The role of working memory on associative learning under uncertainty
Previous research has found that in a stable associative learning environment, humans selectively attend to reliable cues whilst suppressing attention towards unreliable cues, demonstrating attentional exploitation. However, in an uncertain and unpredictable learning environment, heightened attention towards both reliable and unreliable cues has been observed, demonstrating attentional exploration (e.g., Beesley et al. 2015). It has been suggested that the latter attentional behaviour reflects information-seeking whereby people attempt to reduce the uncertainty experienced. However, studies have found that this heightened attention does not appear to facilitate learning, demonstrating an incomplete explanation for this behaviour. Previous research found that uncertainty monitoring can place considerable demands on working memory resources (e.g., Coutinho et al. 2015). Therefore, it may be important to consider the role of working memory. The load theory (e.g., Lavie et al. 2004) suggests that high working memory load can lead to poor attentional control (i.e., greater distractor interference; slower target detection). However, it is currently unclear whether working memory plays a role in how we direct attention and form associative knowledge.
To explore this, in a dual-task eye-tracking experiment, load was manipulated within-subjects with a secondary task. Participants were asked to perform either a short-term memory (digit-recall) or a working-memory task (serial-subtraction) during the associative learning task. To manipulate uncertainty, participants were presented with either deterministic (certain) or probabilistic (uncertain) associative relationships. If attentional exploration observed under uncertainty was the result of high working memory load, participants in the certain condition should show increase overall attention to cues (particularly towards the non-predictive cues) and an attenuation of the predictivness effect when placed under high load. However, if attentional exploration is uniquely driven by uncertainty, the predictivness effect should instead be observed in both load conditions. Preliminary behavioural and eye-gaze data suggest that attention and associative learning are not disrupted by working memory load under certain or uncertain learning environments, demonstrating that attentional exploration observed under uncertainty was not driven by high working memory load.
Experiment 1
# A tibble: 1 × 4
# Groups: participant [1]
participant degree_WM_acc n percent
<fct> <fct> <int> <dbl>
1 209 perfect_engagement 1 1.28# A tibble: 1 × 4
# Groups: participant [1]
participant degree_WM_acc n percent
<fct> <fct> <int> <dbl>
1 209 perfect_engagement 0 0# A tibble: 4 × 2
participant p2_excluded_n
<fct> <int>
1 115 1
2 208 1
3 220 1
4 222 1# A tibble: 4 × 2
participant p2_excluded_n
<fct> <int>
1 115 1
2 208 1
3 220 1
4 222 1 load participant variable n mean
L:38 101 : 2 prob_outcome:76 Min. : 6.0 Min. :0.22
H:38 102 : 2 1st Qu.: 9.0 1st Qu.:0.60
103 : 2 Median :10.0 Median :0.90
104 : 2 Mean : 9.5 Mean :0.78
105 : 2 3rd Qu.:10.0 3rd Qu.:1.00
106 : 2 Max. :10.0 Max. :1.00
(Other):64
sd se ci
Min. :0.00 Min. :0.000 Min. :0.00
1st Qu.:0.00 1st Qu.:0.000 1st Qu.:0.00
Median :0.32 Median :0.100 Median :0.23
Mean :0.27 Mean :0.088 Mean :0.20
3rd Qu.:0.50 3rd Qu.:0.163 3rd Qu.:0.37
Max. :0.53 Max. :0.176 Max. :0.41
# A tibble: 4 × 2
participant p1_excluded_n
<fct> <int>
1 119 1
2 206 1
3 213 1
4 214 1# A tibble: 5 × 2
degree_WM_acc percent
<fct> <dbl>
1 egaged_near_miss 2.06
2 Fail 7.74
3 H_in_L 3.26
4 L_in_H 0.917
5 perfect_engagement 86.0 Methods
Participants
[1] 22[1] 4.8[1] 1.9
# A tibble: 2 × 2
condition n
<int> <int>
1 1 18
2 2 16Forty-three participants were recruited from Lancaster University to take part in a 45-minute experiment. Participants were compensated £7.50 for their time. The final sample consisted 34 participants, 18 in the certain condition and 16 in the uncertain condition (see Post-Data-Collection Exclusion of Participants) (mean age = 21 years, SD = 5, 22 participants identified as females, 12 as males. Twenty-seven reported English as their first language.
Participants also reported the highest level of mathematics education they have achieved. Eleven completed post-16 mathematics, 11 completed secondary school mathematics, four completed a Bachelor’s degree in mathematics or a related field, four has a Master’s degree in mathematics or a related field, four received some university/ college mathematics without formal degree.
Materials
All experimental tasks used were created in PsychoPy builder version 2022.2.4 (Peirce et al. 2019) presented on a XX’’ monitor with 1920 x 1080 pixels resolution. Eye movements were recorded using Tobii’s Pro Spectrum eye tracker, sampling at 300 Hz. A standard Tobii issue forehead rest was used to stabilize participant’s head position during the eye-tracking portion of the experiment. Participants eyes were positioned approximately 55 cm away from the monitor. Eye gaze data were analysed with the EyeTools package in R (Beesley & Ivory, 2024).
Secondary Task
To ensure consistent positive value final answers, the number prompts ranged from 24 to 99. Each number is duplicated once in the number bank to compile enough numbers to fulfill 140 trials. All auditory stimuli were played via the PC’s built in speakers with volume was set at 40%. The auditory number prompts were generated using Google Cloud’s sound-to-speech software in English with a female voice. The default “A” note in PsychoPy, played for 500ms per beat was used as the metronome tone. The experimenter used the keyboard to input participants verbal responses.
