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# Measuring Discrimination Abilities of Monk Parakeets Between Discreet and
Continuous Quantities Through a Digital Life Enrichment Application

Jérémy Barbay<EMAIL_ADDRESS>0000-0002-3392-8353 ,  Fabián Jaña Ubal
<EMAIL_ADDRESS>and  Cristóbal Sepulveda Álvarez<EMAIL_ADDRESS>
Departamento de Ciencias de la Computación (DCC), Universidad de ChileAvenida
Beauchef 851SantiagoRegion MetropolitanaChile8370448

###### Abstract.

Ain et al. measured three African Grey (_Psittacus erithacus_) parrot’s
discrimination abilities between discreet and continuous quantities. Some
features of their experimental protocol make it difficult to apply to other
subjects and/or species without introducing a risk for some bias, as subjects
could read cues from the experimenter (even though the study’s subjects
probably did not). Can digital life enrichment techniques permit us to
replicate their results with other species with less risk for experimental
bias, with a better precision, and at lower cost? Inspired by previous
informal digital life enrichment experiments with parrots, we designed and
tested a web application to digitally replicate and extend Ain et al.’s
experimental setup. We were able to obtain similar results to theirs for two
individuals from a distinct species, Monk Parakeets (_Myiopsitta Monachus_),
with increased guarantees against potential experimental biases, in a way
which should allow to replicate such experiments at larger scale and at a much
lower cost.

Animal Computer Interaction, Comparative Cognition Study, Continuous and
Discreet Comparative Abilities, Digital Life Enrichment, Monk Parakeet

††ccs: Applied computing Computer-assisted instruction††ccs: Applied computing
Interactive learning environments††ccs: Human-centered computing User
interface design††ccs: Applied computing Agriculture††ccs: Applied computing
Computer games

Figure 1. The Monk Parakeet Tina selecting the largest value out of two
displayed, in heap mode.

A monk parakeet in front of the touch screen of a grey smart phone ”Galaxy
Note 9” reaches to select the largest disk out of four, below the title
”What’s more?”.

Figure 2. The Monk Parakeet Lorenzo selecting the largest value out of four
displayed, in disk mode.

A monk parakeet in front of the touch screen of a grey smart phone ”Galaxy
Note 9” reaches to select the largest disk out of four, below the title
”What’s more?”.

##  1\. Introduction

Al Aïn et al. (2008) measured the discrimination abilities between discrete
and continuous quantities of three African Grey parrots (_Psittacus
erithacus_), showing that their accuracy in choosing between two small
quantities was inversely correlated with the ratio between the difference
between the two quantities and the largest quantity.

Generalizing the experimental protocol described and implemented by Al Aïn et
al. (2008) to other subjects or species present some difficulties. The fact
that the experimenter knows which answer was expected from the subjects is not
an issue in their study because it was previously verified that the three
subjects were unable to read such cues from human experimenters, but it means
that the replication of such protocol is limited to individuals (from the same
or from other species) which inability to read cues has been previously
demonstrated. Beyond such a weakness, the cost of the experimental set-up and
of the analysis of the video recordings of the experiments reduces the
probability that such a protocol will be replicated with other subjects from
the same species, or with subjects from the many other species of parrots
existing around the world.

Touchscreens have been successfully used for experiments in life enrichment
(Perdue et al., 2012; Kohn, 1994; Coghlan et al., 2021a) and in Comparative
Psychology (Egelkamp and Ross, 2018), with individuals from various nonhuman
species. Could digital life enrichment techniques allow to replicate Al Aïn et
al. (2008)’s results at a lower cost, but with a better precision, and less
potential experimental bias? Which additional advantages could a digital
variant bring?

A Cockatoo parrot playing Candy Crush on a large tablet.

Figure 3. A Cockatoo playing the game “Candy Crush” (picture used with the
authorisation of the author).

Figure 4. The Cockatoo Isabelle playing the game “Candy Crush” under the
guidance of Jennifer Cunha from Parrot Kindergarten (picture used with the
authorisation of the author).

A Monk Parrot playing a piano app on a grey cell phone lying on the table.

Figure 5. Monk Parakeet playing the piano music application “Mini Piano Lite”
in order to learn to use touchscreen interfaces with a wide active surface.

Figure 6. The Monk Parakeet Lorenzo playing the piano music application “Mini
Piano Lite” in order to learn to use touchscreen interfaces with a wide active
surface.

Two Monk Parrots playing steel drum music on cell phone apps, each with their
own device.

Figure 7. Monk Parakeets playing the steel drum music application “Meditation
Drum” in order to learn how to properly aim when using touchscreen interfaces.

Figure 8. The Monk Parakeets Tina (left) and Lorenzo (right) playing the steel
drum music application “Meditation Drum” to learn how to aim when using
touchscreen interfaces.

Inspired by previous informal Digital Life Enrichment experiments such as a
Cockatoo playing the video game Candy Crush (Figure 8), or Monk Parakeets
learning to use touch interfaces by playing music on it (Figures 8 and 8), we
designed, tested and used a web application InCA-WhatIsMore to digitally
replicate and extend Al Aïn et al. (2008)’s experimental setup. We obtained
similar results to that of Ain et al. for two individuals of a distinct
species of parrots, Monk Parakeets (_Myiopsitta Monachus_), using an
experimental protocol with increased guarantees against potential experimental
biases, at a lower set-up cost, with additional advantages brought by the
digital context, such as automatic logging and increased subject’s agency.
After describing a selection of concepts and results in the research area of
comparative psychology (Section 2), we describe the application InCA-
WhatIsMore (Section 3), an experimental protocol (including separate
development, training and testing phases) based upon it (Section 4), an
implementation of this protocol and an analysis of its results (Section 5),
and we conclude with a recapitulation of our results, a discussion of their
potential weaknesses and a perspective on future research (Section 6).

##  2\. Nonhuman Cognition

The cognitive abilities of nonhuman animals, traditionally less studied than
that of human ones, has been receiving more attention in the last half
century. Such studies started with the animals perceived to be “closest” to
humankind, such as apes, and has spread more recently to birds (Pepperberg,
1999; Al Aïn et al., 2008; Cunha and Clubb, 2018). We describe a general
overview of some projects and results about the cognitive abilities of some
ape and bird species (Section 2.1); Al Aïn et al. (2008)’s study of the
discrimination abilities of some parrots (Section 2.2); how devices
(analogical and digital) were introduced to nonhumans in order to improve
their well being, and often study their abilities at the same time (Section
2.3); how the distrust in results obtained by improper experimental protocols
has plagued scientific research in this area in the past (Section 2.4); and
how some general guiding principles in the design of experimental protocols
permit scientists to avoid such experimental biases (Section 2.5).

###  2.1. Comparative Psychology

Comparative psychology refers to the scientific study of the behavior and
mental processes of non-human animals (referred to as “nonhumans” thereafter),
especially as these relate to the phylogenetic history, adaptive significance,
and development of behavior in many different species, from insects to
primates. Pepperberg (2020) describes the history of the field of Comparative
Psychology of Intelligence in the last 30 years.

2020-ExoticsCon-ReadingComprehensionSkillsInAGoffinSCockatoo-Cunha

Cunha and Clubb (2018)

###  2.2. Discrimination Abilities in African Grey parrots

Al Aïn et al. (2008) tested the discrimination abilities of African Grey
(_Psittacus erithacus_) parrots on discrete and continuous amounts. More
precisely, they investigated the ability of three African grey parrots to
select the largest amount of food between two sets, in two types of
experiments. In the first experiment type, the subjects were tested on
discrete quantities via the presentation of two quantities of sunflower seeds
(Deli nature Beyers Belgium), between 1,2,3,4 and 5 seeds. In the second
experiment type, the subjects were tested on continuous quantities via the
presentation of two quantities of parrot formula, with amounts between
0.2,0.4,0.6,0.8 and 1 ml. For each experiment, the two amounts were presented
simultaneously and were visible at the time of choice. Albeit the subjects
sometimes failed to choose the largest value, they always performed above
chance, their performance improving when the difference between amounts was
the greatest.

