Presented to the Department of Industrial Systems Engineering
De La Salle University of Manila
Term 2, A.Y. 2022-2023
In partial fulfillment of the course
Cognitive Ergonomics Laboratory
(LBYIE3C - EC2)
Experiment Report 3:
Information Theory
Submitted by:
Cu, Hans Nicolson C.
Dacanay, Aeron
Guarnes, Jan
Tan, Hans Daineal C.
San Juan, Jarvy
Submitted to:
Ms. Jazmin Tangsoc
I.
Objectives
For this experiment, the group was tasked to prove the Hick Hyman’s law by developing
their own experiment containing multiple levels. The specific objective(s) are as follows:
A. To prove Hick Hyman’s Law which states that as the number of information bits
increases, the decision time also increases logarithmically (Hyman, 1953)
II.
Methodology (Procedure and Bits Per Level)
For this experiment, 30 subjects will be chosen conveniently. They will be asked to sort a
set of 32 blue and orange cards in 3 different ways. These cards will also have numbers in their
centers and shapes in their top left. After completing the task, their times to complete the
respective sorting(s) will be recorded and analyzed in the statistical software Minitab using the
regression function.
A. Materials and Tools
1. Stack of 32 cards - The main tool for this will be half a deck of custom
cards created by the group, as described above.
2. Minitab
3. Google Sheets
B. Procedure
1. Level 1 - Separate by color - Subjects will be given the deck face down
and will be asked to separate the cards according to their color (Blue and
Orange). They will be timed for the total time it takes them to sort the
whole deck into the 2 categories.
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑏𝑖𝑡𝑠 = 𝑙𝑛(𝑁) /𝑙𝑛 2; 𝑁 𝑖𝑠 𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑒𝑞𝑢𝑎𝑙𝑙𝑦 𝑙𝑖𝑘𝑒𝑙𝑦 𝑒𝑣𝑒𝑛𝑡𝑠
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑏𝑖𝑡𝑠 = 𝑙𝑛(2) /𝑙𝑛 2 = 1 𝑏𝑖𝑡
2. Level 2 - Separate by Color and Shape - Following that, the subjects will
be asked to sort the cards according to their Colors and Shapes. This will
have them separate the cards into 4 piles.
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑏𝑖𝑡𝑠 = 𝑙𝑛(4) /𝑙𝑛 2 = 3 𝑏𝑖𝑡
3. Level 3 - Separate by color, shape, and value - Finally, the subjects will be
asked to sort the cards according to their colors, values, and shapes. This
should separate the deck into 16 different piles, with 2 cards for each . The
subjects will be timed for how long it takes them to finish the whole deck.
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑏𝑖𝑡𝑠 = 𝑙𝑛(16) /𝑙𝑛 2 = 4 𝑏𝑖𝑡
III.
Results and Discussion
According to Eberly College of Science (n. d.), the fitted line plot is one of the tools to be
able to obtain the regression equation between a predictor and a response variable. Additionally,
it also provides a scatter plot of the data. According to Wu, et al. (2018), Hick Hyman’s Law
describes the increasing amount of reaction time as the number of information increases.
Therefore, there is an expected increase in the reaction time of the subjects as their level
progresses. A cognitive study conducted by Schmitz & Voss (2012) also used linear regression to
analyze the relationship between a working memory task and response time.
Figure 1.1 Graph of the Regression Equation from Minitab Results
Graphing the regression equation generated from the Minitab Software, it is seen that there is a
positive relationship between the y variable ‘Time’ and the x variable ‘Level’. It is also seen that
the values have huge increments between each variable which is a graphical representation of the
logarithmic increase of the response time as the information bits or level increases. The fitted
line plot of the data gathered from this experiment shows that there is an R-squared value of
0.7211. This being close to 1 indicates that the dependent variable, the time, is explained by the
variation of the independent variable, the levels. In other words, there is a strong positive
correlation between levels and reaction time. Additionally, the data has a p-value of 0.000 which
means that there is a significant difference in time from one level to another, further proving
Hick Hyman’s Law. As the number of levels and information to organize increases, the longer
time it takes for the respondents to finish.
IV.
Recommendations
In order to manage or lower reaction times as information increases, several measures
could be done to meet a system’s specific needs, through practice and general exercising of the
mind, body, and visual senses. According to Heiman (2014), repeatedly performing a specific
task can help an individual gain experience and have an increase in familiarity with the
decision-making process of the assigned task. This helps them simplify their approach to the task
and be more effective by developing cognitive shortcuts that can speed up the decision-making
process, while maintaining accuracy in their decisions. Mindfulness training was explored by
Mrazek et al. in their study in 2013. Results of their study suggest that a boost in cognitive
performance, specifically in reading comprehension and working memory capacity, is caused by
the two-week mindfulness training course that helps in reducing mind wandering when
performing tasks. Meanwhile, a paper by Pourazar et al. (2017) proposes the use of a virtual
reality training tool to improve reaction times in children with cerebral palsy. In their study, the
MANOVA test was used, where it presented a significant difference between subjects that had
undergone the treatment, and the control group. Similarly, studies show that regular boxing
training over a 12-week period significantly improves the reaction time of subjects’ right hand in
the context of boxing training (Çakmakçi et al., 2019). Another study supporting the
recommendation of having a regular 12-week training of boxing is the study conducted by Roig
et al.(2013) where it was mentioned that memory can be improved by having cardiovascular
exercise. It was stated in the paper that although a long-term cardiovascular exercise do not show
a significant effect on memory improvement, it does help in decreasing the time spent on
information processing, thus enhancing one’s decision making skills. As for the acute exercises
such as running and cycling, memory can be improved in a time-dependent manner. Finally, a
study by Rodrigues, Loureiro and Caramelli (2013), posited that long-term musical training
improves the reaction time in simple reaction tests that consist of simply reacting to the
appearance of an asterisk on a screen in front of them. This was explained in that musicians are
used to reacting to stimuli very quickly and in conjunction with each other, such as the music
score, the movement of the conductor, and the movement of their fellow musicians.
