Biomedical Statistical Methods
Start from one idea: statistics is the discipline of reasoning about a population from a sample, while being honest about uncertainty. You can never measure every pregnant woman in South Africa. You measure some of them, then ask how far your sample answer is likely to sit from the truth. Every method in this chapter — t test, ANOVA, regression, survival analysis, a diagnostic test's sensitivity — is a different tool for that one job: turning a noisy sample into an estimate plus a stated uncertainty.
Two consequences follow, and the whole chapter is built on them. First, the answer is never a single number; it is an estimate with a confidence interval, and a p value that says how surprising the data would be if there were truly no effect. Second, the method is chosen by the outcome and the data structure, not by a software menu. Mean haemoglobin, severe PPH (yes/no), number of antenatal visits, time from PPROM to delivery, a paired pre/post pain score, and women nested within clinics are six different data structures, and each demands a different tool. A single "significant p value" tells you nothing about whether the model respected those structures.
The FCOG Primary examiner rarely expects calculation. The expected skill is interpretation: what does the method estimate, what assumptions does it make, what bias remains, and what clinical mistake follows if the method is misread? This chapter therefore builds from the ground up — first what data is and how variability behaves, then what an estimate, a confidence interval and a p value actually mean, and only then the analysis methods themselves and the diagnostic-test arithmetic you will meet daily in screening.
The Raw Material: Types of Data
Before any test, name the data. The type of variable decides everything downstream, because each type carries a different amount of information and behaves differently when you summarise or model it.
| Data type | Meaning | O&G example | Typical summary |
|---|---|---|---|
| Continuous (quantitative) | A measurement on a spectrum | Maternal weight, haemoglobin, blood pressure, birthweight | Mean (SD) if symmetric; median (IQR) if skewed |
| Ordinal | Ordered categories without equal spacing | CTG category, pain score, disease stage | Median, proportions in each category |
| Categorical (nominal) | Unordered groups | Ethnicity, blood group, district of birth | Counts and proportions |
| Binary | Two categories only (a special case of categorical) | Pregnant or not, severe PPH yes/no, alive or dead | Proportion, risk |
| Count | Non-negative whole numbers of events | Antenatal visits, postoperative infections | Rate per unit of exposure |
| Time-to-event | Time until something happens, with follow-up that varies | Time from PPROM to delivery, time to cancer recurrence | Survival probability, median time |
The single most common beginner error is to treat an ordinal score as if it were continuous, or to average a skewed measurement as if it were symmetric. Blood loss is the classic trap: it is continuous but heavily right-skewed because a few catastrophic haemorrhages drag the mean far above what a typical woman experiences. A median with interquartile range, or a binary "severe PPH" threshold, is usually more honest and more clinically useful than a mean.
Describing Data: Centre, Spread and Distribution
A sample is described by where it sits (centre) and how widely it varies (spread). The mean is the arithmetic average; the median is the middle value once the data are ordered. The mean is pulled toward extreme values, so for skewed data the median is the more representative centre. Spread is described by the standard deviation (SD) for symmetric data, or the interquartile range (IQR) for skewed data.
Many continuous measurements approximate a normal (Gaussian) distribution — the symmetric bell-shaped curve. Its defining property is that a fixed proportion of values falls within a fixed number of SDs of the mean: about 95% of values lie within 1.96 SDs of the mean (and roughly 90% within 1.65 SDs, 99% within 2.58 SDs). This is why reference ranges in obstetrics — fetal biometry centiles, normal ranges for biochemical markers — are built on the distribution of measurements rather than on a single cut-off. A value is "abnormal" because of where it sits in the distribution of values, not because of an arbitrary line.
Other distributions matter for other data types. The binomial distribution describes binary data (the proportion of women who have a caesarean). The Poisson distribution describes counts or rates of events occurring at a roughly constant rate over time (infections per woman-year). The chi-squared distribution underlies tests of proportions in tables. You do not need the equations; you need to recognise that the right test depends on which distribution reasonably describes the data.
Estimates, Standard Error and the Confidence Interval
Here is the step that separates statistics from arithmetic. Your sample mean is not the population mean — it is one estimate of it, and if you repeated the study you would get a slightly different number each time. The spread of those hypothetical repeated estimates is captured by the standard error (SE), which is the SD of the sampling distribution of the estimate. Note the difference that examiners test: the SD describes how much individuals vary; the SE describes how precisely the study has pinned down the average. The SE shrinks as the sample grows, which is precisely why larger studies give tighter answers.
From the SE we build the confidence interval (CI), the single most useful number in clinical research. A 95% CI is the range that, on repeated sampling, would contain the true value 95% of the time. Read it three ways at once: its midpoint is the best estimate, its width is the precision (a wide CI means an underpowered or noisy study), and where its ends sit relative to the no-effect value tells you about significance. For a difference in means or a risk difference the no-effect value is 0; for a ratio (risk ratio, odds ratio, hazard ratio) it is 1. A CI that crosses the no-effect value is compatible with no true effect.
Always prefer the CI to a bare p value. "Caesarean rate fell by 4% (95% CI 1% to 7%)" tells a clinician the size and the certainty of the effect; "p = 0.02" tells them only that something happened.
Hypothesis Testing, P Values and the Two Errors
Classical testing sets up a null hypothesis of no difference, then asks: if the null were true, how surprising would data this extreme be? That probability is the p value. A small p value means the data sit awkwardly with "no effect"; it does not measure the size of the effect, the probability that the null is true, or clinical importance. A statistically significant result on a trivial effect, in a huge sample, can be clinically irrelevant; a clinically important effect in a small study can be "non-significant" purely from lack of power.
Two errors define the trade-off, and both have an obstetric cost:
| Error | What happens | O&G consequence |
|---|---|---|
| Type I error (alpha) | Declaring an effect that is not real (false positive) | Adopting an ineffective intervention; usual threshold alpha = 0.05 |
| Type II error (beta) | Missing an effect that is real (false negative) | Abandoning a treatment that actually works because the study was too small |
Power is 1 minus beta — the probability of detecting an effect that truly exists, conventionally set at 80% or 90%. A study's sample size is calculated in advance from the effect worth detecting, the variability of the outcome, alpha and the desired power. This is why an apparently "negative" trial can be uninformative: absence of evidence is not evidence of absence when the study never had the power to find the effect. When you read a non-significant result, always ask whether the CI was wide enough to hide a clinically important effect.