## Introduction

## Task-order coordination in DT situations

## Rationale of the current study

## Experiment 1

## Material and methods

### Participants

### Stimuli and task

### Design and procedure

## Results

_{01}provides information which of these two models better fit the data, with values larger than 1 providing evidence for the model not including the interaction effect and values smaller than 1 providing evidence for a model including this interaction (Raftery, 1995; Wagenmakers, 2007). A model not including the TASK × ORDER interaction would support the idea that increasing WM load would have no effect monitoring-related processes, whereas a model specifying this interaction would indicate the modulation of monitoring-related processes by WM load.

### Comparison between same-order and different-order trials

_{p}

^{2}= 0.821, indicating a general decrement in performance under high WM load. In line with previous research on task-order coordination (De Jong, 1995; Kübler et al., 2018), responses for task 1 were faster in same-order trials (m = 1065 ms) than those in different-order trials (m = 1103 ms), F(1, 22) = 15.307, p = 0.001, η

_{p}

^{2}= 0.410.

_{p}

^{2}= 0.442, this performance benefit for same-order compared to different-order trials was modulated by the factor WM LOAD. In low-load blocks, RT 1 was significantly shorter in same-order trials (m = 955 ms) than in different-order trials (m = 1022 ms), t(22) = 5.523, p < 0.001, d = 1.151. Contrarily, in high-load blocks, RT 1 in same-order (m = 1175 ms) and in different-order trials (m = 1183 ms) did not differ significantly, t(22) = 0.728, p = 0.475, d = 0.103 which was also supported by an BF

_{01}= 3.600. Thus, in line with our assumption, increasing WM demands resulted in a reduced performance benefit for same-order versus different-order trials.

_{p}

^{2}= 0.725. Overall, mean error rates decreased from same-order trials (m = 4.8%) to different-order trials (m = 3.2%), F(1, 22) = 11.199, p = 0.003, η

_{p}

^{2}= 0.337. Additionally, this decrease in errors from same-order to different-order trials was modulated by the factor WM LOAD, F(1, 22) = 5.832, p = 0.024, η

_{p}

^{2}= 0.210. While under low load error rates in task 1 did not differ between same-order trials (m = 2.2%) and different-order trials (m = 1.6%), t(22) = 1.297, p = 0.208, d = 0.212 BF

_{01}= 2.179, under high load, we found a performance benefit for different-order trials (m = 4.9%) compared to same-order trials (m = 7.3%), t(22) = 3.583, p = 0.002, d = 0.740. In sum, under low load we could not find any performance difference between same-order and different-order trials on the basis of task 1 errors, while under high load we found a benefit for different-order compared to same-order trials. This pattern of results for error rates might be explained by a possible speed-accuracy tradeoff. More specifically, while in the low-load condition participants can re-apply the task-order set of the previous trial in same-order trials, in the high-load condition demands on task-order coordination are increased in same-order trials since the task-order set of the previous trial does not reside in WM anymore and a new task-order set has to be activated. This might result in a more cautious processing strategy resulting in increased RTs and concurrently reduced error rates.

_{p}

^{2}= 0.863. Additionally, we found a significant effect of the factor TASK ORDER, F(1, 22) = 16.413, p = 0.001, η

_{p}

^{2}= 0.427, reflecting a RT benefit for same-order trials (m = 1239 ms) relative to different-order trials (m = 1277 ms).

_{p}

^{2}= 0.260. Further analyses revealed that in low-load blocks RT 2 was shorter in same-order trials (m = 1100 ms) compared to different-order trials (m = 1163 ms), t(22) = 5.364, p < 0.001, d = 1.127. In high-load blocks, the difference between same-order trials (m = 1377 ms) and different-order trials (m = 1390 ms) did not reach significance, t(22) = 0.984, p = 0.336, d = 0.071, BF

_{01}= 2.964, mirroring the findings in task 1.

