Inductive Inference and Replications: A Bayesian Perspective

A probabilistic model is proposed to assess the value of replications. The corrob-oration of a theory is shown to be a function of the number of replications, the number of successful outcomes, and our initial beliefs. An adaptive control model provides the optimal policy for continuing replications, given the accumulated evi-dence for the theory, the preCision deemed necessary, and the cost of replicating. T his article develops a Bayesian analysis ofinductive inference to obtain insights into the rational basis for assessing the value of replications. It is motivated by recent articles on replication research and theory testing (Brinberg, Lynch, and Sawyer 1992; Monroe 1992a, 1992b; Wells 1993) and long-standing concerns about the insufficient value attached to replications (Sawyer and Peter 1983). Brinberg et al. (1992) have recently developed a Bayesian analysis of theory testing in which they show how both confounded and unconfounded experiments