## Introduction

## Response-related interference

### Two hypotheses regarding the nature of the response-related interference

#### Evidence for the motor-bottleneck hypothesis

#### Evidence for the response-monitoring hypothesis

## The present study

Hypotheses and results | Predictions | ||
---|---|---|---|

RT2 | S2-LRP | LRP-R2 | |

The motor-bottleneck hypothesis | Reduced Task-2 difficulty effect when Task-1 requires a motor response (Go trials) relative to when it does not (NoGo trials) | Consistent effect of Task-2 difficulty regardless of Task-1 motor requirement | LRP-R2 in the easy condition of Task 2 is longer when Task-1 requires a response (Go trials) than when it does not (NoGo Trials) |

The response-monitoring hypothesis | Consistent Task-2 difficulty effect regardless of Task-1 motor requirement | Main effect of Task-1 motor requirement (longer S2-LRP by Task-1 motor response) | Consistent LRP-R2 |

## Experiment 1

### Method

#### Participants

_{age}= 23.57, age range = 18–46), seven participants were African American, eleven were White (non-Hispanic), two were Asian, and one reported multiple ethnicities. Three reported being left-handed and all reported normal or corrected-to-normal vision.

#### Stimuli and apparatus

^{1}

#### Design and procedure

## Results

Task | Task-1 Motor response | Task-2 Difficulty | SOA | ||||
---|---|---|---|---|---|---|---|

Short (100 ms) | Long (900 ms in Experiment 1; 1200 ms in Experiment 2) | ||||||

RT (ms) | ACC (%) | RT (ms) | ACC (%) | ||||

Experiment 1 | Task 1 | Go | Easy | 1118 | 85 | 1199 | 91 |

Difficult | 1171 | 91 | 1226 | 93 | |||

NoGo | Easy | – | 91 | – | 93 | ||

Difficult | – | 90 | – | 92 | |||

Task 2 | Go | Easy | 1342 | 92 | 790 | 98 | |

Difficult | 1527 | 89 | 1021 | 91 | |||

NoGo | Easy | 1164 | 92 | 692 | 99 | ||

Difficult | 1486 | 88 | 996 | 92 | |||

Experiment 2 | Task 1 | Go | Easy | 1007 | 90 | 1003 | 96 |

Difficult | 1044 | 96 | 980 | 96 | |||

NoGo | Easy | – | 94 | – | 97 | ||

Difficult | – | 95 | – | 97 | |||

Task 2 | Go | Easy | 1301 | 93 | 583 | 98 | |

Difficult | 1468 | 92 | 816 | 92 | |||

NoGo | Easy | 1173 | 92 | 561 | 100 | ||

Difficult | 1459 | 91 | 852 | 93 |

### RT analysis

_{p}

^{2}= 0.190: RT1 was 68 ms longer at the long SOA than at the short SOA. There was also a main effect of Task-2 difficulty on RT1, F(1, 25) = 6.763, p = 0.015, η

_{p}

^{2}= 0.213: RT1 was 40 ms longer in the difficult condition of Task 2 than in the easy condition. However, SOA and Task-2 difficulty did not show a significant interaction effect on RT1, F(1, 25) = 2.097, p = 0.160, η

_{p}

^{2}= 0.077.

_{p}

^{2}= 0.955. According to the response-selection bottleneck hypothesis (Pashler, 1984, 1994; Welford, 1952), such an increase of RT2 at the short SOA is due entirely to the postponement of the response selection of Task 2 during Task-1 response selection (i.e., the cognitive slack), without any motor-related interference. Contrary to this assumption, the need for a Task-1 motor response lengthened RT2 by 86 ms: RT2 was slower in the Go trials (1170 ms) than in the NoGo trials (1085 ms), F(1, 25) = 19.224, p < 0.001, η

_{p}

^{2}= 0.435, supporting the hypothesis of response-related interference. As predicted by both hypotheses being tested, such an effect of Task-1 motor requirement on RT2 was more prominent at the short SOA (110 ms) than at the long SOA (62 ms), F(1, 25) = 5.320, p = 0.030, η

_{p}

^{2}= 0.175. Looking at this differently, the overall delay of RT2 at the short SOA relative to the long SOA (the PRP effect) was 481 ms in the NoGo trials while it was 529 ms in the Go trials. That is, when Task 1 requires a motor response, the PRP effect is even greater, suggesting that response-related interference contributes to the PRP effect that typically involves Task-1 motor response.