Associative Learning Task
The context of the learning task was based on Beesley et al. (2015)‘s task. Illustrations of fictitious molecules and mutants were used to represent the cues and outcomes, respectively. The configurations of the fictitious molecules and the spheres representing atoms varied; however, each were made up of three blue and three red ’atoms’. - stimuli size (cue, outcome) Participants used the mouse to select their response.
Design
Table 1. outlines the design. In a 2 x 2 x 2 mixed factorial design, load (low vs high) and predictiveness (predictive vs non-predictive cue) were manipulated within-subjects and uncertainty was manipulated between-subjects.
Load was introduced with a secondary task and manipulated between-associations, where cues A and B were exclusively presented under low and high load, respectively. On low load trials, participants engaged in a secondary verbal digit-recall task (i.e., short-term memory load). On high load trials, they engaged in a verbal serial-subtraction task (i.e., working memory load). The pacing of the secondary task was calibrated to the individual participant. Metronome tones were played on both trials to ensure consistent perceptual input across load conditions. Participants were asked to recall the number prompt at every beep in the low load, or subtract from the number prompt continuously at every beep in the high load.
On each trial, participants were shown two different cues, however, unbeknownst to the participant, only one of them is predictive of the outcome. For example, given the cues A and X, A is the predictive, whilst X is the non-predictive cue. The associations were deterministic in the certain condition and probabilistic in the uncertain condition. Specifically, each predictive cue was paired with one outcome predominately on 80% of trials and the other outcome on 20% of trials.
As a result of load being manipulated between associations, cue A was always presented under high load and cue B under low load, causing the load instructions to coincidentally become another predictor of the outcome. Therefore, an additional phase was implemented where participants were presented with the same associations, however only under low load for 20 trials. Effectively, removing the load-outcome associations. Performance in this phase was used to identify and subsequently remove participants who had inadvertently relied on the load to predict the outcomes.
| Phase 1 | Phase 2 | |||
|---|---|---|---|---|
| Condition | Load | Association | Load | Association |
| Certain | Low | AX – O1 | AX – O1 | |
| AY – O1 | AY – O1 | |||
| High | BX – O2 | BX – O2 | ||
| BY – O2 | Low | BY – O2 | ||
| Uncertain | Low | AX – O1 (80%), O2 (20%) | AX – O1 (80%), O2 (20%) | |
| AY – O1 (80%), O2 (20%) | AY – O1 (80%), O2 (20%) | |||
| High | BX – O2 (80%), O1 (20%) | BX – O2 (80%), O1 (20%) | ||
| BY – O2 (80%), O1 (20%) | BY – O2 (80%), O1 (20%) |
Table 1. experiment 1 design
Procedure
Participants were tested individually in a quiet laboratory. Participants first completed a calibration exercise to determine the optimal metronome pacing for each participant in the serial subtraction task. They were asked to subtract three from a given number continuously and a metronome tone was played to pace their response. Participants were asked to produce an answer aloud at every beep. Starting with the longest pacing, four different metronome speeds options were included, 24 bpm (2.5s/ operation), 30 bpm (2s/ operation), 40 bpm (1.5s/ operation), 60 bpm (1s/ operation). Participants experienced a total of 13 practice trials. Each practice trial comprised three metronome beeps. The experimenter recorded the last answer participants produced. Participants were tested a minimum of three trials per metronome speed. If participants answered correctly on at least two out of three of the trials in a level, they advanced to the next metronome pace. If they achieve at least two out of three incorrect trials, they move back to a slower metronome pace (or remained at the same pacing if that was the slowest pacing option). If they fail to move past a certain pacing, they were tested at the same speed until all 13 practice trials were completed. The optimal pacing was determined by the first pacing speed to achieve four correct trials whilst being able to produce an answer in time with each beep, i.e., if participants produced the correct answer but responded after a delay following any one of the three tones in a trial, it would still be considered an unsuccessful trial. The experimenter then implemented the pacing one level slower than their optimum pacing determined in the calibration exercise in the dual-task portion to accommodate for the dual-task nature of the experiment. For example, if a participant’s optimal pacing was 60 bpm, they completed the secondary task in the dual-task portion at 40 bpm.
Participants then answered the demographic questions relating to their age, gender, whether English is their first language, and their highest level of mathematical educational attainment. In the dual-task portion of the experiment, participants were fitted to the forehead rest and completed a nine-point eye tracker calibration and validation until a satisfactory calibration was achieved. The experimenter was sat perpendicular to the participant to input their verbal response on the serial subtraction task using the keyboard. In the instructions, participants were asked to play the role of a professor who had discovered a net set of molecules which could be used to create different mutants, tasked with figuring out which molecule creates which mutant. However, they have an equally important deadline due shortly and must multitask by completing a series of mathematical operations while conducting their assignment. They either had to repeatedly recall the digit presented, or perform a serial subtraction task depending on the instructions shown. Participants were instructed that both task of of equal importance and to try their best to maintain accuracy on both task simultaneously.
