The joint distribution criterion and the distance tests for selective probabilistic causality

Area of Science:

• Psychology
• Statistics
• Mathematics

Background:

• Selective influence is crucial for understanding causal relationships in experiments.
• Existing criteria for selective influence were limited to simple experimental designs.
• Generalizing these criteria is essential for analyzing complex factorial experiments.

Purpose of the Study:

• To formulate a general definition and criterion for selective influence in arbitrary factorial designs.
• To extend existing distance tests for selective influence to accommodate complex experimental setups.
• To provide a unified framework for analyzing selective influence across diverse research areas.

Main Methods:

• Development of a general definition and a necessary and sufficient condition (joint distribution criterion) for selective influence.
• Extension of distance tests, previously applied to two-by-two designs, to arbitrary sets of factors and random variables.
• Application of the generalized distance tests to all extractable two-by-two designs within a given factorial structure.

Main Results:

• A precise mathematical criterion (joint distribution criterion) for selective influence is established for generalized random variables.
• Distance tests are successfully generalized, providing necessary conditions for selective influence in complex designs.
• The generalized distance tests are shown to be applicable by examining all constituent two-by-two designs.

Conclusions:

• The joint distribution criterion offers a robust method for assessing selective influence in complex experimental settings.
• The generalized distance tests provide a practical and simplified approach to analyzing selective influence in arbitrary factorial designs.
• This work unifies the study of selective influence across various experimental complexities, enhancing statistical rigor.