_{p}

^{2}= 0.858. As discussed earlier (see also Table 1), the critical test between the motor-bottleneck and the response-monitoring hypotheses concerns whether such a Task-2 difficulty effect is reduced at the short SOA when Task 1 requires a motor response and whether there is a three-way interaction across the three experimental factors (the two-way interaction between Task-1 motor requirement and Task-2 difficulty appears at the short SOA but not at the long SOA). Looking at the short SOA only, the comparison between Go trials and NoGo trials with respect to the Task-2 difficulty effect showed that the difficulty effect was significantly smaller in the Go trials (185 ms) than in the NoGo trials (332 ms), F(1, 25) = 39.721, p < 0.001, η

_{p}

^{2}= 0.614. Such a reduction in the Task-2 difficulty effect by the Task-1 motor response indicates that the response-related bottleneck occurs after the response-selection stage of Task 2, consistent with the motor-bottleneck hypothesis; in contrast, the response-monitoring hypothesis does not allow such a reduction because of the assumption that Task-1 motor requirement affects the stages before the response selection of Task 2. Looking at the long SOA, there was another significant interaction between Task-1 motor requirement and Task-2 difficulty, F(1, 25) = 12.227, p = 0.002, η

_{p}

^{2}= 0.328: similar to the interaction pattern at the short SOA, the difficulty effect was significantly smaller in the Go trials (231 ms) than in the NoGo trials (304 ms). Although the significant three-way interaction across Task-1 motor requirement, Task-2 difficulty, and SOA indicated that this latter interaction at the long SOA (reduced Task-2 difficulty due to Task-1 motor response) was not as strong as the one at the short SOA, F(1, 25) = 4.846, p = 0.037, η

_{p}

^{2}= 0.162, such a modulation of Task-2 difficulty by Task-1 motor requirement even at the long SOA was somewhat unexpected. Both hypotheses predicted a significant difficulty effect at the long SOA regardless of the Task-1 motor requirement. We discussed the possible cause the Task-2 difficulty modulation by Task-1 motor requirement even at the long SOA in the discussion section of this experiment.

### Accuracy (ACC) analysis

_{p}

^{2}= 0.637. ACC1 was greater when Task 2 was difficult (92%) than when it was easy (90%), F(1, 25) = 11.840, p = 0.002, η

_{p}

^{2}= 0.321. The effect of Task-2 difficulty on ACC1 was greater at the short SOA (− 3%) than at the long SOA (− 1%), F(1, 25) = 4.509, p = 0.044, η

_{p}

^{2}= 0.153. The difficulty effect was also greater in the Go trials (− 4%) than in the NoGo trials (1%), F(1, 25) = 18.821, p < 0.001, η

_{p}

^{2}= 0.429. There was also a significant three-way interaction across the three experimental factors, indicating that the Task-2 difficulty effect on ACC1 was greater at the short SOA than at the long SOA but only in the Go trials (− 4%), while it was the same across SOAs in the NoGo trials (1%), F(1, 25) = 6.532, p = 0.017, η

_{p}

^{2}= 0.207.

_{p}

^{2}= 0.684. Task-2 difficulty manipulation showed the expected effect on ACC2: 95% vs. 90% in the compatible and non-compatible conditions, F(1, 25) = 28.842, p < 0.001, η

_{p}

^{2}= 0.536. There was a significant interaction between Task-2 difficulty and SOA, F(1, 25) = 8.495, p = 0.007, η

_{p}

^{2}= 0.254, suggesting that the difficulty effect was smaller at the short SOA (4%) than at the long SOA (7%). However, Task-1 motor requirement did not show any significant main or interaction effects on ACC2 (ps > 0.05).

### LRP analysis

Task-1 Motor response | Task-2 Difficulty | SOA | ||||
---|---|---|---|---|---|---|

Short (100 ms) | Long (900 ms in Experiment 1; 1200 ms in Experiment 2) | |||||

S2-LRP | LRP-R2 | S2-LRP | LRP-R2 | |||

Experiment 1 | Go | Easy | 705 | − 96 | 266 | − 104 |

Difficult | 860 | − 114 | 810 | − 82 | ||

NoGo | Easy | 564 | − 110 | 255 | − 90 | |

Difficult | 1072 | − 117 | 364 | − 122 | ||

Experiment 2 | Go | Easy | 910 | − 111 | 230 | − 119 |

Difficult | 1365 | − 106 | 302 | − 95 | ||

NoGo | Easy | 632 | − 165 | 228 | − 134 | |

Difficult | 1168 | − 122 | 706 | − 109 |

### Discussion

_{p}

^{2}= 0.184. However, again, neither hypothesis assumed that Task 2 would be modulated by Task-1 motor requirement at the long SOA.

## Experiment 2

### Method

#### Participants

_{age}= 21, age range = 18–33), two participants were African American, 11 were White (non-Hispanic), and one was Asian. Two reported being left-handed and all reported normal or corrected-to-normal vision.

#### Stimuli and procedure

## Results

### RT analysis

_{p}

^{2}= 0.476. Specifically, the effect of Task-2 difficulty on RT1 was reversed at the long SOA (− 23 ms) compared to the short SOA (37 ms).