The experimental setup was completely analogical. A permanent table was set-up
in the aviary, and two black pieces of cardboard were used to present food
item (sunflower seeds or parrot formula). For each experiment, different
amounts of either seeds or parrot formula were placed on each piece of
cardboard. The experimenter put the subject for 5 seconds in a position from
which they could observe the two sets, then placed them on the table at equal
distances from the two sets, letting them chose one set to it while removing
the ignored set. The position of the sets (small and large) was pseudo-
randomized: the larger set was never presented more than two times on the same
side and was presented as often on the right side as on the left side.

In the experimental setup described by Al Aïn et al. (2008), subjects could
eventually read involuntarily cues from the experimenter: even though the
experimenter was standing behind the subject, at equal distances from each
set, not pointing to it, looking at the subject, aiming to avoid communicating
any cue to the subject, the experimenter _knew_ where the largest quantity
was. While it was not an issue in Al Aïn et al. (2008)’s study because the
authors demonstrated in a previous study that the subjects were not able to
use any gazing cue, the protocol should not be applied as such to other
subjects without verifying their inability to read such cues, adding to the
cost of implementing such protocol.

Avoiding giving cues to the subject is hard even for a professionally trained
experimenter (Trestman, 2015). Requiring either such training or a separate
study to insure that the subject cannot read cues from the experimenter
restricts the applicability of a protocol to laboratories. For example, in the
context of _citizen science_ projects (Gura, 2013) where non professional
experimenters (such as zoo personal or simple citizen) guide the experiments,
a masked protocol (defined in Section 2.5) where the experimenters _ignore_
what the correct answer is (because they did not receive the information that
the subject did) would be more robust against subjects reading cues from the
experimenter. We describe in section 3 an application allowing for such an
alternate experimental setup which, if not exactly equivalent to that of Al
Aïn et al. (2008) (e.g. the reward is not proportional to the quantity
selected), presents the advantage of being “experimenter-masked”, inspired by
some of the life enrichment experiences described in the next section.

###  2.3. Life Enrichment and Cognition studies

One can study cognitive abilities of nonhumans through life enrichment
activities in general, and through digital ones in particular. General
preoccupation for the welfare of captive nonhumans is at least 150 years old.
Kohn (1994) dates the first legislation about zoo animal welfare to 1876, with
the “Cruelty to Animals Act” in the “Criminal Code of Canada”. Since then, the
list of duties of such institutions has grown to include not only the basic
welfare tenets of adequate feed, water, shelter, sanitation and veterinary
care of their nonhuman residents, but also higher level concerns such as the
handling and training of the nonhuman residents, their psychological well-
being, the design of their enclosures, the preservation of their species,
issues of environmental and conservation, and programs to breed captive
nonhumans. Kohn (1994) mentions (in 1994) the “ _emerging field of
psychological well-being in captive animals_ ”, incorporating physical health,
normal and captive behavior, and interactions with the enclosure environments
and mentioning how environmental enrichment is an important component of this
issue. He goes on to list innovations in life enrichment such as specialized
toys and puzzle feed boxes (but no digital applications).

Yet, the use of digital applications to measure nonhuman abilities seems to
predate Kohn (1994)’s report by at least 10 years. In his discussion of the
impact of game-like computerized tasks designed to promote and assess the
psychological well-being of captive nonhuman, Washburn (2015) refers to a
three decade old history in 2015, placing the beginning of such use sometimes
around 1985. In 1990, Richardson et al. (1990) describe a quite complete
Computerized Test System. They tested their system with a population of rhesus
monkeys, but defend its potential as a “ _rich and robust testing environment
for the cognitive and neuro-psychological capacities of great apes, rhesus
monkeys, mentally retarded and normally developing children, and adults_ ”, so
that subjects from various populations can be tested under comparable
conditions in such a way that “ _control is increased over testing conditions_
”. They mention that “ _the animals readily started to work even when the
reward was a small pellet of chow very similar in composition to the chow just
removed from the cage_ ”, and that “ _the tasks have some motivating or
rewarding of their own_ ”.

Nonhuman subjects seem to enjoy participating in cognitive studies involving
game-like digital applications. Washburn (2015) describes, among various other
anecdotes, how game-like application for apes were developed as early as 1984,
and how the subjects “ _chose to work on joystick-based tasks, even though
they did not need to perform the game-like tests in order to receive food_ ”,
and “ _opted for computer task activity over other potential activities that
were available to them_ ”. He goes on to mention how such game-like activities
have been used to study various cognitive phenomena such as the ability to
learn, memory, attention, perception, categorization, numerical cognition,
problem solving, the ability to reason, the ability to make decisions, meta-
cognition, social cognition and language. Among the details reported on the
methodology, he mentions that incorrect responses typically produced auditory
feedback, frequently accompanied by a time-out period, but that no other
punitive method was used to promote productivity, accuracy or rapid
responding. Lastly, he describes evidence that the nonhumans are not only
motivated by food rewards, but also by the enjoyment of the tasks themselves:
when given a choice between completing trials for pellets or receiving pellets
for free but not being able to play the game-like tasks during the free-pellet
period, the monkeys chose to work for their reward.

The use of digital applications might benefit nonhuman in less directed ways
too, by raising awareness and respect of t their cognitive abilities among the
public. Coghlan et al. (2021b) examined how digital technologies can be used
to improve ethical attitudes towards nonhumans (focusing on nonhuman apes kept
in zoos) by introducing digital technologies in zoos for both animal
enrichment and visitor education. Both analogical and digital setups must be
careful to avoid experimental biases: we describe two particularly relevant
ones to this work in the next section.

###  2.4. Experimental Biases

The history of Comparative Psychology has been prone with fights about the
validity of methodologies and results: Pepperberg (2016) describes various
such tensions between researchers about the cognition of animals, with some
accusing other researchers in the field to be “ _liars, cheats and frauds_ ”,
and she highlights how sign language researchers were accused of “ _cuing
their apes by ostensive signals_ ” and of “ _consistently over-interpreting
the animals’ signs_ ”. We explore here two issues relevant to the
experimentation protocol described in this work, namely _selective reporting
bias_ (Section 2.4.1) and the _“Clever Hans” effect_ (Section 2.4.2).

####  2.4.1. Selective Reporting Bias

Selection biases occur in a survey or experimental data when the selection of
data points is not sufficiently random to draw a general conclusion. Selective
reporting biases are a specific form of selection bias whereby only
interesting or relevant examples are cited. Cognitive skills can be
particularly hard to study in nonhumans, requiring unconventional approaches
but often presenting the risk of such biases. For example, an experimenter who
would present a subject repeatedly with the same exercise could be tempted to
omit or exclude bad performances (eventually attributing them to a “bad mood”
of the subject, which stays a real possibility) and report only on good
performances, creating a biased representation of the abilities of the
subject, a selective reporting bias.

Whereas Bates and Byrne (2007) defends the use of anecdotes in comparative
psychology, he does so “ _provided certain conditions are met_ ” so that to
avoid such biases. defining an _anecdotal method_ in five steps:

  1. (1)

Source Material Assembly;

  2. (2)

Definition of the extraction process;

  3. (3)

Categorization of extracted records;

  4. (4)

Labeling of each record with a level of evidence (from ambiguous to highly
suggestive);

  5. (5)

Hypothesis generation to guide future studies.

He emphasises the “ _need to use neutral descriptions of behaviour that avoid
implicit interpretation, recorded by experienced and knowledgeable observers
immediately after the occurrence of the event._”, and that all observations of
rare events should be made available for later analysis by the anecdotal
method. We describe how to use a digital application to systematically log the
result and easily avoid such bias in Section 3. Another type of bias is that
of the subject reading cues from the experimenter, which we describe in the
next section.