Each trial began with the load instructions (which asked participants to either ‘remember’ or ‘count back in THREEs’) presented for 2000 ms. Then the auditory number prompt was played with a speaker icon displayed in the screens center. The associative learning task began at 1.5 metronome tones… They selected an outcome via mouse click. After a valid click was registered, a yellow frame was displayed around the selected outcome for 500 ms to show the chosen outcome. After which, feedback was provided. If the correct outcome was selected, ‘CORRECT!’ in green font appeared. If the wrong outcome was selected, ‘INCORRECT!’ in red font appeared. The correct outcome was highlighted with a green frame around it. Feedback stimuli were presented for 1000 ms. The metronome tones continued until feedback concluded or until the associative learning portion of the trial timed out. The text ‘Final answer’ then appeared for the experimenter to input participants verbal response produced in response to the last metronome tone played. If participants failed to produce the answer corresponding to the last metronome tone within 5000 ms, the text ‘TIMEOUT - TOO SLOW’ appeared in red font. Feedback on the secondary task was never provided.
If participants failed to respond with a valid mouse click within the 10000 ms time limit in the associative learning portion, ‘TIMEOUT - TOO SLOW’ was displayed in red font. No feedback was given on those trials. Participants did not proceed to the final memory probe portion of the secondary task on those trials. There was a 1000 ms intertrial interval. The cursor position was recentered at the beginning of every trial during the associative learning portion.
There are 120 trials in phase 1 and 20 trials in phase 2. The trials were divided into four trials per block (35 blocks in total). Each association pair is presented once every block in random order with the constraint that the same association pair cannot appear in consecutive order (i.e., the last trial in a block and the first trial of the subsequent block). The same load trial did not appear in more than four consecutive trials. In the uncertain condition, each unique rare trials (i.e., the less probable outcome) occurred once every 20 trials (per epoch).
Post-Data-Collection Exclusion of Participants
One failed to perform the serial-subtraction task accurately on above 50% of trials in each load condition, resulting in insufficient trials in each condition for meaningful analysis. Additionally, participants who likely formed associations between load type and outcome rather than using the cue-outcome associations to perform were removed. Specifically, participants with probable outcome response accuracy that dropped to 50% or below in phase 2 (epoch 7) were excluded, resulting in four other participants being excluded. Moreover, the emergence of the predictiveness effect relies on participants having successfully acquired the cue-outcome outcome associations. Therefore, employing an exclusion criterion widely adopted by similar paradigms (e.g., Don and Livesey 2015; Easdale, Le Pelley, and Beesley 2019; Le Pelley and McLaren 2003), four were further excluded from the final data set.
Data preparation
Trials were divided into epoch for analysis purposes. Each epoch contained five consecutive blocks. There were six epoch in phase 1 and one epoch in phase 2.
Only data from phase 1 were included in the final analysis. Data from phase 2 were not analysed beyond for participant exclusion purposes (see Post-Data-Collection Exclusion of Participants).
Results
Secondary Task
Participants showed higher accuracy in low load (M in certain condition = 0.89; M in uncertain condition = 0.88) than high load trials (M in certain condition = 0.82 ; M in uncertain condition = 0.8) in both conditions.
Participants also responded faster on the secondary task in low load (M in certain condition = 1.29 s; M in uncertain condition = 1.52 s) than high load trials (M in certain condition = 1.6 s; M in uncertain condition = 2.01 s) in both conditions.
Associative Learning Task
Behavioural data
Bayes factor analysis
--------------
[1] condition + epoch + load + condition:load + participant : 1.7e+21 ±1.9%
[2] condition + epoch + condition:epoch + load + condition:load + participant : 7.5e+20 ±1.9%
[3] condition + epoch + load + participant : 4.8e+20 ±1.5%
[4] condition + epoch + condition:epoch + load + participant : 1.9e+20 ±1.2%
[5] epoch + load + participant : 1.9e+20 ±0.63%
[6] condition + epoch + load + condition:load + epoch:load + participant : 2.3e+19 ±4.1%
[7] condition + epoch + condition:epoch + load + condition:load + epoch:load + participant : 9.9e+18 ±4.9%
[8] condition + epoch + load + epoch:load + participant : 5.9e+18 ±1.4%
[9] condition + epoch + condition:epoch + load + epoch:load + participant : 2.6e+18 ±5%
[10] epoch + load + epoch:load + participant : 2.5e+18 ±4%
[11] condition + epoch + condition:epoch + load + condition:load + epoch:load + condition:epoch:load + participant : 3.2e+17 ±3.4%
[12] condition + epoch + participant : 5.4e+16 ±1.3%
[13] epoch + participant : 2.2e+16 ±0.2%
[14] condition + epoch + condition:epoch + participant : 1.7e+16 ±1.1%
[15] condition + load + condition:load + participant : 2738 ±1.4%
[16] condition + load + participant : 1494 ±0.98%
[17] load + participant : 617 ±1.1%
[18] condition + participant : 2.4 ±0.44%
Against denominator:
meanRT ~ participant
---
Bayes factor type: BFlinearModel, JZSA Bayesian anova was conducted with RT as an dependent variable. The strongest model contained the factors condition, epoch, load, along with the condition x AOI interaction term with participant as the random effect, BF10 = 1.7 × 1021 ± 1.92%.