_{p}

^{2}= 0.987 (see Table 2 and lower panels in Fig. 5). As we had expected, the current PRP effect was greater than the one in Experiment 1 (505 ms), F(1, 38) = 17.983, p < 0.001, η

_{p}

^{2}= 0.321, suggesting that the new long-SOA condition further separated the two tasks than the corresponding condition did in Experiment 1, minimizing the interferences between tasks at the long SOA.

_{p}

^{2}= 0.242. As expected, in Experiment 2, the effect of Task-1 motor requirement on RT2 was smaller than the corresponding effect in Experiment 1 (86 ms)—it was less than half of the effect in Experiment 1, which was a marginally significant reduction, F(1, 38) = 3.593, p = 0.066, η

_{p}

^{2}= 0.086. However, there was still a significant effect of Task-1 motor requirement on RT2 at the short SOA (69 ms), F(1, 13) = 13.975, p = 0.002, η

_{p}

^{2}= 0.518, which disappeared at the long SOA (-7 ms), F(1, 13) = 0.158, p = 697, η

_{p}

^{2}= 0.012. Therefore, the new long-SOA condition seemed to reduce the response-related interference at the long SOA. Notably, as in Experiment 1, the overall delay of RT2 at the short SOA relative to the long SOA—the PRP effect—was more prominent in the Go trials (685 ms) than in the NoGo trials (610 ms), indicating that when Task 1 requires a motor response, the PRP effect is even greater, supporting the contribution of the response-related interference in the typical PRP effect involving Task-1 motor response.

_{p}

^{2}= 0.816, which was similar to the corresponding effect in Experiment 1 (268 ms), F(1, 38) = 0.019, p = 0.890, η

_{p}

^{2}= 0.001. Again, the primary focus of the current study is whether this Task-2 difficulty effect is reduced at the short SOA due to Task-1 motor response and whether there is a three-way interaction across the three experimental factors (the two-way interaction between Task-1 motor requirement and Task-2 difficulty appears at the short SOA but not at the long SOA). Looking at the short SOA only, as in Experiment 1, there was a significant reduction of Task-2 difficulty effect due to Task-1 motor response, F(1, 13) = 9.199, p = 0.010, η

_{p}

^{2}= 0.414: Task-2 difficulty effect was 167 ms in the Go trials while it was 286 ms in the NoGo trials (119 ms reduction), indicating absorption of the Task-2 difficulty effect by the response-related bottleneck, consistent with the motor-bottleneck hypothesis. Somewhat unexpectedly, looking at the long SOA only, there was still a significant reduction of the difficulty effect in the Go trials (233 ms) than in the NoGo trials (291 ms)—58 ms reduction, suggesting a residual response-related interference even in the new long-SOA condition in Experiment 2. Finally, there was a marginally significant three-way interaction across Task-1 motor requirement, Task-2 difficulty, and SOA, F(1, 13) = 2.782, p = 0.119, η

_{p}

^{2}= 0.176 (see lower panels in Fig. 5). Notably, consistent with the motor-bottleneck hypothesis, in the NoGo trials, the difficulty effect was consistent across SOAs (286 ms at the short SOA vs. 291 ms at the long SOA), F(1, 13) = 0.057, p = 0.816, η

_{p}

^{2}= 0.004; however, in the Go trials, the difficulty effect was significantly reduced at the short SOA than at the long SOA (167 ms at the short SOA vs. 233 ms at the long SOA), F(1, 13) = 9.686, p = 0.008, η

_{p}

^{2}= 0.427. Such a prominent reduction in the Task-2 difficulty effect due to the Task-1 motor response at the short SOA relative to the long SOA is the most distinguishable prediction of the motor-bottleneck hypothesis.

### ACC analysis

_{p}

^{2}= 0.688. Participants performed significantly better when Task 2 was difficult (96%) than when it was easy (94%), F(1, 13) = 7.126, p = 0.019, η

_{p}

^{2}= 0.354. Such an effect of Task-2 difficulty on ACC1 was even greater at the short SOA (− 4%) than at the long SOA (0%), F(1, 13) = 4.735, p = 0.049, η

_{p}

^{2}= 0.267. There was a significant three-way interaction across Task-2 difficulty, SOA, and Task-1 motor requirement, suggesting that the greater effect of Task-2 difficulty on ACC1 at the short SOA than at the long SOA was even greater in the Go trials (− 3%) than in the NoGo trials (− 1%), F(1, 13) = 5.981, p = 0.029, η

_{p}

^{2}= 0.315.

_{p}

^{2}= 0.713. Task-2 difficulty manipulation showed the expected effect on ACC2: 96% vs. 92% in the easy and difficult conditions, F(1, 13) = 6.765, p < 0.022, η

_{p}

^{2}= 0.342. There was a significant interaction between Task-2 difficulty and SOA, F(1, 13) = 26.664, p < 0.001, η

_{p}

^{2}= 0.672, suggesting that the difficulty effect was smaller at the short SOA (1%) than at the long SOA (7%). However, Task-1 motor requirement did not show any significant main or interaction effects on ACC2 (ps > 0.05).