####  2.4.2. “Clever Hans” effect

Among such methodological issues resulting in experimental biases, the most
iconic one might be the eponymous horse nicknamed “Clever Hans” which appeared
to be able to perform simple intellectual tasks, but in reality relied on
involuntary cues given by not only by their human handler, but also a variety
of human experimenters, as related by Trestman (2015):

> “ _In the early years of the 20th century an unlikely and controversial
> celebrity rose to fame in Germany and internationally: a horse, aptly named
> Clever Hans, who apparently displayed a startling aptitude in mathematics as
> well as music theory, not to mention the ability to identify colors and
> individual people by name, read German, and answer a variety of questions in
> normal spoken German. He responded to questions primarily via a code based
> on repeatedly tapping his right hoof, in combination with other responses
> such as nodding or shaking his head to indicate yes or no, and pointing to
> objects or photographs with his nose._ ”

The story is famous of course for how it illustrates how nonhumans can often
more easily learn to read cues from the experimenter than to solve the problem
asked from them. One ignores such rules not only at its own risk, but at the
risk of hurting a whole research area: in her recapitulation of the history of
animal language studies, Pepperberg (2016) describes how coverage of issues
about the validity of Comparative Psychology methodologies and results in the
public media in 1980 moved government agencies to respond to the blow-back by
cutting off the funding for all of the related studies. While issues such as
over interpreting subject’s signs or selectively reporting experimental
reports can be avoided with the appropriate amount of rigor (eventually with
some computerized help, as discussed in Section 6.1.8), avoiding having
subjects reading experimenter’s cues requires special care to be taken when
designing the experimental protocol: we describe in the next section some
guiding principles which exclude the very possibility of such biases from
experimentation results.

###  2.5. Masked Experimental Protocols

It is possible to avoid the confusion between a subject’s ability to read cues
from the experimenter from its ability to answer the tests presented to them
by such an experimenter. The principle is quite simple: make sure that the
experimenter does not know the test, by having a third party out of reach from
the subject’s reading to prepare the test. Whereas such experimental setup was
historically referred to as a ”Blind Setup” or a ”Blinded Setup”, we follow
the recommendations of Moris et al. (Morris D, 2007) and prefer the term of
”masked” to the term ”blind” when describing the temporary and purposeful
restricted access of the experimenter to the testing information.

In an analogical setting, the set-up of a masked experimental protocol is more
costly than that of less careful ones. For example, Cunha and Clubb (2018)
describe an experimental protocol where an assistant prepares a pile of prompt
cards, which the experimenter presents to the subject without looking at their
content until after the subject responded, in order to know whether to praise
and reward them or not. We describe our digital set-up for a masked
experimental protocol in Section 3.2: the digital device completely replaces
the assistant, and assists the experimenters, telling him whether the subject
answered correctly or not. As long as the device is placed in such a position
that the subject can see the visual display but the experimenter cannot, there
is physically no way for the subject to read cues from the experimenter, hence
avoiding the _“Clever Hans” effect_.

In the next section, we describe an application designed so that to facilitate
a type of “masked” experimental set-up, in which it is guaranteed that the
ability of the subject to read cues from the experimenter does not affect the
result of the experiment, as the experimenter himself ignores the question
(and hence its correct answer) being asked to the subject.

##  3\. Application

We developed a web application InCA-WhatIsMore as a simple combination of
JavaScript, CSS and HTML using libraries from the Svelte project, made
available on a simple web-page. While its simple structure (described in
Section 3.1) was originally developed as a simple mock-up to visualize how a
simple web application could help setting up masked experiments (described in
Section 3.2) with extensive logging abilities (described in Section 3.3), it
was found complete enough to be used as a final application, and the structure
to be simple enough that even the subjects themselves could navigate it.

###  3.1. Application’s Structure

The web application is composed of four views. The first two, the Main Menu
(described in Figures 12 and 16) and the Gaming View (which can be seen in
Figures 26 and 19 among others), are especially designed to be navigable by
nonhuman subjects. The access to the two others, the settings (see Figures 16
to 16) and the information views are tentatively restricted to the
experimenters by requesting the long pressing of a button.

Screenshot of the menu of the application “What is more”.  Screenshot of the
menu of the web application.

Figure 9. The main menu of the application is designed so that the subject can
choose in which visualisation mode it wishes to play, in the hope to support a
sense of agency.  Figure 10. The main menu of the application is designed so
that the subject can choose in which visualisation mode it wishes to play, in
the hope to support a sense of agency. The name of the application and the
collaborations were blurred to protect the anonymity of the submission.

Monk Parakeet choosing an option in the menu of the application “What is
More”.  Monk Parakeet choosing an option in the menu of the application.

Figure 11. Both subjects quickly learned to select a display mode to start a
game, but did not seem to show a preference for a display mode in particular.
Figure 12. Both subjects quickly learned to select a display mode to start a
game, but did not seem to show a preference for a display mode in particular.
The name of the application and the collaborations were blurred to protect the
anonymity of the submission.

Screenshot of the first third of the settings menu. Screenshot of the first
third of the settings menu, dedicated to the log generation.

Figure 13. The logs are exported in the top part of the setting page of the
application. Figure 14. The logs are exported in the top part of the setting
page of the application. The names were blurred to protect the anonymity of
the submission.

Screenshot of the second third of the settings menu, dedicated to the
appearance and difficulty of exercises.

Figure 15. The part of the setting page dedicated to the appearance and
difficulty of the exercises.

Screenshot of the last third of the settings menu, dedicated to game features
and sound feedback.

Figure 16. The part of the setting page dedicated to the game features and
sound feedback.

####  3.1.1. Main Menu

The view of the main menu is accessed when the application is opened: see
Figure 12 for a screenshot, and Figure 12 for a picture of a subject using it
to select a display mode. From this view, the user can navigate to the other
views of the application. On the center of the screen are four figures, each
one representing a different visualisation mode used on a random value. Two of
such modes are discrete: one is representing the value as a number of dots on
a dice face, the other on a 3 by 3 grid (as that of the dice) but as a heap of
dots. The two other modes are more continuous: one is representing each value
by a recipient more or less filled with liquid according to the value, the
other by a circle of radius growing with the value. The user (let it be the
experimenter or the subject) can pick any of the four display modes in order
to start the game in it. At the bottom of the screen stands a button to access
the settings section, activated after a long press (which length is set up in
the setting view).

####  3.1.2. Gaming view

The most important view is the gaming view, allowing the subject to “play”:
see Figure 26 for a screenshot, and Figures 2, 2, 23, 23, and 26 for pictures
of subjects playing the game. The view displays a set of values in some
display mode, requesting the user to choose the largest one. Each action
triggers an audio feedback, indicating if it was correct or wrong. After a
given number of exercises, the game ends and give an audio feedback about how
the score for this game placed with two boundaries (boundaries which can be
modified in the settings page, as well as the words being vocalized in each
audio feedback). The view has also an exit button on the top left corner
intended to be usable by the user, and a settings button actionable by long
pressing it by a parameterized amount of time.

####  3.1.3. Settings

Whereas the subject can choose the display mode in which they prefer to play,
and exit the game view to change it at any time, other settings are accessible
on a more technical view, designed for the experimenter to set-up other
aspects of the software: the settings view (Figures 16 and 16). As the visual
and sound outputs of touch screen devices were designed for humans, and as
very little is known about the adequateness of such outputs for nonhumans, the
software was designed so that to maximize the control given to each
experimenter on the visual and sound output of the application, so that each
experimenter can find the most adapted settings to the characteristics of the
species and/or subjects with which the software is used. As such, the software
permits the experimenter to change, among other things, the color schemes and
the number of the values displayed, the domain from which such values are
randomly chosen, and the number of questions before a game is ended: it is
hoped that such parameters will be useful in future studies.

####  3.1.4. About

This last view, a priory accessed only by the experimenters, displays various
information about the application, such as its version, an overview of
features soon to be added and recently added, instructions of usage use,
references and acknowledgments to collaborators.

We describe how to use such a web application so that to implement a masked
experimentation protocol where the subject cannot read any clue from the
experimenter, because the experimenter ignores the question given to the
subject.

