Medical Statistics: inference, error and critical appraisal
Scope
Medical statistics tests data types, descriptive measures, sampling and distributions, hypothesis testing, confidence intervals, choice of statistical test, study design and critical appraisal.
Core rules
- Data type determines the test: categorical data use chi-square or Fisher's exact test; continuous normally distributed data use t-tests or ANOVA; non-normal data use Mann–Whitney or Kruskal–Wallis.
- Type I error (alpha) is rejecting a true null hypothesis; type II error (beta) is failing to reject a false one; power = 1 − beta.
- A p-value is the probability of data at least as extreme as those observed, assuming the null hypothesis is true; it is not the probability that the null is true.
- A 95% confidence interval that excludes the null value corresponds to p < 0.05.
Worked example
A trial reports a mean blood pressure reduction of 4 mmHg with a 95% CI of 1.2 to 6.8 mmHg and p = 0.006. Reasoning: the interval excludes zero and p < 0.05, so the difference is statistically significant; the width of the interval also indicates precision. Clinical significance is a separate judgement - whether a 4 mmHg fall matters for outcomes cannot be read from the p-value.
Traps that cost marks
- Interpreting a p-value as the probability that the null hypothesis is true.
- Using an unpaired t-test on paired data.
- Reading correlation as causation, or assuming a small p-value means a large effect.
- Confusing standard deviation (spread of observations) with standard error (precision of a mean).