Biostatistics for paediatric exams — formative SAQs

SAQ 1 (10 marks)

You are asked to interpret an abstract reporting a new therapy for a childhood illness. It states a mean difference in symptom duration with a p-value of 0.04, but the 95 percent confidence interval is wide and crosses zero. ^[9]

1. Explain what a 95 percent confidence interval represents and why an interval crossing zero changes the interpretation of the p-value. (4) ^{[9] [5]}
2. Define a Type I and a Type II error, statistical power, and how the sample size influences each. (3) ^[3]
3. Describe how you would convey this result to the family. (3) ^{[4] [5]}

Model answer

A 95 percent confidence interval is the range of values that, over many repeated samples, would capture the true population effect 95 times in 100; it expresses both the size and the precision of the estimate in a single band. When the interval crosses zero for a difference, it is compatible with both a benefit and a harm, so the result is not statistically significant at the 0.05 level, and the quoted p-value of 0.04 cannot stand alone against an interval that includes the null. The confidence interval always takes precedence, because it carries the information the p-value omits — the magnitude and the precision. ^{[9] [5]}

A Type I error is a false positive, rejecting a true null hypothesis, and its rate is alpha. A Type II error is a false negative, failing to reject a false null, and its rate is beta. Statistical power is one minus beta, the probability of detecting a true effect, and it rises as the sample size grows. The standard error of the mean shrinks with the square root of the sample size, so larger samples narrow the confidence interval and raise power; a wide, null-crossing interval is the fingerprint of a small, underpowered study. ^[3]

To convey the result, give the effect size and its confidence interval in absolute terms a family can weigh, explain that the interval includes both a meaningful benefit and essentially no effect, and be honest that the study was too small to be certain. Where the choice is preference-sensitive, present the uncertainty plainly and let the family share the decision, with a plan to revisit it as larger evidence appears. ^{[4] [5]}