Experiment 3b: Dynamic RDK Direction Judgement, Highlight Selection, 4 Tasks, 500 msec Error Penalty
knowlabUnimelb
2021-09-17
Last updated: 2022-11-09
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| File | Version | Author | Date | Message |
|---|---|---|---|---|
| Rmd | 67e1aac | knowlabUnimelb | 2022-11-09 | Publish data and analysis files |
Ruby Steinberg1, Ami Eidels2, and Daniel R. Little1
1 The University of Melbourne, 2 The University of Newcastle
Method
Participants
[NEED TO ADD A SUMMARY OF PARTICIPOANT INFORMATION: HOW MANY TESTED, DEMOGRAPHIC INFORMATION, HOW WERE PARTICIPANTS REIMBURSED, HOW MANY ASSIGNED TO EACH CONDITION]
Design
[NEED TO ADD A DESCRIPTION OF THE EXPERIMENTAL DESIGN]
Data Cleaning
Subjects completed the experiment by clicking a link with the uniquely generated id code. Subjects were able to use the link multiple times; further, subjects were able to exit the experiment at any time. Consequently, the datafile contains partially completed data for some subjects which needed to be identified and removed.
[NEED TO ADD A DESCRIPTION OF THE NONLEARNERS]
Data Analysis
We first summarize performance by answering the following questions:
Task completions
- How many tasks are completed on average?
[ADD ANALYSIS DESCRIPTION]
| condition | phase | mean |
|---|---|---|
| fixed | untimed | 3.940217 |
| fixed | deadline | 3.260949 |
| random | untimed | 3.959569 |
| random | deadline | 2.986595 |
[ADD DESCRIPTION OF ANALYSIS OF TASK COMPLETIONS]
RDK performance
We next analysed performance on the RDK discriminations. We then asked:
- What was the average completion time and accuracy of the easy, medium, hard, and very hard tasks?
[ADD DESCRIPTION OF PLOT]
[ADD DESCRIPTION OF PLOT]
We further broke down RTs by condition, deadline, and difficulty.
| condition | phase | difficulty | n | Mean.Correct | SE.Correct | Mean.RT | SE.RT | Mean.crt | SE.crt |
|---|---|---|---|---|---|---|---|---|---|
| fixed | untimed | easy | 657 | 0.85 | 0.01 | 822.48 | 37.98 | 971.61 | 53.40 |
| fixed | untimed | medium | 519 | 0.79 | 0.02 | 891.70 | 34.45 | 1130.46 | 46.03 |
| fixed | untimed | hard | 464 | 0.70 | 0.02 | 1228.99 | 55.87 | 1762.00 | 87.63 |
| fixed | untimed | v. hard | 430 | 0.55 | 0.02 | 1515.19 | 74.21 | 2734.84 | 152.49 |
| fixed | deadline | easy | 1298 | 0.83 | 0.01 | 465.52 | 8.00 | 553.71 | 11.53 |
| fixed | deadline | medium | 1212 | 0.80 | 0.01 | 494.56 | 9.66 | 602.84 | 14.36 |
| fixed | deadline | hard | 1236 | 0.70 | 0.01 | 513.57 | 10.40 | 690.85 | 15.95 |
| fixed | deadline | v. hard | 1218 | 0.56 | 0.01 | 499.76 | 11.86 | 779.68 | 21.79 |
| random | untimed | easy | 726 | 0.79 | 0.02 | 765.15 | 24.28 | 974.58 | 36.37 |
| random | untimed | medium | 540 | 0.79 | 0.02 | 872.71 | 32.56 | 1100.37 | 43.28 |
| random | untimed | hard | 464 | 0.68 | 0.02 | 1167.30 | 64.40 | 1712.89 | 92.52 |
| random | untimed | v. hard | 470 | 0.50 | 0.02 | 1363.75 | 56.18 | 2690.44 | 121.83 |
| random | deadline | easy | 1406 | 0.77 | 0.01 | 426.38 | 7.36 | 534.63 | 10.78 |
| random | deadline | medium | 1223 | 0.76 | 0.01 | 462.86 | 8.98 | 591.85 | 14.07 |
| random | deadline | hard | 1170 | 0.67 | 0.01 | 533.75 | 10.70 | 746.89 | 18.79 |
| random | deadline | v. hard | 1136 | 0.55 | 0.01 | 593.29 | 13.23 | 969.95 | 25.14 |
Reward Rate
[ADD DESCRIPTION]
Optimality in each condition
- What is the proportion of easy, medium, hard, and very hard tasks selected first, second, third or fourth? [ADD DESCRIPTION]
- Do the marginal distributions differ from uniformity?
