Asymmetric switch costs as sequential difficulty effects

Abstract

When switching between tasks of unequal difficulty, there is often a larger switch cost for the easy task than for the difficult task. The authors propose a new account of these asymmetric switch costs based on sequential difficulty effects. They argue that the asymmetry arises from impaired performance after a difficult trial regardless of whether the task switches or repeats. Empirical support for this idea is provided in two experiments on arithmetic task switching in which asymmetries are observed for secondary difficulty manipulations, even in the context of arithmetic task repetitions. The authors discuss how their sequential difficulty account might explain asymmetric restart costs in addition to asymmetric switch costs and how sequential difficulty effects might be explained by resource depletion involving executive control or working memory.

Keywords:

• Task switching
• Sequential effects
• Asymmetry
• Task difficulty
• Mental arithmetic

Acknowledgments

This research was supported by Office of Naval Research Grant N00014–03–1–0115 and National Institute of Mental Health Grant MH068243. We thank Rick Bryck and an anonymous reviewer for their comments on a previous version of this article.

Notes

¹ In the General Discussion, we consider an alternative, construct-based definition of difficulty. However, the performance-based definition will suffice for introducing our sequential difficulty account.

² The confound between task transitions and difficulty transitions is similar in many respects to the confound between task transitions and cue transitions in cued task-switching studies with one cue per task, where task switches always involve cue switches, and task repetitions always involve cue repetitions. There is now abundant evidence that the switch costs observed in cued task switching reflect a combination of two sequential effects, one associated with task transitions and one associated with cue transitions (e.g., Logan & Bundesen, 2003; Logan, Schneider, & Bundesen, 2007; Mayr & Kliegl, 2003; Schneider & Logan, 2005, 2007). We suggest that asymmetric switch costs reflect an analogous combination of sequential effects.

³ We consider addition and subtraction to be the basic “tasks” in our experiments, so “task switching” involves a transition from addition to subtraction or vice versa. This is consistent with how addition and subtraction have been classified in past studies (e.g., Baddeley et al., 2001; Biederman, 1973; Buchler et al., 2008; Derakshan et al., 2009; Ellefson et al., 2006; Jersild, 1927; Rubinstein et al., 2001; Spector & Biederman, 1976). We do not treat secondary difficulty manipulations as introducing different tasks, so there can be a change in difficulty without a nominal task switch. This classification scheme is open to debate, but we note that tasks can be defined at different levels of abstraction (much like objects, R. Brown, 1958; Rosch, 1978; events, Morris & Murphy, 1990; Rifkin, 1985; and actions, Vallacher & Wegner, 1987), and there is no apparent consensus in the task-switching literature as to the level at which tasks should be defined.