Modelling Assumptions & Limitations

This lesson examines the assumptions that underlie statistical models, the limitations of these models, and how to communicate uncertainty when drawing conclusions from data. Understanding when and why models break down is a higher-order skill that distinguishes strong A-Level candidates.

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Why Assumptions Matter

Every statistical model is built on a set of assumptions. If these assumptions are satisfied, the model provides reliable results. If they are violated, the results may be misleading or invalid.

At A-Level, you are expected to:

1. State the assumptions of the model you are using.
2. Assess whether these assumptions are reasonable in the given context.
3. Discuss the consequences if the assumptions are not met.

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Key Assumptions

1. Independence

What it means: The outcome of one observation does not affect the outcome of any other observation.

Where it is required:

• Binomial distribution: Each trial must be independent of the others.
• Hypothesis testing: The data values in the sample must be independent.
• Correlation and regression: The observations should be independent (e.g., not collected from consecutive days where one day's weather influences the next).

When it may be violated in the LDS: