Why Any of This Exists
Start with the single fact that everything else hangs on: you can never measure the whole population, so you measure a sample and try to infer the population from it. You will never weigh every baby born in South Africa this year, treat every woman with postpartum haemorrhage, or follow every PPROM pregnancy to delivery. You see a sample. The population — the true, unmeasurable answer — stays hidden. Statistics is the discipline of saying, honestly, how far your sample might be from that hidden truth.
This one idea generates almost every concept in this chapter. If you repeated the same study tomorrow with a new sample of the same size, you would get a different number. Not because anyone made a mistake, but because samples vary. So the result you report is one draw from a cloud of possible results. Everything that follows — distributions, standard error, confidence intervals, p values, parametric versus nonparametric, the choice of test — is bookkeeping for that variability. Once you hold "my number is a noisy estimate of a hidden truth" in your head, the rest stops being a list of recipes and becomes a logic you can reconstruct under exam pressure.
A statistical test, then, is never the first step. The first step is defining the outcome, the denominator, the exposure, the comparator, the independence structure, and the primary hypothesis. A p value from the wrong test is not a small error; it is a precise answer to the wrong question.
Primary FCOG candidates are not expected to derive formulae. They are expected to recognise common tests, know when paired and independent data differ, understand parametric versus nonparametric reasoning, and interpret p values alongside effect sizes and confidence intervals. This chapter builds that reasoning from the bottom up.
Step One: What Kind of Number Is It?
Before any distribution, test or p value, name the data type, because the data type controls everything downstream. There are four common types and one structural complication.
| Data type | What it is | O&G example |
|---|---|---|
| Continuous (quantitative) | A measurement on a continuous scale | Birthweight, haemoglobin, blood pressure, blood loss in mL |
| Ordinal | Ordered categories with no fixed numerical spacing | Pain score none/mild/moderate/severe, tumour stage |
| Categorical (nominal) | Unordered groups | Mode of delivery, ethnicity, clinic of booking |
| Binary | A special two-category case | Caesarean yes/no, alive/dead, severe PPH yes/no |
| Time-to-event | Time until an event, where follow-up differs between women | Time from PPROM to delivery, time to recurrence |
Time-to-event data are different in kind, not just in scale: a woman classified as "not yet delivered" may simply not have been followed long enough. That incomplete observation is called censoring, and it is why survival methods exist (more on this below).
The reason data type matters so much is that how a number is generated shapes how it is distributed, and the distribution dictates which summaries and tests are honest. So the next step is to think about the shape of the data.
Step Two: Distributions — the Shape a Variable Takes
A statistical distribution is not just a mathematical curve; it usually reflects how the clinical variable is generated. A handful of named distributions cover most of what you will meet.
- Normal (Gaussian) distribution — the symmetric bell curve. It arises when a value is the sum of many small independent influences, which is why measurements like birthweight or adult height are roughly normal. It is also the engine behind much of medical statistics because of a deeper result: even when raw data are not normal, the average of a large sample behaves normally.
- Binomial distribution — describes counts of yes/no events out of a fixed number of trials (how many of 50 deliveries were caesarean). For large samples it is well approximated by the normal distribution.
- Poisson distribution — describes counts of events occurring at some rate over time or population (infections per 1,000 births, eclampsia cases per year). It needs a denominator and an exposure window.
- Chi-square distribution — arises from squaring and summing normal-type quantities, and underpins tests that compare observed against expected counts in categories.
These named shapes are tools, not facts about your particular dataset. Whether your data actually follow one of them is an empirical question you answer by looking.
| Variable | Why it behaves that way | Statistical consequence |
|---|---|---|
| Birthweight | Many small biological influences add together | Often near-normal; mean/SD and linear models reasonable if groups comparable |
| Blood loss | Severe haemorrhage creates a long high tail | Right-skewed; median/IQR, transformation, or clinically meaningful thresholds |
| Length of stay | A minimum stay plus a few complicated recoveries | Skewed; rank-based or count/time models |
| Caesarean birth | Event yes/no with a denominator | Binomial; risk, risk difference, RR or OR with CI |
| Perinatal death rate | A rare count over births or time | Poisson-type; rate and denominator, often wide CI |
| Time to delivery after PPROM | Follow-up can end before the event or transfer | Survival methods, not simple means |
Symmetric, Skewed, or Peaked
When data are normally distributed, the mean, median and mode coincide. When they are skewed, the long tail drags the mean away from the median: in right (positive) skew — typical of blood loss and length of stay — the mean sits above the median; in left (negative) skew the mean sits below. Kurtosis describes how heavy the tails are and how peaked the centre is, independent of skew; heavy tails mean extreme values are more common than a normal curve predicts, which destabilises mean-based methods.
This is why plotting the data is not cosmetic. A histogram, scatter plot or run chart reveals skew, heavy tails, outliers, ceiling effects, coding errors, seasonality or a denominator change before a test is chosen. In O&G audits the data-generating process may also include referral changes, strike periods, blood stock-outs, new definitions, or missing files — none of which any statistical test can fix. Eyeballing the shape is the single most useful, most skipped step.
Step Three: Describing the Data Honestly
Once you know the shape, summarise it with statistics that match it.
| Quantity | Plain meaning | When to use it |
|---|---|---|
| Mean | The arithmetic average | Symmetric continuous data |
| Median | The middle value; 50% lie above, 50% below | Skewed data or when outliers distort the mean |
| Mode | The commonest value | Categorical/ordinal data, or to flag bimodality |
| Range | Largest minus smallest | Quick spread, but driven entirely by extremes |
| Variance | Average squared distance from the mean | A building block; rarely reported directly |
| Standard deviation (SD) | Square root of variance — typical distance of a value from the mean | Spread of the data in symmetric distributions |
| Interquartile range (IQR) | The middle 50%, 25th to 75th centile | Spread of skewed data, reported with the median |
The summary must fit the shape. For symmetric data, report mean and SD. For skewed data — blood loss, length of stay — report median and IQR, because a single severe haemorrhage can drag the mean somewhere no individual woman actually was.
The One Distinction Candidates Confuse: SD Versus SE
This trips up almost everyone, so anchor it firmly. The standard deviation (SD) describes how spread out the individual observations are. The standard error (SE) describes how spread out the sample mean would be if you repeated the whole study many times. SE is the SD of the imaginary cloud of repeated study means, and it is roughly the SD divided by the square root of the sample size.