Bayes factor analysis
--------------
[1] condition + epoch + participant : 1.4e+19 ±0.65%
[2] epoch + participant : 6.4e+18 ±0.32%
[3] condition + epoch + load + condition:load + participant : 5.7e+18 ±2.9%
[4] condition + epoch + load + participant : 2e+18 ±7.4%
[5] epoch + load + participant : 8.6e+17 ±2.2%
[6] condition + epoch + condition:epoch + participant : 7.7e+17 ±3.2%
[7] condition + epoch + condition:epoch + load + condition:load + participant : 3e+17 ±1.7%
[8] condition + epoch + condition:epoch + load + participant : 9.7e+16 ±1.8%
[9] condition + epoch + load + condition:load + epoch:load + participant : 8.8e+16 ±1.8%
[10] condition + epoch + load + epoch:load + participant : 3.1e+16 ±4.6%
[11] epoch + load + epoch:load + participant : 1.3e+16 ±0.98%
[12] condition + epoch + condition:epoch + load + condition:load + epoch:load + participant : 4.5e+15 ±1.4%
[13] condition + epoch + condition:epoch + load + epoch:load + participant : 1.4e+15 ±1.4%
[14] condition + epoch + condition:epoch + load + condition:load + epoch:load + condition:epoch:load + participant : 9.6e+14 ±2.6%
[15] condition + participant : 2.1 ±1.4%
[16] condition + load + condition:load + participant : 0.36 ±2%
[17] condition + load + participant : 0.27 ±1.9%
[18] load + participant : 0.13 ±0.69%
Against denominator:
prop_acc ~ participant
---
Bayes factor type: BFlinearModel, JZSIn terms of accuracy, the model containing the factors condition and AOI, along with the condition x AOI interaction with participant as the random effect received the strongest support, BF10 = 1.4 × 1019 ± 0.65%. More importantly, including load as an additional factor did not improve model fit BF = 7.09 ± 7.45%.
Eye data
Bayes factor analysis
--------------
[1] condition + epoch + condition:epoch + AOI + condition:AOI + pID : 1304 ±2.7%
[2] condition + epoch + condition:epoch + AOI + condition:AOI + epoch:AOI + pID : 538 ±1.8%
[3] condition + epoch + AOI + condition:AOI + pID : 379 ±17%
[4] condition + AOI + condition:AOI + pID : 184 ±2.9%
[5] condition + epoch + condition:epoch + AOI + condition:AOI + epoch:AOI + condition:epoch:AOI + pID : 150 ±9.1%
[6] condition + epoch + condition:epoch + load + AOI + condition:AOI + pID : 149 ±1.8%
[7] condition + epoch + AOI + condition:AOI + epoch:AOI + pID : 118 ±1.2%
[8] condition + epoch + condition:epoch + AOI + pID : 78 ±1.3%
[9] condition + epoch + condition:epoch + load + AOI + condition:AOI + epoch:AOI + pID : 64 ±2.8%
[10] condition + epoch + load + AOI + condition:AOI + pID : 41 ±5.3%
[11] condition + epoch + condition:epoch + AOI + epoch:AOI + pID : 30 ±3.5%
[12] condition + epoch + condition:epoch + load + AOI + condition:AOI + load:AOI + pID : 23 ±1.8%
[13] condition + load + AOI + condition:AOI + pID : 22 ±6.1%
[14] condition + epoch + AOI + pID : 22 ±1.4%
[15] condition + epoch + condition:epoch + load + condition:load + AOI + condition:AOI + pID : 19 ±5.1%
[16] condition + epoch + condition:epoch + load + AOI + condition:AOI + epoch:AOI + condition:epoch:AOI + pID : 16 ±2.5%
[17] condition + epoch + load + AOI + condition:AOI + epoch:AOI + pID : 15 ±4.5%
[18] condition + AOI + pID : 13 ±0.79%
[19] condition + epoch + condition:epoch + pID : 11 ±0.76%
[20] condition + epoch + condition:epoch + load + AOI + condition:AOI + epoch:AOI + load:AOI + pID : 10 ±2.4%
[21] epoch + AOI + pID : 9.5 ±0.95%
[22] condition + epoch + condition:epoch + load + AOI + pID : 9 ±1.4%
[23] condition + epoch + condition:epoch + load + condition:load + AOI + condition:AOI + epoch:AOI + pID : 7.6 ±3.4%
[24] condition + epoch + AOI + epoch:AOI + pID : 7.6 ±3.7%
[25] condition + epoch + condition:epoch + load + condition:load + AOI + condition:AOI + load:AOI + condition:load:AOI + pID : 7.4 ±44%
[26] condition + epoch + load + AOI + condition:AOI + load:AOI + pID : 6.4 ±8.4%
[27] AOI + pID : 5.9 ±0.58%
[28] condition + epoch + load + condition:load + AOI + condition:AOI + pID : 5.1 ±6.2%
[29] condition + epoch + condition:epoch + load + AOI + epoch:AOI + pID : 3.5 ±2.4%
[30] condition + load + AOI + condition:AOI + load:AOI + pID : 3.4 ±3.2%
[31] condition + epoch + pID : 3.4 ±0.7%
[32] epoch + AOI + epoch:AOI + pID : 3.3 ±1.9%
[33] condition + load + condition:load + AOI + condition:AOI + pID : 2.8 ±3.5%
[34] condition + epoch + condition:epoch + load + condition:load + AOI + condition:AOI + load:AOI + pID : 2.8 ±2.1%
