DECOMPOSITIONS OF RESPONSE-TIMES - AN ALMOST GENERAL-THEORY

被引:25
作者
DZHAFAROV, EN [1 ]
SCHWEICKERT, R [1 ]
机构
[1] PURDUE UNIV,W LAFAYETTE,IN
关键词
D O I
10.1006/jmps.1995.1029
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Response time (RT) whose distribution depends on two external factors can sometimes be presented as an algebraic combination of two random variables, component times, each of which is selectively influenced by one of these factors. The algebraic operation connecting these component times (such as addition or ''minimum of the two'') is referred to as the decomposition rule. We consider a broad subclass of associative and commutative decomposition rules, and for any operation from this subclass we construct a decomposition test, a relationship between observable RTs that must hold ii these RTs are decomposable by means of this operation. The decomposition tests are constructed under The assumption that RT components are either stochastically independent or perfectly positively stochastically interdependent (in which case they are increasing functions of a common random variable). The decomposition tests generalize the summation test proposed by Ashby & Townsend (1980) and Roberts & Sternberg (1992) for additive decompositions into stochastically independent components. Under the assumption of perfect positive stochastic interdependence, a successful decomposition test is not only necessary but also sufficient for the RT decomposability by means of the corresponding operation. Under the assumption of stochastic independence, it is possible that a decomposition test is successful but RTs cannot be decomposed by any operation. Cinder both assumptions, however, a successful decomposition test recovers the true decomposition rule essentially uniquely. For a given decomposition rule, the component times themselves cannot be determined uniquely, and the stochastic relationship between them generally has to be assumed rather than recovered from the decomposition tests. (C) 1995 Academic Press, Inc.
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页码:285 / 314
页数:30
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