

A weighting correction relies on information and modelling assumptions; it cannot guarantee removal of unobserved nonresponse bias.

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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