The joint distribution criterion and the distance tests for selective probabilistic causality
The joint distribution criterion and the distance tests for selective probabilistic causality
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DOI：
10.3389/fpsyg.2010.00151
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发表时间：
2010-01-01
影响因子：
3.8
通讯作者：
Kujala, Janne V.
中科院分区：
文献类型：
--
作者：
Dzhafarov, Ehtibar N.;Kujala, Janne V.
为任意一组外部因素制定一般定义和标准（必要和充分条件），以选择性地影响一组相应的随机实体（广义随机变量，在任意观察空间中具有值），在每次处理中联合分布（一组因子值恰好包含每个因子的一个值）。当且仅当满足以下条件（称为联合分布准则）时，随机实体才会有选择地受到相应因素的影响：存在一组联合分布的随机实体，每个因素的每个值都有一个实体，使得与处理相对应的该集合的每个子集都作为该处理的原始变量进行分配。先前在二乘二析因设计中为两个随机变量制定的选择性影响的距离检验（必要条件）（Kujala 和 Dzhafarov，2008，J. Math. Psychol. 52, 128-144）已扩展到任意的因子和随机变量集。事实证明，概括是最简单的：距离测试应该应用于从一组给定因素中提取的所有二乘二设计。
A general definition and a criterion (a necessary and sufficient condition) are formulated for an arbitrary set of external factors to selectively influence a corresponding set of random entities (generalized random variables, with values in arbitrary observation spaces), jointly distributed at every treatment (a set of factor values containing precisely one value of each factor). The random entities are selectively influenced by the corresponding factors if and only if the following condition, called the joint distribution criterion, is satisfied: there is a jointly distributed set of random entities, one entity for every value of every factor, such that every subset of this set that corresponds to a treatment is distributed as the original variables at this treatment. The distance tests (necessary conditions) for selective influence previously formulated for two random variables in a two-by-two factorial design (Kujala and Dzhafarov, 2008, J. Math. Psychol. 52, 128-144) are extended to arbitrary sets of factors and random variables. The generalization turns out to be the simplest possible one: the distance tests should be applied to all two-by-two designs extractable from a given set of factors.