[35] condition + epoch + load + AOI + pID : 2.6 ±3%
[36] condition + epoch + load + condition:load + AOI + condition:AOI + epoch:AOI + pID : 2.6 ±31%
[37] condition + epoch + condition:epoch + load + AOI + condition:AOI + epoch:AOI + condition:epoch:AOI + load:AOI + pID : 2.5 ±2.3%
[38] condition + pID : 2.4 ±5.7%
[39] condition + epoch + load + AOI + condition:AOI + epoch:AOI + load:AOI + pID : 2.3 ±2.4%
[40] condition + epoch + condition:epoch + load + condition:load + AOI + condition:AOI + epoch:AOI + condition:epoch:AOI + pID : 2.1 ±2.8%
[41] condition + load + AOI + pID : 1.5 ±1.1%
[42] epoch + pID : 1.5 ±2.1%
[43] condition + epoch + condition:epoch + load + AOI + load:AOI + pID : 1.4 ±2%
[44] condition + epoch + condition:epoch + load + pID : 1.3 ±1.2%
[45] condition + epoch + condition:epoch + load + condition:load + AOI + condition:AOI + epoch:AOI + load:AOI + condition:load:AOI + pID : 1.2 ±21%
[46] condition + epoch + condition:epoch + load + condition:load + AOI + pID : 1.2 ±3.2%
[47] condition + epoch + condition:epoch + load + condition:load + AOI + condition:AOI + epoch:AOI + load:AOI + pID : 1.2 ±2%
[48] epoch + load + AOI + pID : 1.1 ±1.4%
[49] condition + epoch + load + AOI + epoch:AOI + pID : 0.93 ±4.2%
[50] condition + epoch + load + condition:load + AOI + condition:AOI + load:AOI + condition:load:AOI + pID : 0.85 ±7%
[51] condition + epoch + load + condition:load + AOI + condition:AOI + load:AOI + pID : 0.75 ±7.1%
[52] load + AOI + pID : 0.69 ±0.82%
[53] condition + epoch + condition:epoch + load + AOI + epoch:AOI + load:AOI + pID : 0.56 ±4%
[54] condition + epoch + condition:epoch + load + epoch:load + AOI + condition:AOI + pID : 0.55 ±5.9%
[55] condition + load + condition:load + AOI + condition:AOI + load:AOI + condition:load:AOI + pID : 0.48 ±3.5%
[56] condition + load + condition:load + AOI + condition:AOI + load:AOI + pID : 0.46 ±6.1%
[57] condition + epoch + load + AOI + load:AOI + pID : 0.44 ±5.6%
[58] condition + epoch + condition:epoch + load + condition:load + AOI + epoch:AOI + pID : 0.42 ±2.3%
[59] condition + epoch + load + condition:load + AOI + condition:AOI + epoch:AOI + load:AOI + condition:load:AOI + pID : 0.4 ±9.8%
[60] epoch + load + AOI + epoch:AOI + pID : 0.39 ±1.4%
[61] condition + epoch + load + pID : 0.39 ±1.2%
[62] condition + epoch + condition:epoch + load + condition:load + AOI + condition:AOI + epoch:AOI + condition:epoch:AOI + load:AOI + condition:load:AOI + pID : 0.38 ±3.5%
[63] condition + epoch + load + condition:load + AOI + pID : 0.34 ±5.2%
[64] condition + epoch + condition:epoch + load + condition:load + AOI + condition:AOI + epoch:AOI + condition:epoch:AOI + load:AOI + pID : 0.33 ±3.9%
[65] condition + load + pID : 0.27 ±1.8%
[66] condition + epoch + load + condition:load + AOI + condition:AOI + epoch:AOI + load:AOI + pID : 0.27 ±2.1%
[67] condition + load + AOI + load:AOI + pID : 0.26 ±1.9%
[68] condition + epoch + condition:epoch + load + epoch:load + AOI + condition:AOI + epoch:AOI + pID : 0.22 ±1.8%
[69] condition + load + condition:load + AOI + pID : 0.21 ±3%
[70] epoch + load + AOI + load:AOI + pID : 0.19 ±4.6%
[71] condition + epoch + condition:epoch + load + condition:load + AOI + load:AOI + pID : 0.19 ±3.7%
[72] epoch + load + pID : 0.18 ±0.77%
[73] condition + epoch + condition:epoch + load + condition:load + pID : 0.17 ±6.5%
[74] condition + epoch + load + epoch:load + AOI + condition:AOI + pID : 0.14 ±2.9%
[75] condition + epoch + load + AOI + epoch:AOI + load:AOI + pID : 0.14 ±2.2%
[76] load + pID : 0.12 ±1.3%
[77] load + AOI + load:AOI + pID : 0.12 ±6%
[78] condition + epoch + load + condition:load + AOI + epoch:AOI + pID : 0.11 ±2.3%
[79] condition + epoch + condition:epoch + load + condition:load + epoch:load + AOI + condition:AOI + pID : 0.095 ±21%
[80] condition + epoch + condition:epoch + load + epoch:load + AOI + condition:AOI + load:AOI + pID : 0.082 ±2.8%
[81] condition + epoch + condition:epoch + load + condition:load + AOI + epoch:AOI + load:AOI + pID : 0.077 ±11%
[82] epoch + load + AOI + epoch:AOI + load:AOI + pID : 0.06 ±1.4%
[83] condition + epoch + condition:epoch + load + epoch:load + AOI + condition:AOI + epoch:AOI + condition:epoch:AOI + pID : 0.059 ±3.2%
[84] condition + epoch + load + epoch:load + AOI + condition:AOI + epoch:AOI + pID : 0.058 ±10%
[85] condition + epoch + load + condition:load + AOI + load:AOI + pID : 0.05 ±1.9%
