In Proceedings of ICCM - 2007- Eighth International Conference on Cognitive Modeling. 299 - 304. Oxford, UK: Taylor & Francis/Psychology Press.
Modeling the Range of Performance on the Serial Subtraction Task Frank E. Ritter1 (
[email protected]), Michael Schoelles3, Laura Cousino Klein2, and Sue E. Kase1 1
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College of Information Sciences and Technology, and Biobehavioral Health Department The Pennsylvania State University, University Park, PA 16802 USA 3
Cognitive Science Department, Rensselaer Polytechnic Institute, Troy, NY 12180 USA Abstract
We present a model of serial subtraction, a task where subjects repeatedly subtract a 1- or 2-digit number from a 4-digit number. The model performs 4 min. blocks of these subtractions like subjects do. The current model replicates part of the pace and % correct for group data. Because performance on this task varies widely between subjects, we explore what it means to match the data distribution. We find that our model represents individual subjects better than group means. We can start to model a distribution of performance and illustrate some of what this approach will entail.
Introduction Serial subtraction, repeatedly subtracting a 1- or 2-digit number from a 4 digit number is part of the Trier Social Stressor Task (TSST, Kirschbaum, Pirke, & Hellhammer, 1993). This is an interesting task for two reasons. One reason is that it has been used over 100 times in published articles to study the effects of stress on physiology (e.g., Kudlielka, Buske-Kirschbaum, Hellhammer, & Kirschbaum, 2004; Nater et al., 2006; Taylor et al., 2006; Tomaka, Blascovich, Kelsey, & Leitten, 1993). It is a cognitive task used to cause stress, but we don’t know how it’s performed—there is only one report on how well it is performed (Tomaka, Blascovich, Kelsey, & Leitten, 1993), and this report only provides data on one 4-min. block. The second reason it is interesting is that subtraction is an interesting task in its own right and as a component task to many other tasks. It involves many cognitive mechanisms making it a good task to study cognition, not just the biobehavioral effects of laboratory stress. Real world tasks that use subtraction include air traffic control, navigation, and piloting the wide range of vehicles that use angular directions. It would be useful to have a cognitively plausible model of performance of subtraction. This model would serve as an explanation and summary of task performance, helping to summarize
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regularities, and a model would also be the starting point of a theory of how cognition changes with stress. Because the task requires not only executive control and memory but interaction with the verbal system as well, a model will be able to quantify the constraints that these subsystems of cognition impose on the task. These requirements suggest that the model be constructed on an embodied cognitive architecture (Anderson, in press). Previous work with an earlier model has shown that the general pattern of high level results (i.e., number of attempts per 4-min. block and percent correct) with serial subtraction can be predicted (Ritter, Reifers, Klein, Quigley, & Schoelles, 2004), and we have used this approach to describe how popular theories of stress could influence performance on this task (Ritter, Reifers, Schoelles, & Klein, 2007). The next steps, presented here, are to create more detailed predictions of performance and compare these predictions to more detailed subtraction performance data than has been previously presented. The remainder of this paper presents a serial subtraction experiment, the architecture and model, subtraction data, and a comparison of the model with human data. The model’s predictions match the individual data fairly well, and provide lessons for understanding how serial subtraction is performed. The model-data comparison also makes suggestions for the further development of cognitive architectures.
The Serial Subtraction Experimental Data As part of a larger project on the biobehavioral effects of stress in men and women, serial subtraction was administered as part of the TSST. Several aspects of serial subtraction performance were recorded. We present several of them here as an initial summary of performance on serial subtraction. They are taken from a more complete report (Ritter, Bennett, & Klein, 2006).
Subjects Thirty-six healthy women and 20 men, 18-30 years of age (µ=21.1) were recruited to participate in a study examining hormonal responses to stress.
Method All subjects participated in the same protocol, which consisted of a baseline rest period, the TSST challenge period (approximately 30 min.), and a recovery period. Following informed consent and a baseline rest period, participants were asked to complete the TSST which consisted of: (a) preparing a 3.5-min. speech on a personal failure, which they were told would be recorded for later observation, and then (b) completing two blocks of serial subtraction across a 15-min. period. The first subtraction set required counting backwards from a 4-digit number by 7’s; the second set required counting backwards by 13’s. Subjects’ serial subtraction answers were corrected against a list of answers from the starting 4-digit number. When an incorrect answer was given, the subject was told to “Start over at ”. At 2 min. into each 4min. session, subjects were told that “2-minutes remain, you need to hurry up”. Performance on the first block of 7’s and first block of 13’s were recorded on the experimenter’s scoring sheets. Part way through the study a mark to indicate where the 2-min. warning occurred was added to measure pace of the subtractions. Subjects were paid $30 for their time at the end of the study.
it to this data assuming that the variance in each case is equivalent. If we do so, for number of attempts and number correct there is not a reliable difference between this data and Tomaka et al.’s (1994) threatened condition t(36) 4, p
