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MathidiaMathematics Academy
Regression and hypothesis testing
Lesson 55 of 75
Review

Statistical evaluation

Objective. Critique models, samples, tests and conclusions.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Statistical evaluation is the critical review of a whole statistical process — the sampling method, the model chosen, the hypothesis test performed and the conclusion drawn — to judge whether the results are trustworthy. Good evaluation checks that the sample was representative and large enough, that the assumed distribution (e.g. normal or binomial) actually fits the data, that the test matched the hypotheses correctly, and that conclusions are stated with appropriate caution rather than overclaiming. For example, a conclusion should say "there is evidence at the 5% level that..." rather than "this proves...". Evaluation also considers whether non-response bias or an unrepresentative sampling frame weakens the result.

Worked example

A survey tests opinions using only self-selected online respondents. Give a statistical evaluation of this sampling method and its effect on conclusions.

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Illustrated card showing ?
  1. 1Identify the sampling method: self-selected (volunteer) sample
  2. 2Such samples are not representative, since only motivated people respond
  3. 3This introduces response bias, skewing results from the true population
  4. 4Conclusion: findings cannot be safely generalised to the whole population

Answer: The self-selected sample causes bias, so conclusions cannot be generalised reliably

Concept mastery

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Practice

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Common mistake. Students write "the test proves the hypothesis is true", overstating certainty. A hypothesis test only gives evidence for or against H0 at a stated significance level, never proof.

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