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Linguistic typology compares structural properties across languages using explicit criteria for grouping constructions. It can ask which patterns recur, which combinations are rare, and whether a proposed generalization survives a wider sample. The World Atlas of Language Structures exemplifies this approach by coding documented properties as comparable features.^[ref]

Consider word order. Three distinct elements have $3!=6$ possible permutations, but logical possibility alone says nothing about their distribution in languages. A published comparison must define which constructions count: the atlas's chapter on subject, object and verb order restricts its main comparison to specified transitive declarative constructions.^[ref]

For an original counting example, a sample containing six languages of one type and four of another gives proportions $0.6$ and $0.4$. Those proportions describe that sample. Sampling bias, missing observations and shared historical relationships can prevent them from estimating how common the types are more generally. An unrecorded feature must also remain distinct from an observed absence.

Sampling bias is a systematic distortion arising when the sampling mechanism makes the observed sample unrepresentative of the target statistical population for the estimand of interest. It is distinct from random sampling variability and from other causes of the bias of an estimator.

Suppose a population has equal-sized groups with values zero and ten, so its mean is five. If independent sampling with replacement chooses the first group with probability $0.9$, the sample mean has expectation one and converges to one as the sample grows. More data reduce its random variation without removing the selection bias. Known selection probabilities can support a design-based correction, but a group never sampled cannot be recovered merely by assigning larger weights to observed units.

Statistical sampling selects observations from a target statistical population through an explicit selection procedure or statistical model. It links observed values to the larger collection about which conclusions are sought. The accessible sampling frame and the statistical population need not coincide, which can cause sampling bias even in a large statistical sample.

For a finite statistical population with values $y_1,\dots ,y_N$, suppose every unit has known positive inclusion probability ${\pi }_i$. If $s$ is the selected statistical sample, thenis an unbiased estimator of the total $Y={\sum }_i{y}_i$. Indeed, writing the sum with inclusion indicator functions gives $\mathbb{E}\hat{Y}={\sum }_i{y}_i{\pi }_i/{\pi }_i=Y$. Under simple random sampling without replacement of size $n$, ${\pi }_i=n/N$, so $\hat{Y}/N$ is the sample mean. The selection procedure also determines dependence between selected units and the resulting sampling variability; unbiasedness alone does not specify its size.

A statistician develops or applies methods for collecting data and learning from it under uncertainty. The work connects experimental design, probability models, estimation and statistical hypothesis testing. For example, deciding how many independent observations to collect requires linking the desired precision of a confidence interval to the variation expected under a statistical model. Interpreting results also requires examining sampling bias, missing data and assumptions about dependence.