We tested whether the marginal distributions were different from uniformally random selection using the fact that the mean rank is distributed according to a \(\chi^2\) distribution with the following test-statistic: \[\chi^2 = \frac{12N}{k(k+1)}\sum_{j=1}^k \left(m_j - \frac{k+1}{2} \right)^2\] see (Marden, 1995).
| condition | phase | chi2 | df | p |
|---|---|---|---|---|
| fixed | untimed | 61.67 | 3 | 0.00 |
| fixed | deadline | 1117.99 | 3 | 0.00 |
| random | untimed | 11.01 | 3 | 0.01 |
| random | deadline | 52.93 | 3 | 0.00 |
[ADD DESCRIPTION]
We compared the location conditions and phases using chi-2 analysis.
| Comparison | chi2 | df | p |
|---|---|---|---|
| Fixed: Untimed vs Deadline | 185.47 | 15 | 0.00 |
| Random: Untimed vs Deadline | 15.05 | 15 | 0.45 |
| Untimed: Fixed vs Random | 42.97 | 15 | 0.00 |
| Deadline: Fixed vs Random | 376.88 | 15 | 0.00 |
- How optimal were responses?
Selection model
We can treat each task selection as a probabilistic choice given by a Luce’s choice rule (Luce, 1959), where each task is represented by some strength, \(\nu\). The probability of selecting task \(i_j\) from set \(S = \left{i_1, i_2, ..., i_J \right}\), where J is the number of tasks, is:
\[p\left(i_j |S \right) = \frac{\nu_{i_j}}{\sum_{i \in S} \nu_{i}} \].
Plackett (1975) generalised this model to explain the distribution over a sequence of choices (i.e., ranks). In this case, after each choice, the choice set is reduce by one (i.e., sampling without replacement). This probability of observing a specific selection order, \(i_1 \succ ... \succ i_J\) is:
\[p\left(i_j |A \right) = \prod_{j=1}^J \frac{\nu_{i_j}}{\sum_{i \in A_j} \nu_{i}} \],
where \(A_j\) is the current choice set.
Sampling distribution anlaysis
In order to characterise performance, we examined three sampling distributions for comparison to our data. The first is the sampling distribution of edit distances from optimal assuming that orders are sampled uniformly at random. The second distribution assumes that the first choice was optimal but the remaining orders are sampled at random. Finally, the third distributions assumes that the first two choices are selected optimally but that the remaining are randomly selected. It is clear that the mode of the distribution moves from a distance of 3 to a distance of 0 as the sampling distribution summarises orders which better conform to optimality.
To characterise the optimality of each condition at each point in the experiment, we first computed the ks-test statistic between the data (the average partial distance data) and the random order distribution and the first-two optimal distribution. Since smaller ks-statistics indicate a closer match between the distributions, we then took the ratio of the ks-statistics (random over first two-optimal). Values less than one indicate that the data are more consistent with random than optimal responding. Values greater than one indicate that the data are more consistent with optimal rather than random responding.
This figure efficiently summarises the main result: responding is more optimal in the fixed deadline condition particularly during the last ten trials; in the random deadline conditions, responding was closer to a random sampling distribution than to an optimal sampling distribution.
Selection Choice RTs
| condition | phase | mrt_sel1 | mrt_sel2 | mrt_sel3 | mrt_sel4 |
|---|---|---|---|---|---|
| fixed | untimed | 1641 | 1412 | 1334 | 1234 |
| fixed | deadline | 800 | 830 | 808 | 788 |
| random | untimed | 1695 | 1337 | 1248 | 1210 |
| random | deadline | 897 | 947 | 895 | 772 |
| condition | phase | sd_sel1 | sd_sel2 | sd_sel3 | sd_sel4 |
|---|---|---|---|---|---|
| fixed | untimed | 27.331356 | 18.458250 | 16.559479 | 9.895521 |
| fixed | deadline | 6.956076 | 6.061463 | 5.203364 | 4.363523 |
| random | untimed | 32.260859 | 14.697222 | 10.662332 | 9.092194 |
| random | deadline | 8.252353 | 7.631601 | 5.605028 | 4.199206 |
sessionInfo()R version 4.1.3 (2022-03-10)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 10 x64 (build 19042)
Matrix products: default
locale:
[1] LC_COLLATE=English_Australia.1252 LC_CTYPE=English_Australia.1252
[3] LC_MONETARY=English_Australia.1252 LC_NUMERIC=C
[5] LC_TIME=English_Australia.1252
attached base packages:
[1] stats4 grid stats graphics grDevices utils datasets
[8] methods base
other attached packages:
[1] pmr_1.2.5.1 jpeg_0.1-9 rstatix_0.7.0 lme4_1.1-29
[5] Matrix_1.4-0 png_0.1-7 reshape2_1.4.4 knitr_1.38
[9] hrbrthemes_0.8.0 english_1.2-6 gtools_3.9.2 DescTools_0.99.45
[13] forcats_0.5.1 stringr_1.4.0 dplyr_1.0.8 purrr_0.3.4
[17] readr_2.1.2 tidyr_1.2.0 tibble_3.1.6 ggplot2_3.3.5
[21] tidyverse_1.3.1 workflowr_1.7.0
loaded via a namespace (and not attached):
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[5] rprojroot_2.0.3 fs_1.5.2 gld_2.6.5 rstudioapi_0.13
[9] proxy_0.4-27 farver_2.1.0 fansi_1.0.3 mvtnorm_1.1-3
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