Numbers—census data, tax records, trade statistics, casualty counts—are sources requiring careful interpretation. Quantitative evidence reveals large-scale patterns and provides argumentative weight, but numbers are not objective; they reflect what was counted, how, and by whom. Statistical analysis has power; statistical misuse misleads as much as any bad evidence.
You have already learned to classify sources and assess their strengths and limitations. Quantitative evidence — numbers drawn from census records, tax rolls, trade ledgers, parish registers, mortality tables — presents a distinctive version of those challenges. Numbers carry an aura of objectivity that prose does not, and this is exactly why they require more critical scrutiny, not less. A figure appearing in a table feels precise and definitive in a way that a contemporary's description of "many deaths" does not. That apparent precision can mislead.
The first critical skill is understanding what was counted and why. Medieval tax records don't enumerate people; they enumerate taxable households, excluding the very poor who paid nothing. Parish registers record baptisms, not births — infants who died before baptism disappear from the record entirely. Census categories change across decades: the US Census changed its racial classification scheme multiple times, meaning that apparent population changes in certain categories reflect definitional changes rather than demographic ones. Any time you use a historical number, you must ask: what institution created this record, for what administrative purpose, and who was systematically excluded from it?
Sampling and aggregation introduce a second layer of complexity. Quantitative historians often work with samples from large archives: they analyze ten percent of court records, or all wills from a particular town over a twenty-year period. The validity of inferences depends on whether the sample is representative of the population of interest — a question that requires knowing how the sample was constructed and what selection biases might be present. Aggregation raises the related problem of ecological fallacy: inferring individual behavior from group averages. If a county with high poverty has high crime rates, that tells you about the county, not about any individual poor person in it.
Used well, quantitative methods reveal patterns that no amount of reading individual sources could uncover. The Cambridge Group for the History of Population and Social Structure used parish register data to reconstruct demographic patterns for preindustrial England with extraordinary precision — showing that English family size, marriage age, and population growth differed systematically from continental patterns. Robert Fogel and Stanley Engerman used plantation records and shipping manifests to analyze the economics of American slavery at a scale that transformed the field, even as their methods remained contested. The lesson is not that numbers are unreliable, but that they are evidence like any other — made by human institutions for human purposes, and to be read accordingly. Statistical power and statistical misuse operate at the same level of sophistication; the historian who commands both is far more dangerous to bad arguments than one who avoids numbers entirely.
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