Long before the mathematical developments that led inexorably to the development of systems factorial technology, the somewhat arduous, but arguably requisite labors which precisely defined parallel and serial architectures had begun (e.g., Townsend, 1969, 1972). Both then and now, what are now referred to as standard serial models and standard parallel models not only play an important role in psychological science, they are often what non-mathematical psychologists are (sometimes in an unschooled fashion) referring to when they up architectural concepts. Interestingly, two strategic and critical properties, and therefore implicit predictions of the canonical serial and parallel models have witnessed little analysis. Thus , standard parallel models predict stochastically independent actual processing timesand therefore total completion times. What do standard serial models predict about this statistic? Similarly, standard serial models predict independent actual processing times and therefore intercompletion times . What do standard parallel models predict about this statistic? Finally, are there psychological questions that pertain to these distinctions and are there any experiments that have emerged to assess the latter. All these matters are targeted for our exposition .
Critical parts of the definitions of standard serial and standard parallel modes refer to stochastic independence. Standard serial models are defined by stochastic independence and identical distributions of their processing times. Processing times in the serial models are identical to the intercompletion time statistics. Similarly , standard parallel models assume stochastically independent and identical processing times. Their processing times are equivalent to the statistic known as total completion times. Little is known about what standard serial models can predict for the total completion time or what standard parallel models can predict for the intercompletion times. Here we demonstrate that standard serial models possess a tendency to predict a positive dependence for the total completion times with that always being true in the case of a single processing order. However, with mixtures of processing orders, standard serial models may predict negative dependence of the total completion times. Comparably, standard parallel models typically predict neither independence of the intercompletion times nor identical distributions. In fact, standard parallel models predict increasing intercompletion times as the individual channels continue to finish. Nevertheless, dramatically increasing hazard functions of the channels can defeat that tendency. And, standard parallel models can predict intercompletion time independence but only when individual channel distributions are exponential. Finally, we use these and ancillary mathematical results to conclude that standard serial and standard parallel models can never perfectly mimic one another. Therefore, our findings set the stage for explicit model testing between these classes .
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Long before the mathematical developments that led inexorably to the development of systems factorial technology, the somewhat arduous, but arguably requisite labors which precisely defined parallel and serial architectures had begun (e.g., Townsend, 1969, 1972). Both then and now, what are now referred to as standard serial models
Critical parts of the definitions of standard serial
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models not only play an important role in psychological science, they are often what non-mathematical psychologists are (sometimes in an unschooled fashion) referring to when they up architectural concepts. Interestingly, two strategic and critical properties, and therefore implicit predictions of the canonical serial and parallel models have witnessed little analysis. Thus
modes refer to stochastic independence. Standard serial models are defined by stochastic independence and identical distributions of their processing times. Processing times in the serial models are identical to the intercompletion time statistics. Similarly
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predict stochastically independent actual processing timesand therefore
assume stochastically independent and identical processing times. Their processing times are equivalent to the statistic known as
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What do
Little is known about what
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predict about this statistic? Similarly, standard serial models predict independent actual processing times and therefore intercompletion times . What do
can predict for the total completion time or what standard parallel models can predict for the intercompletion times. Here we demonstrate that standard serial models possess a tendency to predict a positive dependence for the total completion times with that always being true in the case of a single processing order. However, with mixtures of processing orders, standard serial models may predict negative dependence of the total completion times. Comparably, standard parallel models typically predict neither independence of the intercompletion times nor identical distributions. In fact,
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about this statistic? Finally, are there psychological questions that pertain to these distinctions and are there any experiments that have emerged to assess the latter. All these matters are targeted for our exposition
increasing intercompletion times as the individual channels continue to finish. Nevertheless, dramatically increasing hazard functions of the channels can defeat that tendency. And, standard parallel models can predict intercompletion time independence but only when individual channel distributions are exponential. Finally, we use these and ancillary mathematical results to conclude that standard serial and standard parallel models can never perfectly mimic one another. Therefore, our findings set the stage for explicit model testing between these classes