###  3.2. Masked Experimental Setup

Among other features, the web application was designed to facilitate digital
experiments similar to that performed by Al Aïn et al. (2008) but in a way
such that the experimenter does _not_ know what side the “correct” answer is,
a masked experimental setup. This insures that the subject cannot receive any
voluntary or involuntary cue from the experimenter. Such a purpose is achieved
through the extensive audio feedback system, which aims at notifying the
experimenter about any event which requires their intervention (e.g. rewarding
or encouraging the subject, or acknowledging that the subject does not want to
play this game any more), so that they do not need to check the screen of the
device at any point.

Artistic Rendition of a Masked Experimental Setup.

Figure 17. The Masked Setup. The subject (left) can see the display and hear
the device (center), but the experimenter (right) can only hear the device and
not see its display.

Picture of a Masked Experimental Setup with one Monk Parrot, one digital
device, and one experimenter who cannot see the screen of the device.

Figure 18. Example of masked experimental set-up: the experimenter can hear
the instructions from the device and encourage the subject, but cannot give
any cue about correct answers.

Picture of the experimenter’s view in a Masked Experimental Setup with two
Monk Parrots and two digital devices.

Figure 19. The masked experimental set-up as viewed by the experimenter, with
two subjects participating in the experiment at the same time, each with its
own device.

###  3.3. Logging structure

In non digital experiments in comparative psychology, the experiments is
usually recorded on video so that the video recording can be later processed
in order to generate an extensive log of the interactions of the subject
during the experiment. Such a task is long and tedious, and no video
processing software is yet able to automatize such a process. An important
advantage of a digital experimental set-up such as that allowed by the
software InCA-WhatIsMore is the ability to _automatically_ log the
interactions of the subject with the application.

The logs are exported in the top part of the setting page of the application
(previously described in Figure 16, on page 16). Two formats are available:
the first format, .txt is designed to be easily readable by humans; while the
second format, .csv is more adequate for machine processing. The software
InCA-WhatIsMore generates logs with data to be analyzed by researchers,
including information on both the test performed and the subject’s performance
(see Figure 21 for a short extract, and Figure 27 for a longer one).

Test no, Test Name, Learner, Trainer, C_0, C_1, C_2, C_3, C_4, Value selected
, Correction , Date, Answering Time (ms), Other Parameters 1, dice, Subject,
Experimenter, 1,4,,,, 4,true, [2022-05-19 17:02(25.981)], 7946, background
black, foreground green, bg opacity .2, Value Set [1,2,3,4,5] (...) 81, rect,
Subject, Experimenter, 4,2,3,,, 3,false, [2022-05-19 17:26(55.124)], 4655,
background black, foreground green, bg opacity .2, Value Set [1,2,3,4,5] (...)
180, heap, Subject, Experimenter, 3,2,1,,, 2,false, [2022-05-19 17:35(06.6)],
926, background black, foreground green, bg opacity .2, Value Set [1,2,3,4,5]

Figure 20. A short extract showing four selected lines of the log generated by
the application for the afternoon session of the 19th of May 2022 (deleted
blocks of lines are marked by “(...)”). See Figure 21 for a more readable
reformatting of the same extract. Log entries such as “background black,
foreground green, bg opacity .2” refer to visualisation options, not used in
this work.

Test no | Test Name | C0 | C1 | C2 | C3 | C4 | Value selected | Correction | Date | Other Parameters
---|---|---|---|---|---|---|---|---|---|---
1 | dice | 1 | 4 |  |  |  | 4 | true | [2022-05-19 17:02(25.981)] | Value Set [1,2,3,4,5]
81 | rect | 4 | 2 | 3 |  |  | 3 | false | [2022-05-19 17:26(55.124)] | Value Set [1,2,3,4,5]
180 | heap | 3 | 2 | 1 |  |  | 2 | false | [2022-05-19 17:35(06.6)] | Value Set [1,2,3,4,5]

Figure 21. A more readable format of the log extract from Figure 20, with less
relevant columns removed for readability. Observe that the subject was offered
to choose the largest between 2 (on the first test) and 3 (on the $81$st and
$180$th tests) values, represented as dice (first test), rect ($81$st test)
and heap ($180$th test), and that the subject chose once correctly, and two
times incorrectly, in games where the values were taken from the set
$\\{1,2,3,4,5\\}$, with the precise time and date of each answer duly
recorded. The columns labeled C3 and C4 are empty because no test was
performed requesting the subject to choose the maximal value between 4 or 5.

We describe here the format of the logs in versions $2.x$ of the software. The
first three rows generated within the log indicate information about the test:

  * •

Test Name: The test performed, the value is the type of representation, this
can be ”dice”, ”heap”, ”rect” or ”disc”.

  * •

Learner: The name of the test subject, used to subsequently run analyses such
as performance over time or to differentiate its statistics.

  * •

Trainer: The name of the experimenter. This could be used in later studies
where various experimenters apply the same test to the same subject, to check
for variance in performance from one experimenter to the other.

The following columns indicate quantitative information about the distribution
of quantities within the test, as well as information about the test subject’s
performance.

  * •

C0,C1,C2,C3: The qualitative representation of the quantities delivered, these
can be discrete or their representation in continuous quantities, the order of
distribution of these quantities also indicates the order deployed within the
application, the values being ordered from left to right.

  * •

Value Selected:  The value chosen by the test subject.

  * •

Correction:  The correctness of the value selected by the test subject, being
”true” if it is the largest amount and ”false” otherwise.

The last columns indicate qualitative values about the test, these values
provide information about both the performance and the setup of the test.

  * •

Date: The date on which the test was performed, in timestamp format, including
the precise time in milliseconds.

  * •

Answering Time (ms): The time it takes for the test subject to respond from
the display of the quantities to be chosen, represented in milliseconds. Note
that this is more precise than the simple difference between the times of two
consecutive time stamps, as the application includes (parameterizable) waiting
time between tests, a pause between games, break to return to the menu, etc.

  * •

Other Parameters: Parameters that visually describe the display of the
quantities, such as the color of the background and the color in which the
representations of the quantities are displayed. These parameters were
modified only in the development phase in order to find an adequate color
scheme for the two subjects in particular (see Section 6.2.3 for a discussion
of the sensory variability of general test subjects), but could be used in the
future to adapt the software to other individuals, potentially from other
species with distinct sensory ranges; and to formally study (ethically, see
Section 6.3.5 for a discussion of the related challenges) the limits of the
sensory range of any subject.

In the next section, we describe the training and experimental protocol which
was used to generate the data measured by such logs.

##  4\. Experimentation Protocol

The experimental protocol was divided in three phases, which we describe in
Section 4.1. The precautions taken to protect the well-being of the nonhuman
subjects (described in Section 4.2) were validated by the Institutional Animal
Care and Use Committee (IACUC) (in Spanish “COMITÉ INSTITUCIONAL de CUIDADO y
USO de ANIMALES (CICUA)”) of the researcher’s institution. The statistical
analysis (described in Section 4.3) were scheduled as part of the experimental
protocol, independently from the results of the experiments.

###  4.1. Phases of the protocol

The protocol was implemented in three phases: a phase of _development_ (of the
software) with only one subject (the first one), a phase of _training_ with
two subjects and a mix of unmasked and masked protocols, and a phase of
_testing_ using the masked protocol and collecting data with both subjects.

  * •

During the _development phase_ , a single subject (hereafter referred to as
“the first subject”) interacted with the various prototypes of the software,
in a non masked experimental setting where the experimenter could observe the
display of the screen. Each time the software was modified, it was tested by
two humans subjects before being used by any of the nonhuman subjects, in
order to minimize the potential frustration of the nonhuman subjects while
using a malfunctioning application.

  * •

During the _training phase_ , both subjects were invited to use the software,
each on its own device, in a non masked experimental setting where the
experimenter could observe the display of the screen: see Figures 2, 2, 23,
23, and 26 for pictures of the set-up during the training phase.

  * •

During the _testing phase_ , both subjects were invited to use the software,
each on its own device, this time in a masked experimental setting where the
experimenter could not observe the display of the screen, so that they ignored
the question asked to each subject and could not cue them, and limiting
themselves to encourage and reward each subject according to the feedback
vocalized by the application (see Figures 19 to 19, on page 19, for examples
of masked experimental setups).