_{p}

^{2}= 0.777. The main effect of TASK ORDER did not reach significance, F(1, 22) = 2.005, p = 0.171, η

_{p}

^{2}= 0.084. The interaction of both factors was significant F(1, 22) = 5.324, p = 031, η

_{p}

^{2}= 0.195. The non-significant but numerical benefit on the level of task 2 errors for same-order (m = 2.6%) relative to different-order trials (m = 3.1%) under low WM load, t(22) = 0.885, p = 0.386, d = 0.186, BF

_{01}= 3.260 was reversed in high-load blocks; participants conducted fewer errors in different-order (m = 6.1%) compared to same-order trials (m = 8.1%), t(22) = 2.197, p = 0.039, d = 0.452. Analogously to error rates in task 1, this finding might be explained by a potential speed-accuracy tradeoff (see also task 1 error rates). In sum, increasing WM load reduced performance benefits for same-order trials on the level of RT and error rates for task 1 and task 2. This is in line with the assumption that the task order set cannot be processed efficiently in WM under high load,

### Comparison between fixed-order and random-order blocks

_{p}

^{2}= 0.890. In addition, we found a reliable effect of the factor BLOCK TYPE, F(1, 22) = 62.888, p < 0.001, η

_{p}

^{2}= 0.741, mirrored in increased RT 1 in random-order blocks (m = 1084 ms) compared to fixed-order blocks (m = 845 ms) and indicating the occurrence of monitoring related processes. Importantly, this increase from fixed-order to random-order blocks did not differ between load conditions, as was indicated by the non-significant interaction of the two factors, F(1, 22) = 0.535, p = 0.472, η

_{p}

^{2}= 0.024. This was also supported by a Bayes Factor of BF

_{01}= 3.110 from the respective model comparison, providing evidence for a model only containing the main effects WM LOAD and BLOCK TYPE without further specifying an interaction of these two factors. Thus, we can conclude that increasing WM demands did not affect monitoring related processes.

WM load | ||||
---|---|---|---|---|

Low | High | |||

Fixed-order block | Random-order block | Fixed-order block | Random-order block | |

Experiment 1 | ||||

RT 1 | 738 (204) | 989 (282) | 951 (211) | 1179 (276) |

RT 2 | 851 (230) | 1131 (296) | 1155 (226) | 1384 (264) |

error rate task 1 | 1.9 (2.7) | 1.9 (2.1) | 5.3 (3.4) | 6.1 (2.8) |

error rate task 2 | 3.2 (3.1) | 2.9 (1.7) | 7.4 (4.2) | 7.1 (2.8) |

Experiment 2A | ||||

RT 1 | 885 (325) | 1215 (409) | 1047 (355) | 1319 (438) |

RT 2 | 1031 (323) | 1372 (407) | 1215 (378) | 1498 (465) |

error rate task 1 | 1.0 (1.5) | 2.4 (1.6) | 2.4 (2.2) | 4.0 (2.8) |

error rate task 2 | 3.5 (3.1) | 4.6 (2.9) | 4.5 (3.7) | 5.1 (3.2) |

_{p}

^{2}= 0.763, with more errors being committed in high-load (m = 5.7%) compared to low-load (m = 1.9%) blocks. Neither the effect of the factor BLOCK TYPE, F(1, 22) = 0.457, p = 0.506, η

_{p}

^{2}= 0.020, nor the interactions of the two factors, F(1, 22) = 2.124, p = 0.159, η

_{p}

^{2}= 0.088, was significant. The non-significant interaction is also supported by a Bayes factor of BF

_{01}= 2.561, providing positive evidence for a model that does not specify the interaction of the two factors.

_{p}

^{2}= 0.935. Also, the factor BLOCK TYPE reached significance, F(1, 22) = 62.886, p < 0.001, η

_{p}

^{2}= 0.741, with increased RT 2 in random-order (m = 1258 ms) relative to fixed-order blocks (m = 1003 ms). Similarly to RT 1, this effect of BLOCK TYPE did not differ between both load conditions, as was confirmed by the non-significant interaction of WM LOAD and BLOCK TYPE, F(1, 22) = 2.629, p = 0.119, η

_{p}

^{2}= 0.107. Similarly, the respective model comparison yielded a Bayes factor of BF

_{01}= 2.213, providing no evidence for a modulation of performance differences between both block types due to WM load (i.e., the model does not benefit from the additional inclusion of the interaction of WM LOAD and BLOCK TYPE).

_{p}

^{2}= 0.755. The effect of the factor BLOCK TYPE, F(1, 22) = 0.517, p = 0.480, η

_{p}

^{2}= 0.023, and the interactions of the two factors, F(1, 22) = 0.022, p = 0.884, η

_{p}

^{2}= 0.001, did not reach significance levels. Further support for the non-significant interaction comes from the Bayesian model comparison with a Bayes Factor of BF

_{01}= 3.320. In sum, these results suggest that increasing WM demands in high-load blocks did not affect monitoring related processes. This was indicated by no differences in performance decrements in random-order compared with fixed-order blocks between both load conditions.

