Questions: Quantitative Methods and Statistical Evidence in History

Question 1

A historian finds a medieval tax record listing 500 households in a town. What is the most important limitation to acknowledge when using this figure to estimate the town's actual population?

• A. The figure has likely been rounded to the nearest hundred, introducing imprecision
• B. Tax records enumerate taxable units (households), systematically excluding the very poor who paid no tax — so the actual population was substantially larger
• C. Medieval scribes frequently falsified records, making any specific figure unreliable
• D. The document may not have survived in its original form, making transcription errors likely

Answer: (B)

The critical question for any quantitative historical source is: what was actually counted, and who was excluded by the counting method? Tax records count taxable households, not people. The very poor, who owed nothing, left no trace. Infants and children are not separately counted. Women and servants may be merged into the household figure or excluded. The 500 figure is real evidence — but it measures taxable fiscal units, not inhabitants. Using it as a direct population estimate without adjustment produces systematic undercount. This is the foundational skill: reading what an institutional record was designed to capture, not what you wish it had captured.

Question 2

A historian finds that counties with higher poverty rates have higher rates of property crime, and concludes that low-income individuals are more prone to theft. What logical error has been committed?

• A. Confirmation bias — the historian found data that supports a preexisting belief
• B. Ecological fallacy — inferring individual behavior from group-level statistics
• C. Selection bias — the counties were not representative of the broader population
• D. Simpson's paradox — the aggregate trend reverses when the data is disaggregated

Answer: (B)

Ecological fallacy is the error of attributing to individuals the characteristics observed at the group level. A county-level correlation between poverty and crime rates tells you something about counties, not about any specific individual in those counties. Many non-poor people live in high-poverty counties; many high-crime incidents may involve perpetrators from outside the county. Inferring individual behavior from aggregate data is one of the most common and consequential misuses of quantitative historical and social evidence.

Question 3

Parish register data recording baptisms rather than births will systematically undercount infants who died before being baptized.

• T. True
• F. False

Answer: True

This is a canonical example of the 'what was counted and why' problem. Parish registers were ecclesiastical records of the sacrament of baptism, not civil records of biological birth. Any infant who died in the hours or days between birth and baptism simply did not exist in the register. In periods of high infant mortality, this exclusion is not trivial — it can meaningfully distort mortality estimates, birth rates, and survival calculations. Historians using parish data must account for this systematic gap explicitly.

Question 4

Because quantitative data appears in numerical tables rather than prose, it is inherently more objective and reliable than qualitative historical evidence.

• T. True
• F. False

Answer: False

Numbers carry an aura of precision and objectivity that prose does not, but this appearance can mislead. Every quantitative historical record was created by a human institution for a specific administrative purpose, with its own inclusion rules, exclusion criteria, and definitional choices. The apparent precision of '500 households' is real — but it measures something specific that may not be what the historian needs. Statistical misuse (ecological fallacy, ignoring sampling bias, treating definitional changes as demographic changes) operates at the same level of sophistication as verbal misrepresentation. The historian who treats numbers uncritically is more vulnerable to their errors than one who asks what was counted and why.

Question 5

Explain why changes in the US Census's racial classification scheme across decades complicate the use of census data to track demographic change.

Model answer: When the Census changes how racial categories are defined — which categories exist, how multi-racial individuals are classified, which ethnic groups are merged or separated — an apparent change in the population count for a given category may reflect the new definition rather than any actual demographic change. You are not measuring the same thing across decades; you are measuring different administrative constructions of the same underlying population. Comparing figures across definitional changes conflates two different things: actual demographic shifts and categorical reclassification.

The US Census has changed its racial classification system multiple times: adding 'multiracial' options, reclassifying certain groups, changing whether Hispanic/Latino is a racial or ethnic designation. A historian tracking the 'Mexican-American population' across 1900–2000 using Census data will encounter multiple moments where the category itself changed, meaning the figures cannot simply be read as a continuous time series. This is not a flaw in the data — it is a feature of all administrative data sources that must be identified and accounted for explicitly.