The subjects’ welfare was cared for during each of those three phases: we
describe some of the precautions taken in the next section.

###  4.2. Ethical Precautions

Various precautions were taken to protect both the physical (Section 4.2.1)
and psychological well-being (Sections 4.2.2, 4.2.3 and 4.2.5) of the subjects
during the three phases of the project.

develop how this is in accordance both with the recommendations from Mancini
et al.(2022-FVS-
TheCaseForAnimalPrivacyInTheDesignOfTechnologicallySupportedEnvironments-
PaciManciniNuseibeh; 2022-FAS-
RelevanceImpartialityWelfareAndConsentPrinciplesOfAnAnimalCenteredResearchEthics-
ManciniNannoni; 2019-ACI-AMethodForEvaluatingAnimalUsability-RugeMancini;
Mancini, 2017; 2016-ACMI-
IntroductionFrameworksForACIAnimalsAsStakeholdersInTheDesignProcess-
NorthMancini) and the ACI board, and in the interest of the validity of the
experience and the mental health of the researchers.

Mention 2021-Area-BeyondHumanEthics-Oliver (2019-ACI-
AMethodForEvaluatingAnimalUsability-RugeMancini) (Mancini, 2017)

####  4.2.1. Physical settings

The subjects were hosted in a private residence counting with three aviaries,
each large enough to allow some amount of flight: one “laboratory” building
with meshed windows containing a “Nest” aviary with a simple door, of size
$3\times 1\mbox{m}^{2}$ and $2\mbox{m}$ high, containing a nest, a plant and
various toys and nesting material; one “South” aviary, corridor shaped with
two sets of double doors, of $6\times 1\mbox{m}^{2}$ of surface size and
$2\mbox{m}$ high; and one “North” aviary with one set of double doors, of
$6\times 3\mbox{m}^{2}$ of surface size and $1\mbox{m}$ high. The subjects
were mostly hosted in the “Nest” aviary, but transported to other aviaries
(with their consent) to allow them to fly on slightly larger distances (6m),
getting sun exposure, access distinct physical games and more generally to
vary their stimuli. The sessions of the development, training and testing
phases were almost always realized in a training area next to the opening of
the “Nest” aviary, and in a few occasions insider the larger “North” aviary.
At no point were the subjects food or water deprived: at any point they could
fly to their housing space, where food and water was available. The sessions
always occurred on one of three similar wood frames (see Figure 23), so that
to offer a familiar setting even when the location of the training changed
(e.g. in the “North” aviary). Even though the digital devices had to be
replaced at some point, those were always hold on the same wood structure
(etched with the name of the subject to which it was assigned), so that to
facilitate the recognition of which device was assigned to which subject. The
subjects were weighted on a weekly basis to detect any variation which could
indicate a potential health issue, and brought to a licensed veterinarian
twice a year.

Picture of the experimental set-up in the learning phase, with two devices
side by side and one Monk Parrot interacting with the right one.

Figure 22. Each subject disposes of its own device, placed on wood supports of
distinct sizes, each etched with the name of the subject to which it is
assigned.

Picture of a Monk Parakeet interacting with its assigned device, on a support
at its name.

Figure 23. Each device is placed on a wood support (as opposed to carried by
the experimenter), at a height comfortable to the subject, making the subject
as autonomous as possible.

####  4.2.2. Application Usability

Summarize 2019-ACI-AMethodForEvaluatingAnimalUsability-RugeMancini’s rules. In
order to minimize the potential frustration of the subjects when facing
inadequate answers from the application, each version of the application was
systematically tested by two human subjects, and any issue detected during
such a phase corrected, before being presented to the nonhuman subjects.
During the phase of software development, when a feature of the application
(whether due to an error or to an setting proved to be inadequate) was
encountered to frustrate the subjects, the use of this application was
replaced by another activity until the software was corrected, tested and
separately validated by two human subjects.

####  4.2.3. Sense of Agency

Both physical and virtual aspects of the protocol were designed so that to
maintain a sense of agency in the subjects. READ and maybe mention the last
(April 2022) article from 2022-FAS-
RelevanceImpartialityWelfareAndConsentPrinciplesOfAnAnimalCenteredResearchEthics-
ManciniNannoni about consent The physical setting of the experimentation was
designed so that to insure that the subject’s participation was voluntary
during all three phases of the process: the subjects were invited to come to
the training area (but could, and sometime did, refuse); at any time the
subjects could fly from the training area back to their aviary, to a
transportation pack with a large amount of seeds suspended above the training
area, or to an alternate training area on the side, presenting an alternate
choice of training exercises. Concerning the psychological aspects, the main
menu of the application was designed so that each subject can choose in which
visualisation mode they wish to play (see Figures 12 and 12), and a large
orange “exit” button is present on the playing screen allowing the subject to
signal that they do not wish to play this game any more, prompting the
experimenter to propose alternatives.

Screenshot of the game view of the application.

Figure 24. A screenshot of the game view of the application, asking to choose
the largest disk out of four. Top left is the orange “Exit” button actionable
by the subject. Bottom right is the setting button requesting a long pressure
to be activated. Bottom center is a summary of the game score.

Picture of a Monk Parakeet interacting with the game view of the application,
with the display mode “Disc”.

Figure 25. Monk Parakeet selecting the largest disc out of four. Figure 26.
The Monk Parakeet Lorenzo selecting the largest disc out of four.

The page to adjust parameters controlling the difficulty (e.g. domain and
number of values displayed, length of a game, etc.) of the games, more complex
display and sound choices (e.g. colors and spaces being used in the display,
words pronounced by the software in various situations, etc.), and the details
about the application logs, is accessed via a special button requiring a
longer press, making it harder to access to nonhuman subjects.

####  4.2.4. Nonhuman Privacy issues

Summarize (2022-FVS-
TheCaseForAnimalPrivacyInTheDesignOfTechnologicallySupportedEnvironments-
PaciManciniNuseibeh) and justify that the log data does not constitute
information which could be inferred to be considered private by the nonhuman
subjects.

####  4.2.5. Approval of the experimental protocol by CICUA

All interactions with animals were governed by a protocol reviewed and
approved by the Institutional Animal Care and Use Committee (IACUC) (in
Spanish “COMITÉ INSTITUCIONAL de CUIDADO y USO de ANIMALES (CICUA)”) of the
researchers’ institution, through a form of Experimentation Protocol of
Management and Care of Animals (“Protocolo de Manejo y Cuidado de Animales”).

###  4.3. Statistical Analysis Process

The statistical analysis of the experimental results was designed as part of
the experimental protocol, with the objectives to compute the accuracy of each
subject for each display mode and each size of the set of values presented to
the subject (Section 4.3.1), to compare it with the accuracy of selecting a
value uniformly at random (Section 4.3.2) and to search for correlation
between the answer’s accuracy and some measure on the values presented
(Section 4.3.3).

####  4.3.1. Statistical tools used

The statistical analysis was performed in a python notebook, executed and
shared via the collaborative website https://colab.research.google.com: this
platform was chosen because it is easy to collaborate among peers as well as
to run and replicate statistical analyses. Such python notebook was developed
and tested on the logs generated during the (masked and unmasked) training
sessions, to be used later without major modification on the logs generating
during the masked experimental sessions of the testing phase. The computation
made use of the following libraries:

  * •

pandas is a library written as an extension of numpy to facilitate the
manipulation and analysis of data.

  * •

seaborn and matplotlib are libraries for the visualisation of statistical
data. seaborn was used for the creation of correlation graphs and matplotlib
for heat maps.

  * •

scipy is a free and open source library for Python. It consists of
mathematical tools and algorithms, from this library we use scipy.stats for
the chi-square and binomial tests.

The python notebook operates on the log files via the pandas library. These
logs can be worked individually or concatenated to obtain a large overall
analysis of the test subject.

