Intuitive statistics, or folk statistics, is the cognitive phenomenon where organisms use data to make generalizations and predictions about the world. This can be a small amount of sample data or training instances, which in turn contribute to inductive inferences about either population-level properties, future data, or both. Inferences can involve revising hypotheses, or beliefs, in light of probabilistic data that inform and motivate future predictions. The informal tendency for cognitive animals to intuitively generate statistical inferences, when formalized with certain axioms of probability theory, constitutes statistics as an academic discipline.
Because this capacity can accommodate a broad range of informational domains, the subject matter is similarly broad and overlaps substantially with other cognitive phenomena. Indeed, some have argued that "cognition as an intuitive statistician" is an apt companion metaphor to the computer metaphor of cognition. Others appeal to a variety of statistical and probabilistic mechanisms behind theory construction and category structuring. Research in this domain commonly focuses on generalizations relating to number, relative frequency, risk, and any systematic signatures in inferential capacity that an organism (e.g., humans, or non-human primates) might have.
Background and theory
Intuitive inferences can involve generating hypotheses from incoming sense data, such as categorization and concept structuring. Data are typically probabilistic and uncertainty is the rule, rather than the exception, in learning, perception, language, and thought. Recently, researchers have drawn from ideas in probability theory, philosophy of mind, computer science, and psychology to model cognition as a predictive and generative system of probabilistic representations, allowing information structures to support multiple inferences in a variety of contexts and combinations. This approach has been called a probabilistic language of thought because it constructs representations probabilistically, from pre-existing concepts to predict a possible and likely state of the world.
Probability
Statisticians and probability theorists have long debated about the use of various tools, assumptions, and problems relating to inductive inference in particular. David Hume famously considered the problem of induction, questioning the logical foundations of how and why people can arrive at conclusions that extend beyond past experiences - both spatiotemporally and epistemologically. More recently, theorists have considered the problem by emphasizing techniques for arriving from data to hypothesis using formal content-independent procedures, or in contrast, by considering informal, content-dependent tools for inductive inference. Searches for formal procedures have led to different developments in statistical inference and probability theory with different assumptions, including Fisherian frequentist statistics, Bayesian inference, and Neyman-Pearson statistics.
Gerd Gigerenzer and David Murray argue that twentieth century psychology as a discipline adopted probabilistic inference as a unified set of ideas and ignored the controversies among probability theorists. They claim that a normative but incorrect view of how humans "ought to think rationally" follows from this acceptance. They also maintain, however, that the intuitive statistician metaphor of cognition is promising, and should consider different formal tools or heuristics as specialized for different problem domains, rather than a content- or context-free toolkit. Signal detection theorists and object detection models, for example, often use a Neyman-Pearson approach, whereas Fisherian frequentist statistics might aid cause-effect inferences.
Frequentist inference
Frequentist inference focuses on the relative proportions or frequencies of occurrences to draw probabilistic conclusions. It is defined by its closely related concept, frequentist probability. This entails a view that "probability" is nonsensical in the absence of pre-existing data, because it is understood as a relative frequency that long-run samples would approach given large amounts of data. Leda Cosmides and John Tooby have argued that it is not possible to derive a probability without reference to some frequency of previous outcomes, and this likely has evolutionary origins: Single-event probabilities, they claim, are not observable because organisms evolved to intuitively understand and make statistical inferences from frequencies of prior events, rather than to "see" probability as an intrinsic property of an event.