[86] condition + epoch + load + condition:load + pID : 0.048 ±1.2%
[87] condition + epoch + condition:epoch + load + epoch:load + AOI + condition:AOI + epoch:AOI + load:AOI + pID : 0.038 ±6.3%
[88] condition + load + condition:load + pID : 0.033 ±2%
[89] condition + epoch + condition:epoch + load + epoch:load + AOI + pID : 0.033 ±2.3%
[90] condition + load + condition:load + AOI + load:AOI + pID : 0.029 ±1.7%
[91] condition + epoch + condition:epoch + load + condition:load + epoch:load + AOI + condition:AOI + epoch:AOI + pID : 0.027 ±2.1%
[92] condition + epoch + load + epoch:load + AOI + condition:AOI + load:AOI + pID : 0.021 ±1.6%
[93] condition + epoch + load + condition:load + AOI + epoch:AOI + load:AOI + pID : 0.02 ±7.6%
[94] condition + epoch + load + condition:load + epoch:load + AOI + condition:AOI + pID : 0.017 ±2.2%
[95] condition + epoch + condition:epoch + load + condition:load + epoch:load + AOI + condition:AOI + load:AOI + condition:load:AOI + pID : 0.012 ±2.4%
[96] condition + epoch + condition:epoch + load + epoch:load + AOI + epoch:AOI + pID : 0.012 ±1.7%
[97] condition + epoch + condition:epoch + load + condition:load + epoch:load + AOI + condition:AOI + load:AOI + pID : 0.01 ±2.5%
[98] condition + epoch + condition:epoch + load + epoch:load + AOI + condition:AOI + epoch:AOI + condition:epoch:AOI + load:AOI + pID : 0.0094 ±3.2%
[99] condition + epoch + load + epoch:load + AOI + pID : 0.0094 ±1.8%
[100] condition + epoch + load + epoch:load + AOI + condition:AOI + epoch:AOI + load:AOI + pID : 0.0083 ±3.3%
[101] condition + epoch + condition:epoch + load + condition:load + epoch:load + AOI + condition:AOI + epoch:AOI + condition:epoch:AOI + pID : 0.0072 ±2.8%
[102] condition + epoch + load + condition:load + epoch:load + AOI + condition:AOI + epoch:AOI + pID : 0.0067 ±2.6%
[103] condition + epoch + condition:epoch + load + epoch:load + AOI + load:AOI + pID : 0.0052 ±2.3%
[104] condition + epoch + condition:epoch + load + condition:load + epoch:load + AOI + condition:AOI + epoch:AOI + load:AOI + condition:load:AOI + pID : 0.0051 ±3.8%
[105] condition + epoch + condition:epoch + load + condition:load + epoch:load + AOI + condition:AOI + epoch:AOI + load:AOI + pID : 0.0049 ±8.9%
[106] condition + epoch + condition:epoch + load + epoch:load + pID : 0.0045 ±1.2%
[107] epoch + load + epoch:load + AOI + pID : 0.004 ±1.2%
[108] condition + epoch + condition:epoch + load + condition:load + epoch:load + AOI + pID : 0.004 ±2.2%
[109] condition + epoch + load + condition:load + epoch:load + AOI + condition:AOI + load:AOI + condition:load:AOI + pID : 0.0033 ±3.1%
[110] condition + epoch + load + epoch:load + AOI + epoch:AOI + pID : 0.0033 ±3.8%
[111] condition + epoch + load + condition:load + epoch:load + AOI + condition:AOI + load:AOI + pID : 0.0032 ±12%
[112] condition + epoch + condition:epoch + load + epoch:load + AOI + condition:AOI + epoch:AOI + load:AOI + epoch:load:AOI + pID : 0.0024 ±2.3%
[113] condition + epoch + condition:epoch + load + epoch:load + AOI + epoch:AOI + load:AOI + pID : 0.002 ±4%
[114] condition + epoch + load + condition:load + epoch:load + AOI + condition:AOI + epoch:AOI + load:AOI + condition:load:AOI + pID : 0.0016 ±25%
[115] condition + epoch + load + epoch:load + pID : 0.0016 ±11%
[116] condition + epoch + condition:epoch + load + condition:load + epoch:load + AOI + epoch:AOI + pID : 0.0015 ±3.3%
[117] condition + epoch + load + epoch:load + AOI + load:AOI + pID : 0.0015 ±7.3%
[118] condition + epoch + condition:epoch + load + condition:load + epoch:load + AOI + condition:AOI + epoch:AOI + condition:epoch:AOI + load:AOI + condition:load:AOI + pID : 0.0015 ±7.5%
[119] epoch + load + epoch:load + AOI + epoch:AOI + pID : 0.0014 ±1.6%
[120] condition + epoch + condition:epoch + load + condition:load + epoch:load + AOI + condition:AOI + epoch:AOI + condition:epoch:AOI + load:AOI + pID : 0.0013 ±12%
[121] condition + epoch + load + condition:load + epoch:load + AOI + pID : 0.0012 ±2.6%
[122] condition + epoch + condition:epoch + load + condition:load + epoch:load + AOI + load:AOI + pID : 0.0011 ±41%
[123] condition + epoch + load + condition:load + epoch:load + AOI + condition:AOI + epoch:AOI + load:AOI + pID : 0.001 ±2.6%
[124] condition + epoch + condition:epoch + load + condition:load + epoch:load + condition:epoch:load + AOI + condition:AOI + pID : 0.00085 ±5.5%