####  4.3.2. Binomial Tests

The average accuracy of each subject for each display mode and each size of
the set of values presented to the subject is then the average of the
Correction entry in the log (replacing True by $1$ and False by $0$) over all
data points matching the criteria. For each such accuracy, we performed a
binomial test in order to decide if such accuracy was substantially better
than that achieved by selecting a value uniformly at random. To calculate the
binomial test we count the ”success” among all the points of the dataset, and
apply the binom_test method in scipy.
$p=binom\\_test(k,n,prob,alternative=^{\prime}greater^{\prime})$, where $k$ is
the total number of successes, $n$ is the total number of attempts, over tests
selecting the maximal value out of two, $prob=0.5$; over tests selecting the
maximal value out of three, $prob=0.33$; and over tests selecting the maximal
value out of four, $prob=0.25$. The greater alternative is used since we are
looking for an accuracy greater or equal to $50\%$ , $33\%$ and $25\%$
respectively. We performed such statistical analysis on the data of each
particular session and on their union, on each particular visualization mode
and on the type of visualisation mode (discrete or continuous) and on all
visualisation modes (see Tables 2, 3, 5 and 6).

####  4.3.3. Pearson Correlation Analysis

In order to compare our results with that of Al Aïn et al. (2008)’s
experiments, we performed a Pearson correlation analysis of the relation
between the accuracy of the subjects’ answers when asked to select the maximal
out of two values on one hand, and the three variables they considered on the
other hand:

  * •

the _sum_ of the values for each test (e.g. from $1+2=3$ to $4+5=9$),

  * •

the _difference_ between the two extreme values presented within a trial (e.g.
from $1$ to $5-1=4$) and

  * •

the _ratio_ of continuous quantities presented, by dividing the smallest
presented value by the largest one (e.g. from $\frac{1}{5}=0.2$ to
$\frac{4}{5}=0.8$).

We describe the results of the experiments and their statistical analysis in
the next section.

##  5\. Results

After relatively long phases of development and training (15 months) using
various domains of values (from $\\{0,1\\}$ to $\\{0,1,\ldots,9\\}$), the
experimental phase was quite short (one week), with all experiments performed
using a masked setup and a domain of values restricted to the set
$\\{1,2,3,4,5\\}$ in order to stay as close as possible to the settings of Al
Aïn et al. (2008)’s study. We summarize the number and content of the logs
obtained (Section 5.1), perform binomial tests on the experimental results
when choosing the maximal value out of two for both subjects (Section 5.2),
perform binomial tests on the experimental results when choosing the maximal
value out of three and four for the first subject (Section 5.3), and perform
various correlation tests between the performance of the subjects and the
_sum_ , _difference_ and _ratio_ of the values presented (Section 5.2.3).

###  5.1. Log results

A testing session typically lasts some 5 to 10 games of 20 questions each,
resulting into a log of 100 to 200 data points: see Figures 20 and 21 for a
shortened example of log, and Figure 27 for a longer one.

