The current literature on test equating generally defines it as the process necessary to obtain score comparability between different test forms. The definition is in contrast with Lord's foundational paper which viewed equating as the process required to obtain comparability of measurement scale between forms. The distinction between the notions…

Identifying patterns in the world requires noticing not only unusual occurrences, but also unusual absences. We examined how people learn from absences, manipulating the extent to which an absence is expected. People can make two types of inferences from the absence of an event: either the event is possible but has not yet occurred, or the event…

This article summarizes a conceptual framework and simple mathematical methods of estimating the probability that one event was a necessary cause of another, as interpreted by lawmakers. We show that the fusion of observational and experimental data can yield informative bounds that, under certain circumstances, meet legal criteria of causation.…

Thermodynamic spontaneity-equilibrium criteria require that in a single-reaction system, reactions in either the forward or reverse direction at equilibrium be nonspontaneous. Conversely, the concept of dynamic equilibrium holds that forward and reverse reactions both occur at equal rates at equilibrium to the extent allowed by kinetic…

Some researchers claim that variability is an operant dimension of behavior. The present paper reviews the concept of operant behavior and emphasizes that differentiation is the behavioral process that demonstrates an operant relation. Differentiation is conceived as change in the overlap between two probability distributions: the distribution of…

Reinforcement learning approaches to cognitive modeling represent task acquisition as learning to choose the sequence of steps that accomplishes the task while maximizing a reward. However, an apparently unrecognized problem for modelers is choosing when, what, and how much to reward; that is, when (the moment: end of trial, subtask, or some other…

The main result of an experiment is typically an estimate of the average treatment effect (ATE) and its standard error. In most experiments, the number of covariates that may be moderators is large. One way this issue is typically skirted is by interpreting the ATE as the average effect for "some" population. Cornfield and Tukey (1956)…

Bayesian orthodoxy posits a tight relationship between conditional probability and updating. Namely, the probability of an event "A" after learning "B" should equal the conditional probability of "A" given "B" prior to learning "B". We examine whether ordinary judgment conforms to the orthodox view. In three experiments we found substantial…

How effective is training frogs to jump? This is perhaps the most frequent question in biology that is subjected to statistical analysis: does a treatment make a difference? One can examine whether there is indeed a training effect, by first assuming the opposite. That is, the authors assume that training has no effect on the mean distance jumped.…

For decisions between many alternatives, the benchmark result is Hick's Law: that response time increases log-linearly with the number of choice alternatives. Even when Hick's Law is observed for response times, divergent results have been observed for error rates--sometimes error rates increase with the number of choice alternatives, and…

Experiments 1 and 2 involved independent groups that received primary reinforcement after a correct match with a probability of 1.0, 0.50 or 0.25. Correct matches that did not produce primary reinforcement produced a conditioned reinforcer. Both experiments revealed little evidence that acquisition or retention was adversely affected by use of…

Cognitive control enables flexible interaction with a dynamic environment. In 2 experiments, the authors investigated control adjustments in the stop-signal paradigm, a procedure that requires balancing speed (going) and caution (stopping) in a dual-task environment. Focusing on the slowing of go reaction times after stop signals, the authors…

Bertrand's paradox (Bertrand 1889 "Calcul des Probabilites" (Paris: Gauthier-Villars)) can be considered as a cautionary memento, to practitioners and students of probability calculus alike, of the possible ambiguous meaning of the term "at random" when the sample space of events is continuous. It deals with the existence of different possible…

There is much debate over the degree to which language learning is governed by innate language-specific biases, or acquired through cognition-general principles. Here we examine the probabilistic language acquisition hypothesis on three levels: We outline a novel theoretical result showing that it is possible to learn the exact "generative model"…

Listeners of various languages tend to perceive an illusory vowel inside consonant clusters that are illegal in their native language. Here, we test whether this phenomenon arises after phoneme categorization or rather interacts with it. We assess the perception of illegal consonant clusters in native speakers of Japanese, Brazilian Portuguese,…