Hypothesis Testing in Biostatistics
Hypothesis testing is a structured method for using sample data to assess a claim about a population. It quantifies how compatible the observed results are with a stated null hypothesis.
Learning objectives
- Formulate null and alternative hypotheses.
- Explain significance level, test statistic and p-value.
- Distinguish Type I and Type II errors.
- Select common statistical tests and interpret conclusions correctly.
Core hypotheses
Null hypothesis (H₀): no difference, association or effect exists. Alternative hypothesis (H₁): a difference, association or effect exists. A two-sided alternative allows either direction; a one-sided alternative specifies a direction and must be chosen before analysing data.
Steps in hypothesis testing
- State H₀ and H₁.
- Choose the significance level, commonly α = 0.05.
- Select a test based on variable type, study design and assumptions.
- Calculate the test statistic and p-value.
- Compare p with α and make a statistical decision.
- Interpret the finding in clinical context with effect size and confidence interval.
Type I error
Rejecting a true H₀ (false positive). Its probability is α.
Type II error
Failing to reject a false H₀ (false negative). Its probability is β; power = 1 − β.
Understanding the p-value
The p-value is the probability, assuming H₀ and the model are true, of obtaining results at least as extreme as those observed. If p < α, reject H₀. If p ≥ α, fail to reject H₀. It is not the probability that H₀ is true and does not measure clinical importance.
| Research situation | Typical test | Main assumptions |
|---|---|---|
| Two independent means | Independent t-test | Independent observations, approximate normality |
| Paired before/after means | Paired t-test | Approximately normal paired differences |
| Three or more means | ANOVA | Independence, normality, similar variances |
| Two categorical variables | Chi-square test | Independent observations, adequate expected counts |
| Non-normal two-group data | Mann–Whitney U | Independent ordinal/continuous observations |
Worked interpretation
A trial comparing two treatments reports a mean difference of 6 mmHg, 95% CI 2–10, p = 0.004. At α = 0.05, reject H₀. The data support a difference, while the confidence interval describes plausible effect sizes. Clinical relevance still depends on whether 6 mmHg is meaningful and whether bias or confounding is present.
Common pitfalls
- Changing hypotheses after seeing results.
- Equating statistical significance with clinical significance.
- Ignoring assumptions, multiple comparisons or small samples.
- Saying “accept H₀” instead of “fail to reject H₀”.
Review questions
- Define a p-value.
- Differentiate Type I and Type II errors.
- Which test compares proportions in two independent groups?
Return to the Clinical Medicine Year 2 curriculum
References
- WHO. Basic Epidemiology.
- CDC. Principles of Epidemiology in Public Health Practice.
Educational content only; statistical conclusions should be reviewed with appropriate methodological guidance.