Test no, Test Name, Learner, Trainer, C_0, C_1, C_2, C_3, C_4, Value selected
, Correction , Date, Answering Time (ms), Other Parameters 1, dice, Subject,
Experimenter, 1,4,,,, 4,true, [2022-05-19 17:02(25.981)], 7946, background
black, foreground green, bg opacity .2, Value Set [1,2,3,4,5] 2, dice,
Subject, Experimenter, 1,5,,,, 5,true, [2022-05-19 17:02(30.82)], 3095,
background black, foreground green, bg opacity .2, Value Set [1,2,3,4,5] 3,
dice, Subject, Experimenter, 3,4,,,, 4,true, [2022-05-19 17:02(39.70)], 7981,
background black, foreground green, bg opacity .2, Value Set [1,2,3,4,5] 4,
dice, Subject, Experimenter, 1,4,,,, 4,true, [2022-05-19 17:02(46.295)], 6217,
background black, foreground green, bg opacity .2, Value Set [1,2,3,4,5] 5,
dice, Subject, Experimenter, 2,5,,,, 5,true, [2022-05-19 17:02(51.633)], 4331,
background black, foreground green, bg opacity .2, Value Set [1,2,3,4,5] 6,
dice, Subject, Experimenter, 3,1,,,, 1,false, [2022-05-19 17:03(00.79)], 7440,
background black, foreground green, bg opacity .2, Value Set [1,2,3,4,5] 7,
dice, Subject, Experimenter, 4,1,,,, 1,false, [2022-05-19 17:03(02.938)],
1852, background black, foreground green, bg opacity .2, Value Set [1,2,3,4,5]
8, dice, Subject, Experimenter, 1,2,,,, 2,true, [2022-05-19 17:03(06.86)],
2141, background black, foreground green, bg opacity .2, Value Set [1,2,3,4,5]
9, dice, Subject, Experimenter, 3,2,,,, 2,false, [2022-05-19 17:03(13.478)],
6383, background black, foreground green, bg opacity .2, Value Set [1,2,3,4,5]
10, dice, Subject, Experimenter, 4,5,,,, 5,true, [2022-05-19 17:03(16.578)],
2094, background black, foreground green, bg opacity .2, Value Set [1,2,3,4,5]
11, dice, Subject, Experimenter, 4,5,,,, 5,true, [2022-05-19 17:03(20.412)],
2826, background black, foreground green, bg opacity .2, Value Set [1,2,3,4,5]
12, dice, Subject, Experimenter, 1,4,,,, 4,true, [2022-05-19 17:03(28.740)],
7321, background black, foreground green, bg opacity .2, Value Set [1,2,3,4,5]
13, dice, Subject, Experimenter, 1,2,,,, 2,true, [2022-05-19 17:03(40.376)],
10629, background black, foreground green, bg opacity .2, Value Set
[1,2,3,4,5] 14, dice, Subject, Experimenter, 1,2,,,, 2,true, [2022-05-19
17:03(53.7)], 11624, background black, foreground green, bg opacity .2, Value
Set [1,2,3,4,5] 15, dice, Subject, Experimenter, 4,2,,,, 2,false, [2022-05-19
17:03(57.33)], 3018, background black, foreground green, bg opacity .2, Value
Set [1,2,3,4,5] 16, dice, Subject, Experimenter, 5,1,,,, 1,false, [2022-05-19
17:04(00.23)], 1984, background black, foreground green, bg opacity .2, Value
Set [1,2,3,4,5] 17, dice, Subject, Experimenter, 2,3,,,, 3,true, [2022-05-19
17:04(03.156)], 2127, background black, foreground green, bg opacity .2, Value
Set [1,2,3,4,5] 18, dice, Subject, Experimenter, 4,1,,,, 1,false, [2022-05-19
17:04(07.608)], 3443, background black, foreground green, bg opacity .2, Value
Set [1,2,3,4,5] 19, dice, Subject, Experimenter, 4,3,,,, 3,false, [2022-05-19
17:04(11.969)], 3354, background black, foreground green, bg opacity .2, Value
Set [1,2,3,4,5] 20, dice, Subject, Experimenter, 2,3,,,, 3,true, [2022-05-19
17:04(16.363)], 3386, background black, foreground green, bg opacity .2, Value
Set [1,2,3,4,5] 21, rect, Subject, Experimenter, 4,5,,,, 5,true, [2022-05-19
17:04(31.694)], 7191, background black, foreground green, bg opacity .2, Value
Set [1,2,3,4,5] 22, rect, Subject, Experimenter, 3,4,,,, 4,true, [2022-05-19
17:04(36.330)], 3629, background black, foreground green, bg opacity .2, Value
Set [1,2,3,4,5] 23, rect, Subject, Experimenter, 5,1,,,, 1,false, [2022-05-19
17:04(43.148)], 5810, background black, foreground green, bg opacity .2, Value
Set [1,2,3,4,5] 24, rect, Subject, Experimenter, 4,2,,,, 2,false, [2022-05-19
17:04(44.926)], 772, background black, foreground green, bg opacity .2, Value
Set [1,2,3,4,5] 25, rect, Subject, Experimenter, 1,5,,,, 5,true, [2022-05-19
17:04(46.731)], 798, background black, foreground green, bg opacity .2, Value
Set [1,2,3,4,5] 26, rect, Subject, Experimenter, 1,5,,,, 5,true, [2022-05-19
17:04(51.117)], 3380, background black, foreground green, bg opacity .2, Value
Set [1,2,3,4,5] 27, rect, Subject, Experimenter, 1,5,,,, 5,true, [2022-05-19
17:04(55.855)], 3730, background black, foreground green, bg opacity .2, Value
Set [1,2,3,4,5] 28, rect, Subject, Experimenter, 1,4,,,, 4,true, [2022-05-19
17:05(00.581)], 3718, background black, foreground green, bg opacity .2, Value
Set [1,2,3,4,5] 29, rect, Subject, Experimenter, 3,2,,,, 3,true, [2022-05-19
17:05(05.74)], 3487, background black, foreground green, bg opacity .2, Value
Set [1,2,3,4,5] 30, rect, Subject, Experimenter, 2,4,,,, 4,true, [2022-05-19
17:05(08.885)], 2803, background black, foreground green, bg opacity .2, Value
Set [1,2,3,4,5] 31, rect, Subject, Experimenter, 3,5,,,, 3,false, [2022-05-19
17:05(16.709)], 6818, background black, foreground green, bg opacity .2, Value
Set [1,2,3,4,5] 32, rect, Subject, Experimenter, 4,1,,,, 4,true, [2022-05-19
17:05(18.396)], 678, background black, foreground green, bg opacity .2, Value
Set [1,2,3,4,5] 33, rect, Subject, Experimenter, 4,2,,,, 2,false, [2022-05-19
17:05(22.709)], 3306, background black, foreground green, bg opacity .2, Value
Set [1,2,3,4,5] 34, rect, Subject, Experimenter, 5,3,,,, 3,false, [2022-05-19
17:05(25.95)], 1380, background black, foreground green, bg opacity .2, Value
Set [1,2,3,4,5] 35, rect, Subject, Experimenter, 5,2,,,, 5,true, [2022-05-19
17:05(29.448)], 3347, background black, foreground green, bg opacity .2, Value
Set [1,2,3,4,5] (...) 145, disc, Subject, Experimenter, 4,2,1,,, 2,false,
[2022-05-19 17:32(07.287)], 802, background black, foreground green, bg
opacity .2, Value Set [1,2,3,4,5] 146, disc, Subject, Experimenter, 5,4,3,,,
4,false, [2022-05-19 17:32(26.796)], 18496, background black, foreground
green, bg opacity .2, Value Set [1,2,3,4,5] 147, disc, Subject, Experimenter,
4,5,1,,, 5,true, [2022-05-19 17:32(32.142)], 4334, background black,
foreground green, bg opacity .2, Value Set [1,2,3,4,5] 148, disc, Subject,
Experimenter, 3,5,4,,, 5,true, [2022-05-19 17:32(43.167)], 10015, background
black, foreground green, bg opacity .2, Value Set [1,2,3,4,5] 149, disc,
Subject, Experimenter, 5,4,1,,, 5,true, [2022-05-19 17:32(51.628)], 7448,
background black, foreground green, bg opacity .2, Value Set [1,2,3,4,5] 150,
disc, Subject, Experimenter, 4,2,5,,, 5,true, [2022-05-19 17:32(55.922)],
3283, background black, foreground green, bg opacity .2, Value Set [1,2,3,4,5]
151, disc, Subject, Experimenter, 5,2,3,,, 5,true, [2022-05-19 17:33(00.783)],
3850, background black, foreground green, bg opacity .2, Value Set [1,2,3,4,5]
152, disc, Subject, Experimenter, 1,4,2,,, 4,true, [2022-05-19 17:33(05.553)],
3757, background black, foreground green, bg opacity .2, Value Set [1,2,3,4,5]
153, disc, Subject, Experimenter, 5,1,4,,, 4,false, [2022-05-19
17:33(08.485)], 1921, background black, foreground green, bg opacity .2, Value
Set [1,2,3,4,5] 154, disc, Subject, Experimenter, 5,1,3,,, 5,true, [2022-05-19
17:33(10.272)], 778, background black, foreground green, bg opacity .2, Value
Set [1,2,3,4,5] 155, disc, Subject, Experimenter, 1,5,3,,, 5,true, [2022-05-19
17:33(15.484)], 4204, background black, foreground green, bg opacity .2, Value
Set [1,2,3,4,5] 156, disc, Subject, Experimenter, 5,4,3,,, 4,false,
[2022-05-19 17:33(19.152)], 2658, background black, foreground green, bg
opacity .2, Value Set [1,2,3,4,5] 157, disc, Subject, Experimenter, 4,2,3,,,
3,false, [2022-05-19 17:33(22.15)], 1853, background black, foreground green,
bg opacity .2, Value Set [1,2,3,4,5] 158, disc, Subject, Experimenter,
1,5,3,,, 5,true, [2022-05-19 17:33(24.137)], 1111, background black,
foreground green, bg opacity .2, Value Set [1,2,3,4,5] 159, disc, Subject,
Experimenter, 2,3,5,,, 5,true, [2022-05-19 17:33(27.386)], 2240, background
black, foreground green, bg opacity .2, Value Set [1,2,3,4,5] 160, disc,
Subject, Experimenter, 3,1,4,,, 3,false, [2022-05-19 17:33(30.852)], 2456,
background black, foreground green, bg opacity .2, Value Set [1,2,3,4,5] 161,
heap, Subject, Experimenter, 5,1,3,,, 5,true, [2022-05-19 17:33(40.558)],
3063, background black, foreground green, bg opacity .2, Value Set [1,2,3,4,5]
162, heap, Subject, Experimenter, 4,1,2,,, 4,true, [2022-05-19 17:33(46.447)],
4879, background black, foreground green, bg opacity .2, Value Set [1,2,3,4,5]
163, heap, Subject, Experimenter, 3,4,2,,, 4,true, [2022-05-19 17:33(51.684)],
4225, background black, foreground green, bg opacity .2, Value Set [1,2,3,4,5]
164, heap, Subject, Experimenter, 2,1,4,,, 4,true, [2022-05-19 17:33(54.658)],
1963, background black, foreground green, bg opacity .2, Value Set [1,2,3,4,5]
165, heap, Subject, Experimenter, 2,3,4,,, 4,true, [2022-05-19 17:33(59.410)],
3741, background black, foreground green, bg opacity .2, Value Set [1,2,3,4,5]
166, heap, Subject, Experimenter, 2,1,3,,, 2,false, [2022-05-19
17:34(03.670)], 3247, background black, foreground green, bg opacity .2, Value
Set [1,2,3,4,5] 167, heap, Subject, Experimenter, 5,4,3,,, 3,false,
[2022-05-19 17:34(05.808)], 1128, background black, foreground green, bg
opacity .2, Value Set [1,2,3,4,5] 168, heap, Subject, Experimenter, 2,3,1,,,
3,true, [2022-05-19 17:34(07.846)], 1029, background black, foreground green,
bg opacity .2, Value Set [1,2,3,4,5] 169, heap, Subject, Experimenter,
2,3,5,,, 5,true, [2022-05-19 17:34(19.932)], 11078, background black,
foreground green, bg opacity .2, Value Set [1,2,3,4,5] 170, heap, Subject,
Experimenter, 2,3,4,,, 4,true, [2022-05-19 17:34(25.404)], 4462, background
black, foreground green, bg opacity .2, Value Set [1,2,3,4,5] 171, heap,
Subject, Experimenter, 1,5,2,,, 5,true, [2022-05-19 17:34(31.359)], 4945,
background black, foreground green, bg opacity .2, Value Set [1,2,3,4,5] 172,
heap, Subject, Experimenter, 1,4,5,,, 5,true, [2022-05-19 17:34(35.552)],
3182, background black, foreground green, bg opacity .2, Value Set [1,2,3,4,5]
173, heap, Subject, Experimenter, 2,4,3,,, 4,true, [2022-05-19 17:34(39.311)],
2747, background black, foreground green, bg opacity .2, Value Set [1,2,3,4,5]
174, heap, Subject, Experimenter, 2,4,3,,, 4,true, [2022-05-19 17:34(44.188)],
3867, background black, foreground green, bg opacity .2, Value Set [1,2,3,4,5]
175, heap, Subject, Experimenter, 5,3,1,,, 5,true, [2022-05-19 17:34(48.508)],
3308, background black, foreground green, bg opacity .2, Value Set [1,2,3,4,5]
176, heap, Subject, Experimenter, 3,4,2,,, 4,true, [2022-05-19 17:34(53.468)],
3950, background black, foreground green, bg opacity .2, Value Set [1,2,3,4,5]
177, heap, Subject, Experimenter, 3,2,5,,, 5,true, [2022-05-19 17:34(56.511)],
2032, background black, foreground green, bg opacity .2, Value Set [1,2,3,4,5]
178, heap, Subject, Experimenter, 5,2,4,,, 4,false, [2022-05-19
17:35(02.323)], 4802, background black, foreground green, bg opacity .2, Value
Set [1,2,3,4,5] 179, heap, Subject, Experimenter, 5,2,4,,, 4,false,
[2022-05-19 17:35(04.70)], 737, background black, foreground green, bg opacity
.2, Value Set [1,2,3,4,5] 180, heap, Subject, Experimenter, 3,2,1,,, 2,false,
[2022-05-19 17:35(06.6)], 926, background black, foreground green, bg opacity
.2, Value Set [1,2,3,4,5]

