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“Intentional binding” refers to the finding that people judge voluntary actions and their effects as having occurred closer together in time than two passively observed events. If this effect reflects subjectively compressed time, then time-dependent visual illusions should be altered by voluntary initiation. To test this hypothesis, we showed participants displays that result in particular motion illusions when presented at short interstimulus intervals (ISIs). In Experiment 1 we used apparent motion, which is perceived only at very short ISIs; Experiments 2a and 2b used the Ternus display, which results in different motion illusions depending on the ISI. In support of the time compression hypothesis, when they voluntarily initiated the displays, people persisted in seeing the motion illusions associated with short ISIs at longer ISIs than had been the case during passive viewing. A control experiment indicated that this effect was not due to predictability or increased attention. Instead, voluntary action altered motion illusions, despite their purported cognitive impenetrability.
Atten Percept Psychophys

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—  Assessing the correlations between psychological variabless, such as abilities and improvements, is one essential goal of psychological science. However, psychological variables are usually only available to the researcher as estimated parameters in mathematical and statistical models. The parameters are often estimated from small samples of observations for each research participant, which results in uncertainty (aka sampling error) about the participant-specific parameters. Ignoring the resulting uncertainty can lead to suboptimal inferences, such as asserting findings with too much confidence. Hierarchical models alleviate this problem by accounting for each parameter’s uncertainty at the person- and average levels. However, common maximum likelihood estimation methods can have difficulties converging and finding appropriate values for parameters that describe the person-level parameters’ spread and correlation. In this post, I discuss how Bayesian hierarchical models solve this problem, and advocate their use in estimating psychological variables and their correlations.

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