_{p}

^{2}= 0.427. Also, RT 2 abruptly decreased from the last random order block (m = 1211 ms) to the first fixed-order block (m = 983 ms), F(1, 22) = 10.131, p = 0.004, η

_{p}

^{2}= 0.315. Please note, that this RT difference between the last random-order and the first fixed-order block is similar compared to contrasting random-order and fixed-order blocks collapsed over the entire experiment. Furthermore, in our view, such rapid changes in performance cannot exclusively be accounted for by practice effects. Rather, they are in line with the assumption that both fixed-order and random-order blocks differ in the requirement to employ task-order coordination processes. In the next step, we compared performance in the first random-order block with performance in the last fixed-order block. Also this comparison revealed that RT 1 was slowed down in random-order (m = 1121 ms) compared with fixed-order blocks (m = 876 ms), F(1, 22) = 11.678, p = 0.002, η

_{p}

^{2}= 0.347. Similarly, for RT2 a similar pattern was observed with slower RT in random-order (m = 1304 ms) compared with fixed-order blocks (m = 1005 ms), F(1, 22) = 14.683, p = 0.001, η

_{p}

^{2}= 0.400. Importantly, RT differences between the last random-order block and the first fixed-order block (task 1: m = 244 ms; task 2: m = 228 ms) did not differ compared with RT differences between the first random-order block and the last fixed-order block (task 1: m = 228 ms; task 2: m = 299 ms), t(22) = 0.006, p = 0.996, d = 0.001 for task 1 and t(22) = 0.556, p = 0.584, d = 0.058 for task 2. Additional Bayesian t-tests supported these results with BF

_{01}= 4.573 for task 1 and BF

_{01}= 3.974 for task 2, providing no evidence for any differences between fixed-order and random-order blocks across the course of the experiment. These findings indicate that the difference between fixed-order and random-order blocks can for the most part be accounted for by increased demands on task-order coordination. Thus, based on the additional analyses, we conclude that a performance difference between fixed-order and random-order blocks cannot entirely be explained by the potential practice effect.

## Discussion

## Experiment 2A

## Materials and methods

### Participants

### Apparatus and stimuli

### Design and procedure

## Results

### Working memory updating task

### Comparison between same-order and different-order trials

_{p}

^{2}= 0.249. Additionally, RT 1 was reduced in same-order (m = 1229 ms) compared to different-order trials (m = 1306 ms, see Fig. 3), F(1, 22) = 21.299, p < 0.001, η

_{p}

^{2}= 0.492, indicating the typical finding of RT benefits for same-order versus different-order trials (De Jong, 1995).

_{p}

^{2}= 0.339, the RT benefit for same-order compared to different-order trials was again modulated by the factor WM LOAD. While in low-load blocks RT 1 was significantly shorter in same-order trials (m = 1157 ms) compared with different-order trials (m = 1272 ms), t(22) = 6.946, p < 0.001, d = 1.452, no such benefit for same- (m = 1302 ms) versus different-order trials (m = 1339 ms) could be found in high-load blocks, t(22) = 1.582, p = 0.128, d = 0.328, BF

_{01}= 1.545. Thus, for RT 1, high compared to low WM demands yielded a reduced performance benefit for same-order trials.

_{p}

^{2}= 0.354, indicating that errors in task 1 occurred more often in high-load (m = 4.0%) compared to low-load blocks (m = 2.5%). Neither the main effect of TASK ORDER, F(1, 22) = 2.063, p = 0.165, η

_{p}

^{2}= 0.086, nor the interaction of the two factors, F(1, 22) = 0.692, p = 0.414, η

_{p}

^{2}= 0.030 reached significance.

_{p}

^{2}= 0.242, with slower responses for the high-load (m = 1498 ms) compared to the low-load condition (m = 1372 ms). Additionally, we found a significant main effect for the factor TASK ORDER, F(1, 22) = 15.195, p = 0.001, η

_{p}

^{2}= 0.409, indicating an RT benefit for same-order trials (m = 1404 ms) in contrast to different-order trials (m = 1466 ms).

_{p}

^{2}= 0.369. The significant performance benefit for same-order trials (m = 1319 ms) compared to different-order trials (m = 1425 ms) in low-load blocks, t(22) = 6.632, p < 0.001, d = 1.385, could not be replicated in high-load blocks. Instead, in the latter block type, RT 2 did not differ significantly between same-order (m = 1490 ms) and different-order trials (m = 1507 ms), t(22) = 0.697, p = 0.493, d = 0.150, BF

_{01}= 3.671.

