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The cost of serially chaining two cognitive operations

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Abstract

As Turing (1936, Proceedings of the London Mathematical Society) noted, a fundamental process in human cognition is to effect chained sequential operations in which the second operation requires an input from the preceding one. Although a great deal is known about the costs associated with ‘independent’ (unrelated) operations, e.g., from the classic psychological refractory period paradigm, far less is known about those operations to which Turing referred. We present the results of two behavioural experiments, where participants were required to perform two speeded sequential tasks that were either chained or independent. Both experiments reveal the reaction time cost of chaining, over and above classical dual-task serial costs. Moreover, the chaining operation significantly altered the distribution of reaction times relative to the Independent condition in terms of an increased mean and variance. These results are discussed in terms of the cognitive architecture underlying the serial chaining of cognitive operations.

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Notes

  1. Response grouping is the tendency for participants to wait for the occurrence of Task 2 before initiating their response to Task 1. Procedure to discourage grouping was adapted from Van Selst and Jolicoeur (1994).

  2. For RT analysis, only trials with correct Task 1 and Task 2 responses and correct response order were entered into the analysis. An outlier screening procedure (Van Selst & Jolicoeur, 1994) was used to exclude outlier RTs in each cell for each participant. Less than 3.6% of trials were labelled as outliers in the RT analysis using this approach. Post hoc analyses in each ANOVA of each experiment were conducted using the Bonferroni correction for multiple comparisons.

  3. Most mental operations are Poissonian, increasing the variance linearly with RT; there are, however a few important exceptions (cf. Wagenmakers & Brown, 2007). For example, Sigman and Dehaene (2005) showed that there are manipulations that affect mean RT without affecting the variance, e.g., changing the notation of a number from Arab digits to words in a number comparison task. It was not clear a priori whether the chaining task we inserted between T1 and T2 (which contributes to increased RT) also provided a significant contribution to the variance.

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Acknowledgments

This study was funded by a grant from the Human Frontier Science Program to S. Dehaene, K. Shapiro, P. Roelfsema, M. Sigman and W. Vanduffel.

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Authors and Affiliations

  1. Key Laboratory of Adolescent Cyberpsychology and Behavior, Central China Normal University, Ministry of Education, Wuhan, 430079, China

    Zhao Fan

  2. School of Psychology, Central China Normal University, Wuhan, 430079, China

    Zhao Fan

  3. School of Psychology, Cardiff University, CUBRIC, Cardiff, CF10 3AT, UK

    Krish Singh & Suresh Muthukumaraswamy

  4. Physics Department, University of Buenos Aires, 1428, Buenos Aires, Argentina

    Mariano Sigman

  5. Collège de France, 75005, Paris, France

    Stanislas Dehaene

  6. School of Psychology, Bangor University, Bangor, LL57 2AS, Wales, UK

    Kimron Shapiro

Authors
  1. Zhao Fan
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  2. Krish Singh
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  3. Suresh Muthukumaraswamy
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  4. Mariano Sigman
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  5. Stanislas Dehaene
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  6. Kimron Shapiro
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Corresponding author

Correspondence to Kimron Shapiro.

Appendix 1

Appendix 1

Spatial location switching effects: Experiment 1

With regard to Task 1 RT, a significant main effect of Condition [F(1, 12) = 4.774, p < 0.05] was found comparing the IND-stick to the IND-switch condition. RT1 of the IND-stick condition was 12 ms (SE = 5 ms) faster than RT1 of IND-switch condition. This effect was also mirrored on the accuracy of Task 1 with significantly higher accuracy of Task 1 [F(1, 12) = 9.452, p < 0.011; difference = 1.6%, SE = 0.5%] in the IND-stick condition relative to the IND-switch condition. However, this effect was not significant with regard to the standard deviation of RT1 (p = 0.972).

Turning to Task 2 RT, there was no significant main effect of Condition (p = 0.191). However, switching the spatial location of attention had an effect on Task 2 accuracy [F(1, 12) = 9.452, p < 0.011]. Accuracy of Task 2 was significantly higher (difference = 1.6%, SE = 0.5%, p < 0.011) for the IND-stick relative to the IND-switch condition. However, this effect of Condition difference was not significant with regard to the standard deviation of RT2 (p = 0.313).

Spatial location switching effects: Experiment 2

For RT1, there was a significant two-way interaction of Condition and SOA [F(1, 18) = 10.585, p < 0.005] when comparing the IND-stick to IND-switch conditions. Further post hoc comparisons revealed that this two-way interaction arose when RT1 in the 100 ms SOA IND-stick condition was significantly faster than RT1 in the IND-switch condition (difference = −44 ms, SE = 11 ms, p < 0.002); however, there was no significant differences at 200 ms SOA (p = 0.199). The main effect of Condition was significant [F(1, 18) = 11.409, p < 0.004]; RT1 of IND-stick condition was significantly faster than RT1 of IND-switch condition (difference = −27 ms, SE = 8 ms, p < 0.004). The main effect of SOA was also significant [F(1, 18) = 21.517, p < 0.001] with RT1 in 200 ms SOA condition significantly faster than RT1 in 100 ms SOA condition (difference = −46 ms, SE = 10 ms, p < 0.001). Turning to Task 1 accuracy, there was no significant two-way interaction. The only significant main effect was SOA [F(1, 18) = 18.237, p < 0.001] indicating Task 1 accuracy in 200 ms SOA condition was significantly better than that in 100 ms SOA condition (difference = 10%, SE = 2.4%, p < 0.001). As before, there was no evidence of a speed–accuracy trade-off.

Looking at the STD of RT1, there was no significant two-way interaction. The main effect of the IND-stick versus IND-switch comparison was not significant (p = 0.754). The main effect of SOA was significant [F(1, 18) = 17.026, p < 0.002]. The STD of RT1 in 200 ms SOA condition was significantly smaller than that in 100 ms SOA condition (difference = −26 ms, SE = 6 ms, p < 0.002).

Turning to RT2, there was no significant two-way interaction. The main effect of the IND-stick versus IND-switch comparison was significant [F(1, 18) = 9.881, p < 0.007]. RT2 in IND-stick condition was significantly faster than RT2 in the IND-switch condition (difference = −47 ms, SE = 15 ms, p < 0.007). The main effect of SOA was also significant [F(1, 18) = 23.689, p < 0.001). RT2 in the 200 ms SOA condition was significantly faster than RT2 in the 100 ms SOA condition (difference = −96 ms, SE = 20 ms, p < 0.001). For Task 2 accuracy, there was no significant two-way interaction. The only significant main effect was SOA [F(1, 18) = 15.829, p < 0.002]. Task 2 accuracy at 200 ms SOA condition was significantly higher than Task 2 accuracy in the 100 ms SOA condition (difference = 6%, SE = 1.5%, p < 0.002). As before, accuracy results do not provide any support for a speed–accuracy trade-off.

With regard to the STD of RT2, there was no significant two-way interaction (p = 0.270). The main effect of the IND-stick versus IND-switch comparison was not significant (p = 0.093). The main effect of SOA was not significant (p = 0.276).

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Fan, Z., Singh, K., Muthukumaraswamy, S. et al. The cost of serially chaining two cognitive operations. Psychological Research 76, 566–578 (2012). https://doi.org/10.1007/s00426-011-0375-y

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