Study guides
Statistics
4 guides for this subject — how to prepare, what to practise, and how to know it has gone in.
A practice question
Choose an answer and it is marked, with the explanation. From Statistics Practice Questions: 10 Worked Examples.
A disease has prevalence 1%. A test has sensitivity 90% and a false-positive rate of 10%. Given a positive result, what is the probability that the person has the disease?
The probability is P(D|+) = (0.90 × 0.01) / [(0.90 × 0.01) + (0.10 × 0.99)] = 0.009 / 0.108 = 0.0833, or 8.3%. The strongest distractor is 90%, which is the sensitivity: P(+|D), not the requested P(D|+).
A spoken answer, marked
An examiner's question, answered out loud and marked criterion by criterion. From Statistics Viva Questions: Practise Clear, Defensible Answers.
Examiner
A study estimates a mean difference of 2.4 units, with a 95% confidence interval from 0.3 to 4.5. Interpret the result and explain what the interval means.
The answer identifies a positive estimated difference of 2.4 units.
ImproveName which group has the higher mean and retain the units, if the groups are specified.
The answer describes a plausible range for the population mean difference under the model.
ImproveExplain that a 95% procedure would cover the fixed parameter in 95% of repeated samples, under its assumptions.
The answer notes that the interval excludes zero, but does not overstate the size of the effect.
ImproveSay that the interval suggests a positive difference; practical importance depends on the scale and context.
The answer mentions sampling uncertainty but not the assumptions behind the interval.
ImproveFlag study design and the validity of the standard error or model used.
A strong answerThe estimated mean difference is 2.4 units, with the first group higher if the difference was defined as first minus second. The interval from 0.3 to 4.5 is a range of values reasonably compatible with the data and the model. In repeated samples, a method producing 95% confidence intervals would contain the fixed population difference about 95% of the time, provided its assumptions hold. Since zero is outside this interval, the result is inconsistent with no mean difference at the corresponding two-sided 5% level under the same method. Whether a difference of this size matters in practice depends on the outcome scale and the study context.
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Guides
- How to Study Statistics: A Practical Step-by-Step GuideA practical method for studying statistics: organise your course, practise choosing methods, check assumptions and learn from errors.
- Statistics Flashcards: 18 Core Facts to PractiseStudy 18 statistics flashcards on distributions, estimation, hypothesis tests and regression, with a core checklist and a targeted remediation card.
- Statistics Practice Questions: 10 Worked ExamplesWork through 10 statistics practice questions on probability, distributions, confidence intervals, hypothesis tests and regression.
- Statistics Viva Questions: Practise Clear, Defensible AnswersPractise statistics viva questions on inference, regression and diagnostic testing, with worked spoken answers and a method for explaining your reasoning.
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