Why Historians Need Statistical Thinking

Historical interpretation is always a claim about evidence. Statistical thinking makes those claims more precise.

History has long straddled the divide between the social sciences and humanities. While for much of the past 50 years, particularly with the turn to social and cultural history, the emphasis has been firmly on the interpretive side of the ledger, the increasing amount and kinds of historical data has resurfaced discussion of the field’s social scientific side. Like all social scientists, historians make interpretations about the actions, intentions, causes, effects, and meaning of people and societies on the basis of data, usually a mix of texts, images, and audio recordings across time and space.

Historians’ data is different from that of sociologists or economists in two key ways, however. First, it is much, much larger—it encompasses the past, full stop. Historians often don’t think of their evidence this way, but the entirety of human history is in a meaningful sense fair game for making historical claims. It is entirely common to criticize colleagues for not thinking carefully about excluded evidence—making a claim about the history of the modern Middle East, for example, by drawing on English-language but not Arabic-language sources, or asserting a truth about early modern politics without taking into account the limitations of state archives, or arguing about the causes of a conflict only using evidence produced by the victors.

Second, we draw on observational evidence, but we cannot run our study twice. That is, unlike an experimental setup in psychology, history is an n-of-1 experiment; we might muse about counterfactuals or what-ifs, but ultimately the Reformation happened once, so we cannot test a theory about what might have been different had a particular event not happened or particular person not been born. Likewise, we only have the evidence that remains to assert what it felt like to live on December 1, 1045 or even December 1, 2025. We cannot simply run the study again with new questions or new variables.

Historians navigate these limitations on their evidence in part by making assertions about the representativeness and persuasiveness of the evidence they use—whether a particular statement is typical or unusual; whether an event was unexpected or expected; whether a purported cause is plausible. This is, after all, the normal way academic historians begin our articles, asserting the relevant scope of the problem, laying out what we know already, and explaining how the evidence we draw on will enable us to say something new.

This background is why historians need to engage more directly with statistical thinking. After all, statisticians have spent decades now thinking about what it means to have only a “sample” of evidence from a “population,” or how observational data differs from experimental data, or how to be precise about what is “typical” or “rare” or “unexpected”. We normally associate statistical processing of historical data with the digital or computational humanities, niche fields for colleagues particularly skilled in computers and quantification. Or approaches that have been relegated to economic history after 1970s-era debates over cliometrics and Time on the Cross. But that’s wrong. Every claim we make, about the importance of a particular book or event or person; about the causes of change or resistance to change; about the meaning of an abstract concept in the lives of everyday people, requires us to make assertions about the nature of our evidence as a sample of the population of evidence we could have used. And knowledge of statistical ideas helps to make those assertions more precise.

Take a few basic ideas. Samples, in statistical terms, can be large or small, can be randomly chosen or carefully selected. These differences can, in turn, make big differences in what statisticians can infer about the sample. If you randomly select a sample, then the presumption is that every other sample is comparable in a more meaningful sense than if you hand select a sample. Likewise, statisticians distinguish between different ways of “reducing” evidence to a representative example, for example, the mode of a data set (the data point that occurs the most) compared to the median (the middle data point); and have measures of “spread” to give a sense of how close the median piece of evidence is, for example, to the most dissimilar pieces of evidence.

Historians, implicitly, make similar arguments when they assert that a particular passage is typical for a written source, and then describe how different the rest of the source really is. Or when a historian carefully dissects three court cases to show how a particular legal system works but then asserts that the three cases can stand in for all of the rest. Historians may not quantify such assertions, but we do distinguish between an idea that appears a lot and one that is, for example, “middle-of-the-road,” or between a treatise with a wide distribution of ideas and one that is narrowly focused.

Statisticians have also formalized how to interpret “time series” – showing change in some measure over time—or “natural experiments,” when one can compare data before and after some event and make inferences about the effects of the event on that basis. Historians, of course, make arguments along these lines as well. We may argue that the way something is talked about changes gradually over time, for example, or perhaps that the meaning of an idea changes quite quickly and dramatically after some important rupture, like a political revolution. This, implicitly, requires being able to specify and measure (even if qualitatively) what changes and what does not change over time.

Similarly, statisticians have been working for well over a century to formalize when two associated things might be said to have a causal relationship. Epidemiologists, in particular, have carefully formalized how associations must be strong, specific, and consistent with other evidence of cause and effect to be deemed causal. It is crucial to rule out alternative hypotheses and confounding variables that may complicate a supposed causal relationship. Sometimes for statisticians these arguments are made using a model, like that of a regression equation, which makes mathematical assumptions about variables in a formalized effort to combine them and make predictions. Part of this process is to think carefully about when it is ok to eliminate a variable from the equation, what kinds of effects are significant and which are insignificant.

Historians, too, talk about influences, about necessary or sufficient cause, but often do so without any formalization. We talk about contingent and structural causes, but often without thinking carefully about the implicit model of causation we have in mind. We wouldn’t, of course, expect many historical arguments to be expressible as a mathematical equation, but we do ask why one causal claim is more convincing than others.

Most of us remember with bleary eyes, or perhaps some degree of recollected dread or boredom, the weeks of Statistics 101 when ideas like medians or regressions were presented. It is not that we need to use the vocabulary of statistics in writing our papers, or that we would expect to formulate a model when making claims about causation. But we are as historians making claims about evidence. Even if our historical argument involves closely reading one source as standing in for a particular understanding of a movement’s ideas at one point of time—i.e., if we rely on singularities—we implicitly are claiming that everything else is irrelevant or of less importance, and statistical ideas would help us think through how to make these claims more precise.

And for those of us who are wading through thousands of documents, or hundreds of interconnected people, formal mathematical ideas may of course be especially relevant. But that is, and is likely to remain, the exception. The point, for most of us, is that history remains at the intersection of humanistic and social scientific modes of inquiry and even if you find your own way of arguing firmly on the humanities’ side of things, we benefit from knowing enough of the social scientific side to make clear why our arguments are precise and persuasive.