V.
Conclusion
The objective of this experiment was to prove Hick Hyman’s law. Through the results, it
can be seen that as more information is presented to the subjects of the experiment, the longer it
takes for them to react, thereby proving Hick Hyman’s Law. Also, recommendations on
improving the reaction times in general were also presented by the group. Overall, these
recommendations simply consist of long term training of the mental, visual and/or physical sense
relevant to the specific reaction time test.
VI.
References
Çakmakçı, E., Tatlıcı, A., Kahraman, S., Yılmaz, S., Ünsal, B., & Özkaymakoğlu, C. (2019).
Does once-a-week boxing training improve strength and reaction time? International
Journal
of
Sport,
Exercise
&
Training
Sciences,
88-92.
https://doi.org/10.18826/useeabd.552086
Eberly College of Science. (n.d.). Create a fitted line plot | STAT 501. PennState: Statistics
Online Courses. https://online.stat.psu.edu/stat501/lesson/create-fitted-line-plot
Heiman, S. (2014). A Study on the Perception of Brain Games and their Effect on Memory and
Cognitive
Skills.
Retrieved
from
https://stars.library.ucf.edu/cgi/viewcontent.cgi?article=2574&context=honorstheses199
0-2015
Hyman, R. (1953). Stimulus information as a determinant of reaction time. Journal of
Experimental Psychology, 45(3), 188–196. doi:10.1037/h0056940
Mrazek, M. D., Franklin, M. S., Phillips, D. T., Baird, B., & Schooler, J. W. (2013). Mindfulness
training improves working memory capacity and GRE performance while reducing mind
wandering.
Psychological
science,
24(5),
776–781.
https://doi.org/10.1177/0956797612459659
Pourazar, M., Mirakhori, F., Hemayattalab, R., & Bagherzadeh, F. (2017). Use of virtual reality
intervention to improve reaction time in children with cerebral palsy: A randomized
controlled
trial.
Developmental
Neurorehabilitation,
21(8),
515-520.
https://doi.org/10.1080/17518423.2017.1368730
Rodrigues, A. C., Loureiro, M. A., & Caramelli, P. (2013). Long-term musical training may
improve different forms of visual attention ability. Brain and Cognition, 82(3), 229-235.
https://doi.org/10.1016/j.bandc.2013.04.009
Roig, M., Nordbrandt, S., Geertsen, S. S., & Nielsen, J. B. (2013). The effects of cardiovascular
exercise on human memory: a review with meta-analysis. Neuroscience and
biobehavioral
reviews,
37(8),
1645–1666.
https://doi.org/10.1016/j.neubiorev.2013.06.012
Schmitz, F., & Voss, A. (2012). Decomposing the time course of cognitive processes: An
individual-differences analysis. Intelligence, 40(2), 226-236.
Wu, T., Dufford, A. J., Egan, L. J., Mackie, M., Chen, C., Yuan, C., Chen, C., Li, X., Liu, X.,
Hof, P. R., & Fan, J. (2017). Hick–Hyman law is mediated by the cognitive control
network
in
the
brain.
Cerebral
https://doi.org/10.1093/cercor/bhx127
VII.
Appendices
Appendix A. Custom Cards
Appendix B. Raw Data
Respondent
Level 1
Level 2
Level 3
Cortex,
28(7),
2267-2282.
1
22.9
36.34
79.37
2
22.66
41.33
66.66
3
14.58
21.09
47.34
4
15.08
21.8
71.13
5
15.28
35.64
50.63
6
15.61
23.95
41.24
7
15.17
27.75
49.73
8
20.45
33.45
53.02
9
20.07
32.94
43.07
10
17.41
34.72
42.25
11
18.88
28.25
37.4
12
23.35
30.64
50.04
13
16.58
31.94
42.21
14
16.77
26.06
35.41
15
18.42
23.96
45.12
16
15.12
15.94
32.94
17
12.14
14.32
38.65
18
14.28
18.51
48.64
19
11.68
24.45
60.96
20
12.48
23.28
41.75
21
15.51
25.72
62.97
22
15.86
22.35
53.37
23
14.5
21.85
52.92
24
23.23
21.3
42.45
25
11.99
30.79
67.43
26
14.7
24.68
48.6
27
13.26
26.95
37.34
28
17.88
25.44
40.79
29
19.2
37.56
50.61
30
10.5
27.12
34.46
Appendix C. Minitab Output