_{p}

^{2}= 0.041 for the factor WM LOAD, with F(1, 22) = 0.311, p = 0.583, η

_{p}

^{2}= 0.014 for the factor TASK ORDER, and with F(1, 22) = 0.968, p = 0.336, η

_{p}

^{2}= 0.042 for the interaction of these two factors. In sum, analyses of RTs replicated the findings of Experiment 1, consistent with our assumption that the task-order set cannot be processed efficiently in WM when WM demands are high.

### Comparison between fixed-order and random-order blocks

_{p}

^{2}= 0.544. Additionally, responses on task 1 were slower in random-order blocks (m = 1267 ms) relative to fixed-order blocks (m = 966 ms), F(1, 22) = 65.547, p < 0.001, η

_{p}

^{2}= 0.749. Importantly, this increase from fixed-order to random-order blocks did not differ between both load conditions, as was indicated by the non-significant interaction of these two factors, F(1, 22) = 1.911, p = 0.181, η

_{p}

^{2}= 0.080. This was also supported by a Bayes Factor of BF

_{01}= 3.327 from the Bayesian model comparison, providing evidence for a model only containing the main effects WM LOAD and BLOCK TYPE without further specifying an interaction of these two factors.

_{p}

^{2}= 0.484. Also, more errors could be observed in random-order (m = 3.2%) relative to fixed-order blocks (m = 1.7%), F(1, 22) = 37.975, p < 0.001, η

_{p}

^{2}= 0.633. The interaction between the two factors was not significant, F(1, 22) = 0.283, p = 0.600, η

_{p}

^{2}= 0.013. The non-significant interaction is also supported by a Bayes factor of BF

_{01}= 3.056 providing evidence for a model that does not specify the interaction of the two factors.

_{p}

^{2}= 0.507. Additionally, RT 2 was increased in random- (m = 1435 ms) compared fixed-order blocks (m = 1233 ms), F(1, 22) = 60.476, p < 0.001, η

_{p}

^{2}= 0.733. This increase in RT 2 from fixed-order to random-order blocks did not differ between the low-load and high-load condition, as was indicated by the non-significant interaction of the two factors, F(1, 22) = 1.596, p = 0.220, η

_{p}

^{2}= 0.068. Similarly, the respective model comparison yielded a Bayes factor of BF

_{01}= 2.40, providing no evidence for a modulation of performance differences between both block types due to WM load.

_{p}

^{2}= 0.107, BLOCK TYPE, F(1, 22) = 1.919, p = 0.180, η

_{p}

^{2}= 0.080, nor for their interaction, F(1, 22) = 0.143, p = 0.709, η

_{p}

^{2}= 0.006. Further support for the non-significant interaction comes from the Bayesian model comparison with a Bayes Factor of, BF

_{01}= 3.338. In sum, RT and error data suggest that monitoring related processes were, again, not affected by the WM manipulation. This was indicated by a lacking effect of WM load on performance decrements in random-order relative to fixed-order blocks.

_{p}

^{2}= 0.445. Similarly for task 2, RTs were significantly slower in the last random-order block (m = 1484 ms) compared with the first fixed-order block (m = 1145 ms), F(1, 22) = 6.210, p = 0.021, η

_{p}

^{2}= 0.220. Please note, that this RT difference between the last random-order and the first fixed-order block is similar compared to contrasting random-order and fixed-order blocks collapsed over the entire experiment. Thus, these sudden improvements in performance from one block to the other do not confirm the assumption of practice effects as the only reason for performance differences between fixed-order and random-order blocks. In the next step, we compared performance in the first random-order block with performance in the last fixed-order block. Also this comparison revealed that RT 1 was slowed down in random-order (m = 1373 ms) compared with fixed-order blocks (m = 964 ms), F(1, 22) = 21.378, p < 0.001, η

_{p}

^{2}= 0.493. Similarly, for RT2 a similar pattern was observed with slower RTs in random-order (m = 1573 ms) compared with fixed-order blocks (m = 1129 ms), F(1, 22) = 19.081, p < 0.001, η

_{p}

^{2}= 0.464. Importantly, RT differences between the last random-order block and the first fixed-order block (task 1: m = 303 ms; task 2: m = 339 ms) did not differ compared with RT differences between the first random-order block and the last fixed-order block (task 1: m = 408 ms; task 2: m = 434 ms), t(22) = 0.982, p = 0.337, d = 0.201 for task 1 and t(22) = 0.592, p = 0.560, d = 0.123 for task 2. Additional Bayesian t-tests supported these results with BF

_{01}= 2.998 for task 1 and BF

_{01}= 3.901 for task 2, providing no evidence for any differences between fixed-order and random-order blocks across the course of the experiment. These findings indicate that the difference between fixed-order and random-order blocks can for the most part be accounted for by increased demands on task-order coordination.

