 
Summary: Memory & Cognition
1982, Vol. 10 {2), 125..134
Testing the assumptions of exponential,
additive reaction time models
F. GREGORY ASHBY
Ohio State University, Columbus, Ohio 43210
Two assumptions commonly made by choice reaction time (RT) models are (1) that certain
experimental tasks can be found that cause an extra processing stage to be inserted into
the cognitive process and (2) that the duration of one or more processing stages is random
with an exponential distribution. Few rigorous tests of either assumption exist. This paper
reviews existing tests and presents several new results that can be used to test these
assumptions. First, in the case in which the duration of an inserted stage is exponentially dis
tributed, it is shown that the observable RT density functions must always intersect at
the mode of the density requiring the extra processing stage. Second, when only the first
assumption {Assumption 1) is made, it is shown that the cumulative RT distribution functions
and, in many cases, the hazard functions must be ordered. Finally, when only Assumption 2 is
assumed, it is shown that, under fairly weak conditions, the taft of the RT density function
must be exponential. The first two results are applied to data from a memory scanning experi
ment, and the two assumptions are found to receive tentative support.
An assumption found in many early theories of