[125] condition + epoch + condition:epoch + load + epoch:load + AOI + condition:AOI + epoch:AOI + condition:epoch:AOI + load:AOI + epoch:load:AOI + pID : 7e-04 ±6.3%
[126] epoch + load + epoch:load + AOI + load:AOI + pID : 7e-04 ±6.9%
[127] epoch + load + epoch:load + pID : 0.00062 ±0.82%
[128] condition + epoch + load + epoch:load + AOI + condition:AOI + epoch:AOI + load:AOI + epoch:load:AOI + pID : 0.00058 ±4.1%
[129] condition + epoch + condition:epoch + load + condition:load + epoch:load + pID : 0.00057 ±1.8%
[130] condition + epoch + load + epoch:load + AOI + epoch:AOI + load:AOI + pID : 0.00049 ±2.6%
[131] condition + epoch + condition:epoch + load + condition:load + epoch:load + AOI + condition:AOI + epoch:AOI + load:AOI + condition:load:AOI + epoch:load:AOI + pID : 0.00039 ±4.7%
[132] condition + epoch + load + condition:load + epoch:load + AOI + epoch:AOI + pID : 0.00039 ±2.9%
[133] condition + epoch + condition:epoch + load + condition:load + epoch:load + condition:epoch:load + AOI + condition:AOI + epoch:AOI + pID : 0.00035 ±6.2%
[134] condition + epoch + condition:epoch + load + condition:load + epoch:load + AOI + condition:AOI + epoch:AOI + load:AOI + epoch:load:AOI + pID : 0.00033 ±6.1%
[135] condition + epoch + condition:epoch + load + condition:load + epoch:load + AOI + epoch:AOI + load:AOI + pID : 0.00025 ±4.9%
[136] epoch + load + epoch:load + AOI + epoch:AOI + load:AOI + pID : 0.00021 ±1.2%
[137] condition + epoch + load + condition:load + epoch:load + pID : 0.00018 ±3%
[138] condition + epoch + load + condition:load + epoch:load + AOI + load:AOI + pID : 0.00018 ±2.2%
[139] condition + epoch + condition:epoch + load + condition:load + epoch:load + condition:epoch:load + AOI + condition:AOI + load:AOI + condition:load:AOI + pID : 0.00016 ±4.7%
[140] condition + epoch + condition:epoch + load + epoch:load + AOI + epoch:AOI + load:AOI + epoch:load:AOI + pID : 0.00013 ±2.1%
[141] condition + epoch + condition:epoch + load + condition:load + epoch:load + condition:epoch:load + AOI + condition:AOI + load:AOI + pID : 0.00013 ±4.3%
[142] condition + epoch + condition:epoch + load + condition:load + epoch:load + AOI + condition:AOI + epoch:AOI + condition:epoch:AOI + load:AOI + condition:load:AOI + epoch:load:AOI + pID : 0.00011 ±8.5%
[143] condition + epoch + load + condition:load + epoch:load + AOI + condition:AOI + epoch:AOI + load:AOI + condition:load:AOI + epoch:load:AOI + pID : 9e-05 ±11%
[144] condition + epoch + condition:epoch + load + condition:load + epoch:load + condition:epoch:load + AOI + condition:AOI + epoch:AOI + condition:epoch:AOI + pID : 8.2e-05 ±2%
[145] condition + epoch + condition:epoch + load + condition:load + epoch:load + AOI + condition:AOI + epoch:AOI + condition:epoch:AOI + load:AOI + epoch:load:AOI + pID : 8.1e-05 ±3%
[146] condition + epoch + load + condition:load + epoch:load + AOI + epoch:AOI + load:AOI + pID : 6.7e-05 ±4.2%
[147] condition + epoch + load + condition:load + epoch:load + AOI + condition:AOI + epoch:AOI + load:AOI + epoch:load:AOI + pID : 6.7e-05 ±2.2%
[148] condition + epoch + condition:epoch + load + condition:load + epoch:load + condition:epoch:load + AOI + condition:AOI + epoch:AOI + load:AOI + condition:load:AOI + pID : 6.2e-05 ±3.3%
[149] condition + epoch + condition:epoch + load + condition:load + epoch:load + condition:epoch:load + AOI + condition:AOI + epoch:AOI + load:AOI + pID : 5.1e-05 ±2.5%
[150] condition + epoch + condition:epoch + load + condition:load + epoch:load + condition:epoch:load + AOI + pID : 4.6e-05 ±1.7%
[151] condition + epoch + load + epoch:load + AOI + epoch:AOI + load:AOI + epoch:load:AOI + pID : 3.2e-05 ±2%
[152] condition + epoch + condition:epoch + load + condition:load + epoch:load + condition:epoch:load + AOI + epoch:AOI + pID : 1.9e-05 ±2.6%
[153] condition + epoch + condition:epoch + load + condition:load + epoch:load + AOI + epoch:AOI + load:AOI + epoch:load:AOI + pID : 1.6e-05 ±2.8%
[154] condition + epoch + condition:epoch + load + condition:load + epoch:load + condition:epoch:load + AOI + condition:AOI + epoch:AOI + condition:epoch:AOI + load:AOI + condition:load:AOI + pID : 1.6e-05 ±2.7%
[155] epoch + load + epoch:load + AOI + epoch:AOI + load:AOI + epoch:load:AOI + pID : 1.4e-05 ±1.6%
