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To what extent does the study of history use hypothesis testing? By Hypothesis testing I mean the usage of p-values and significance levels to dictate how an actual event differs from the event by chance;

An example where it could be used in history:

To evaluate the change in attitudes of female politicians since laws in country A was changed. The sample would be all politicians of country A for a single year and evaluate the p value with assumed distribution X~B(sample size, 0.5). This can then be graphed to show that the distribution is becoming less/more/as true. The math would probably take more into account but the basic idea is the same

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    Are you asking how often history employs statistical analyses, or are you asking whether histroy tests theories via mathematics like experimental sciences? Historical claims that are based on a test that is based on a significance test Can you elaborate on what this is supposed to mean, preferably with some concrete examples?
    – Semaphore
    Commented Nov 29, 2020 at 14:06
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    1) Are you asking whether history uses hypothesis, or whether they test hypothesis with a specific statistical method? 2) Mod's don't re-open questions; the community votes. 3) I've revised your title to ask a question - if I made an error, please correct, questions where the title asks a clear question are more likely to get answers.
    – MCW ♦
    Commented Nov 29, 2020 at 14:56
  • "Bailyn is known for meticulous research and for interpretations that sometimes challenge the conventional wisdom, especially those dealing with the causes and effects of the American Revolution. In his most influential work, The Ideological Origins of the American Revolution, Bailyn analyzed pre-Revolutionary political pamphlets to show that colonists believed the British intended to establish a tyrannical state that would abridge the historical British rights." Wikipedia:Bailyn is an example of history through hypothesis.
    – MCW ♦
    Commented Nov 29, 2020 at 14:59
  • Donation of Constantine is another example of historical progress through analysis of a hypothesis - I'm not deeply familiar with the methodology, but I believe that something similar to p-values was used.
    – MCW ♦
    Commented Nov 29, 2020 at 15:01
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    Your second example is not a historical question. Historians deal with the meanings, as in language phenomena, from the surviving documentary record of the past. “Significance” in the statistical sense isn’t important. When previously unanalysed statistical sets are located historians use statistics to derive language meaning from them, and then these meanings are analysed historically.
    – Samuel Russell
    Commented Nov 29, 2020 at 17:41

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It seems to me, you mixed two control methods. One, the practical-level method, is statistics. Yes, it is used, alas, very often, without the understanding of the tool. Historians are seldom good at maths, and the Theory of Probability is one of its most demanding areas. It is known, that even people with good math background, but without deeper knowledge of the ToP, can be easily caught by its numerous paradoxes. (The most simple and famous one: "A family has 2 children, one of them is a boy. What is the probability that another one is a boy, too?" Answer - 1/3.) And understanding statistics without the understanding of ToP is impossible.

Second, is a much more deep and important method - predict-and-check. This is the method that divides science from non-science. It is not connected directly to statistics and, naturally, can be used and is used in history, not predicting the future, but predicting the results of excavations. They cannot be known beforehand but can be predicted by the theory you want to check. Freshly translated or newly found documents can serve the same way.

That method needn't statistics, but demands an even deeper understanding of probabilities - conditional probabilities and probabilities of conditions. Less mechanical counting, but much more thinking and understanding. (I advise HPMOR as a very good popular source and a starting point)

Thank God, the method can be often used on an intuitive level, which is practiced by 90% of scientists. Alas, that can sometimes lead to serious errors.

If you want to cross these methods and to predict the results of statistics, yes, it is possible, but you will be in the area of sociology, economics, and politology (as your example), but not of history. And seriously, you don't want it. You really must know ToP and statistics at a very good level for it. Say, 2-3 years of lections and a thousand solved practical problems. On the base of combinatorics, the theory of sets, and logic, of course.

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  • Very nice. i was not expecting to see Principle of Restricted Choice referenced in this answer when i arrived to read and assess it.
    – Pieter Geerkens
    Commented Nov 29, 2020 at 23:45
  • @PieterGeerkens Thank you. As for me, I prefer the Bayes theorem itself. I do understand formulae, but I do not understand that "explaining" bridge terminology. Alas, the use of probabilities for thinking still waits for its popularizer. Yudkovsky wrote a nice piece of literature that IS the best popular source for now, but it is very far from being easy.
    – Gangnus
    Commented Nov 30, 2020 at 0:01
  • it's the same principle: "a boy" is not "a distinguished boy" (either eldest or youngest), and likewise one of two equivalent cards should not be regarded as distinguished (against competent opponents at any rate). Understanding restricted choice is one prerequisite to becoming an intermediate bridge player, and there are many good explanations of it in bridge terms. But underneath, it's all Bayes' Theorem.
    – Pieter Geerkens
    Commented Nov 30, 2020 at 0:17
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    @PieterGeerkens Thank you, but here is the problem - I never played bridge and I don't know, what are equivalent cards :-). In my 16 I didn't play bridge but read tables of integrals in the mass traffic :-). But seriously, I think it is a great problem - these principles should be understandable for early teens or even preteens, and I don't think the bridge is the best material for them. Neither formulae. And if humans won't learn how to think, we'll simply die off. Now we really are moving by blind leaps.
    – Gangnus
    Commented Nov 30, 2020 at 0:37
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    @cbeleitesunhappywithSX A task must be defined by itself, without any additional assumptions. That is the default. The mentioned task is defined and written by me, here, and is a given piece of text. And as is, has its definite solution. And it is 1/3. Yes, additional assumptions can change the result. But that is correct for practically any task. Such research about different results for different assumptions is important for better understanding the subject, but thank you, I have read them already from Martin Gardner when I was 11.
    – Gangnus
    Commented Dec 1, 2020 at 10:23
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Yes, of course. Suppose archaeologists are excavating a region. On average,they find n pottery shards per hectare. At one dig they count 5n pottery shards. They ask themselves "What are the likelihood of finding 5n pottery shards at a random dig?" Since they have estimated the parameters of the pottery shards distribution for the region they can calculate this. So they calculate it and the answer is that it is incredibly unlikely. "Aha!" they say, "here there must have been a settlement!"

This is an example of hypothesis testing. Another example is trying to reconstruct partially destroyed manuscripts. To fill in the blanks you need statistical methods to model the language the manuscript is written in.

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