## Discussion

## Experiment 2B

## Materials and methods

### Participants

### Design and procedure

## Results

### Comparison between same-order and different-order trials

^{1}Similarly, error rates in task 1 increased from same-order trials (m = 4.2%) to different-order trials (m = 6.3%), t(23) = 2.982, p = 0.007, d = 0.623.

^{2}Error rates in task 2 were not affected by a change in task order, t(23) = 0.909, p = 0.373, d = 0.198. Thus, RT data from task 1 and task 2 demonstrated a performance benefit for same-order relative to different-order trials also when introducing an additional Go/NoGo task with low demands on WM.

### Comparison across experiment 2A and 2B

_{01}with a value larger than 1 would provide evidence for a model not including the interaction effect indicating that the performance difference between same-order and different-order trials was similar across Experiment 2A and Experiment 2B. A Bayes factor BF

_{01}with a value smaller than 1, on the other hand, would provide evidence for a model including this interaction suggesting that the performance difference between both trial types differs between both experiments.

_{p}

^{2}= 0.469, indicating faster RT 1 in same-order (m = 1146 ms) compared to different-order trials (m = 1249 ms). Importantly, this performance benefit for same-order trials did not differ between the low-load condition of Experiment 2A and in Experiment 2B; the interaction of TASK ORDER and EXPERIMENT was non-significant, F(1, 45) = 0.572, p = 0.453, η

_{p}

^{2}= 0.013. The non-significant interaction was also supported by a Bayes factor of BF

_{01}= 2.989, providing evidence for a model that does not specify the interaction of the two factors. The factor EXPERIMENT did not reach significance, F(1, 45) = 0.099, p = 0.755, η

_{p}

^{2}= 0.002, BF

_{01}> 100. Also, when analyzing accuracy data for task 1, we could not find any evidence that the difference in error rates between same-order and different-order trials varied across Experiment 2A and Experiment 2B. This was indicated by the non-significant interaction of the factors TASK ORDER and EXPERIMENT, F(1, 45) = 0.977, p = 0.328, η

_{p}

^{2}= 0.021, as well as by a Bayes factor of BF

_{01}= 2.173 from the respective model comparison. Furthermore, the factor ORDER reached significance, F(1, 45) = 13.176, p = 0.001, η

_{p}

^{2}= 0.226, indicating increased error rates in task 1 for different-order (m = 4.4%) relative to same-order trials (m = 2.8%) across both experiment. The effect of the factor EXPERIMENT, F(1, 45) = 9.042, p = 0.004, η

_{p}

^{2}= 0.167, indicating increased error rates in task 1 in Experiment 2B (m = 4.9%) compared to error rates in Experiment 2A (m = 2.4%).

_{p}

^{2}= 0.406. Importantly, this performance benefit did not differ across both experiments, as the interaction of the factors TASK ORDER and EXPERIMENT was not significant, F(1, 45) = 1.138, p = 0.292, η

_{p}

^{2}= 0.025. Similarly, the respective model comparison yielded a Bayes factor of BF

_{01}= 2.369, favoring a model not specifying the interaction of TASK ORDER × EXPERIMENT and providing further evidence for the assumption that performance differences between same-order and different-order trials did not differ across both experiments. Furthermore, the factor EXPERIMENT was not significant, F(1, 45) = 0.025, p = 0.874, η

_{p}

^{2}= 0.001, BF

_{01}> 100. For error rates in task 2, neither the factors ORDER, F(1, 45) = 0.013, p = 0.909, η

_{p}

^{2}< 0.001, EXPERIMENT, F(1, 45) = 1.696, p = 0.199, η

_{p}

^{2}= 0.036 nor their interaction, F(1, 45) = 1.661, p = 0.204, η

_{p}

^{2}= 0.036, BF

_{01}= 2.194 were significant, with the latter indicating that performance differences between same-order and different-order trials were similar in both experiments. Thus, comparing RT and error rate with data from low-load blocks of Experiment 2A further confirms that switching between an additional Go/NoGo task (with low demands on WM) and a random-order DT did not affect the performance benefits for same-order compared with different-order trials in Experiment 2B.