[156] condition + epoch + condition:epoch + load + condition:load + epoch:load + condition:epoch:load + AOI + load:AOI + pID : 8e-06 ±6.4%
[157] condition + epoch + condition:epoch + load + condition:load + epoch:load + condition:epoch:load + pID : 6.5e-06 ±1.8%
[158] condition + epoch + condition:epoch + load + condition:load + epoch:load + condition:epoch:load + AOI + condition:AOI + epoch:AOI + load:AOI + condition:load:AOI + epoch:load:AOI + pID : 4.7e-06 ±2.8%
[159] condition + epoch + load + condition:load + epoch:load + AOI + epoch:AOI + load:AOI + epoch:load:AOI + pID : 4.4e-06 ±5.8%
[160] condition + epoch + condition:epoch + load + condition:load + epoch:load + condition:epoch:load + AOI + condition:AOI + epoch:AOI + condition:epoch:AOI + load:AOI + pID : 4.1e-06 ±28%
[161] condition + epoch + condition:epoch + load + condition:load + epoch:load + condition:epoch:load + AOI + condition:AOI + epoch:AOI + load:AOI + epoch:load:AOI + pID : 3.6e-06 ±3.3%
[162] condition + epoch + condition:epoch + load + condition:load + epoch:load + condition:epoch:load + AOI + epoch:AOI + load:AOI + pID : 2.8e-06 ±3%
[163] condition + epoch + condition:epoch + load + condition:load + epoch:load + condition:epoch:load + AOI + condition:AOI + epoch:AOI + condition:epoch:AOI + load:AOI + condition:load:AOI + epoch:load:AOI + pID : 1.3e-06 ±3.8%
[164] condition + epoch + condition:epoch + load + condition:load + epoch:load + condition:epoch:load + AOI + condition:AOI + epoch:AOI + condition:epoch:AOI + load:AOI + epoch:load:AOI + pID : 1.1e-06 ±3.6%
[165] condition + epoch + condition:epoch + load + condition:load + epoch:load + condition:epoch:load + AOI + epoch:AOI + load:AOI + epoch:load:AOI + pID : 1.9e-07 ±2.2%
[166] condition + epoch + condition:epoch + load + condition:load + epoch:load + condition:epoch:load + AOI + condition:AOI + epoch:AOI + condition:epoch:AOI + load:AOI + condition:load:AOI + epoch:load:AOI + condition:epoch:load:AOI + pID : 7.1e-08 ±11%
Against denominator:
meanFixTime ~ pID
---
Bayes factor type: BFlinearModel, JZSA bayesian anova was conducted with fixation time as an dependent variable. The results show that the model containing the factors condition and AOI, along with the condition x AOI interaction with participant as the random effect received the strongest support, BF10 = 1.3 × 103 ± 2.72%. More importantly, the model including load as an additional factor showed evidence in favor of the null hypothesis BF = 8.7 ± 9.49%.
Bayes factor analysis
--------------
[1] condition + load + condition:load + pID : 1311473 ±0.97%
[2] load + pID : 746388 ±0.55%
[3] condition + load + pID : 516777 ±4.2%
[4] condition + load + condition:load + epoch + pID : 42158 ±2.5%
[5] load + epoch + pID : 24155 ±0.59%
[6] condition + load + condition:load + epoch + condition:epoch + pID : 16733 ±1.7%
[7] condition + load + epoch + pID : 15926 ±0.76%
[8] condition + load + epoch + condition:epoch + pID : 5456 ±0.97%
[9] condition + load + condition:load + epoch + load:epoch + pID : 1385 ±10%
[10] load + epoch + load:epoch + pID : 679 ±0.66%
[11] condition + load + condition:load + epoch + condition:epoch + load:epoch + pID : 476 ±2.1%
[12] condition + load + epoch + load:epoch + pID : 447 ±1.1%
[13] condition + load + epoch + condition:epoch + load:epoch + pID : 164 ±2.8%
[14] condition + load + condition:load + epoch + condition:epoch + load:epoch + condition:load:epoch + pID : 32 ±4.1%
[15] condition + pID : 0.64 ±0.23%
[16] epoch + pID : 0.026 ±0.4%
[17] condition + epoch + pID : 0.016 ±0.38%
[18] condition + epoch + condition:epoch + pID : 0.0046 ±0.5%
Against denominator:
meanStartTime ~ pID
---
Bayes factor type: BFlinearModel, JZSAnother Bayesian anova was conducted with mean start time of the first fixation to explore whether there were meaningful difference in the time it took to make the first fixation towards the associative learning stimuli between conditions. The strongest model contained condition, load, condition x load interaction term and participant as the random effect, BF10 = 1.3 × 106 ± 0.97%
References
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Peirce, Jonathan, Jeremy R. Gray, Sol Simpson, Michael MacAskill, Richard Höchenberger, Hiroyuki Sogo, Erik Kastman, and Jonas Kristoffer Lindeløv. 2019. “PsychoPy2: Experiments in Behavior Made Easy.” Behavior Research Methods 51 (1): 195–203. https://doi.org/10.3758/s13428-018-01193-y.