Figure 27. A page long example of log generated by the application, obtained
by taking the 35 first and last entries of the log of the masked session on
the afternoon of the 19th of May 2022. One can observe that the session
started with two games selecting the largest of two values, displayed as dice
and as rectangles, and ended with two games selecting the largest of three
values, displayed as discs and heaps.

The testing phase occurred between the 19th of May 2022 and the 26th of May
2022. These experiments used four different display modes (“Dice”, “Heap”,
“Disc” and “Rectangle”), requesting the subject to select the maximal value
out of a set of 2, 3 or 4 values, randomly chosen among a set of five values
$\\{1,2,3,4,5\\}$, in order to produce a setup relatively similar to that of
Al Aïn et al. (2008), with the vast majority of experiments selecting the
maximal out of two values, and only a few out of three or four values. Each
log corresponds to a separate training session and device, containing between
80 and 400 entries (each entry being a separate question and answer). In
total, 14 logs were collected for the first subject, and 5 logs were collected
for the second subject: the first subject was requested to select the maximal
value out of 2,3 or 4 values, while the second subject was requested to select
the maximal value only out of 2 values. Concerning the selection of the
maximal out of 2 values (the setting the most similar to that of Al Aïn et al.
(2008)), the first subject answered 449 dice tests, 400 heap tests, 262
rectangle tests and 103 disc tests, making a total of 1214 tests, while the
second subject answered 190 dice tests 26 rectangle tests and 193 disc tests
making a total of 409 tests. Concerning the selection of the maximal out of 3
values, the first subject answered 249 dice tests, 120 heap tests, 120
rectangle tests, and 99 disc tests, making a total of 588 tests. Concerning
the selection of the maximal out of 4 values, the first subject answered 154
dice tests, 51 heap tests, and 13 disc tests, making a total of 218 tests.

See Table 1 for a summary of the number of data points collected separated by
display modes (“Dice”, “Heap”, “Disc” and “Rectangle”), accumulated by the
type of display mode (“Discrete” or “Continuous”) and accumulated over all
display modes (“Total”). Even though the care to respect the agency of the
subjects introduced great imbalances between the number of data points
collected for each display mode and set size, 2429 data points were gathered
in only one week, through voluntary participation in the subject: this is much
higher than what could be achieved in the same amount of time via traditional
analogical protocols such that of Al Aïn et al. (2008).

Subject | Set Size | Dice | Heap | Discrete | Disc | Rectangle | Continuous | Total
---|---|---|---|---|---|---|---|---
1 | 2 | 449 | 400 | 849 | 103 | 262 | 448 | 1214
1 | 3 | 249 | 120 | 0 | 126 | 120 | 0 | 588
1 | 4 | 154 | 51 | 205 | 13 | 0 | 13 | 218
2 | 2 | 190 | 0 | 190 | 193 | 26 | 219 | 409
1 | total | 852 | 571 | 1054 | 242 | 382 | 461 | 2020
2 | total | 190 | 0 | 190 | 193 | 26 | 219 | 409
total | total | 1042 | 644 | 1244 | 435 | 468 | 680 | 2429
Table 1. Number of data points collected separated by display modes (“Dice”,
“Heap”, “Disc” and “Rectangle”), accumulated by the type of display mode
(“Discrete” or “Continuous”) and accumulated over all display modes (“Total”).
The imbalance between the frequencies of the display modes and between the
amounts of test results for each subjects is explained by the care to support
the agency of the subjects: they could interrupt the session at any time, and
had the option to choose the display mode at any time (even though they seldom
did).

We analyze those results statistically in the following sections.

###  5.2. Selecting the maximal value out of two

Both subjects played the game in the four display modes, the first subject
showing much more interest in participating than the second one, but none of
them marking a particular preference for any display mode. The first subject
showed an average accuracy of $81.79\%$ (Section 5.2.1), the second subject an
average accuracy of $74\%$ (Section 5.2.2). Both performed better when the
values were very different and worse when the values were close (Section
5.2.3), exactly as the three African Grey parrots in (Al Aïn et al., 2008)’s
study.

####  5.2.1. First Subject

The results show a clear ability from the first subject to discriminate the
maximal value out of two quantities. Over all experimentations requesting to
select the maximal value out of two, the first subject responded correctly
$993$ times out of a total of $1214$ trials, corresponding to an average
accuracy of $81.79\%$. A simple binomial tests indicates that the probability
to achieve such an accuracy by answering uniformly at random $1214$ such
binary questions is $p=1.95\cdot 10^{-117}$ (see Table 2 for a more detailed
description of the results, by session and by display mode). It is very likely
that the subject did _not_ answer uniformly at random. Lacking a bias in the
experimental protocol, this seems to indicate a clear ability to discriminate
between the two values being presented.

Analyzing separately the results for each display mode or type of display
mode, corroborates the result and points out some interesting facts: First,
one does not observe any relevant improvement over time, which is explained by
the relatively long period of training before the relatively short period of
testing. Second, over all the subject performed with a slightly better
accuracy for continuous display modes ($88\%$ vs $79\%$) and, surprisingly
(because one would expect the reverse for human, and similar accuracy for
nonhumans), a much better accuracy for the “Heap” display mode over the “Dice”
display mode ($85\%$ vs $74\%$).

Session | Dice | Heap | Discrete | Disc | Rectangle | Continuous | Total
---|---|---|---|---|---|---|---
19,17h | $65(1e^{-1})$ | $60(2e^{-1})$ | $62(7e^{-2})$ | $90(2e^{-4})$ | $75(2e^{-2})$ | $82(2e^{-5})$ | $72(3e^{-5})$
21,17h | $80(5e^{-17})$ | $93(1e^{-15})$ | $84(1e^{-29})$ | $91(3e^{-5})$ | $95(3e^{-14})$ | $94(3e^{-18})$ | $86(6e^{-45})$
23,08h | $80(1e^{-5})$ | $84(2e^{-3})$ | $81(8e^{-8})$ | (no data) | $90(8e^{-15})$ | $90(8e^{-15})$ | $86(1e^{-20})$
23,15h | $70(5e^{-3})$ | $86(1e^{-20})$ | $82(8e^{-21})$ | $88(1e^{-8})$ | (no data) | $88(1e^{-8})$ | $83(1e^{-27})$
24,10h | $66(1e^{-4})$ | (no data) | $66(1e^{-4})$ | (no data) | (no data) | (no data) | $66(1e^{-4})$
24,17h | (no data) | $83(3e^{-16})$ | $83(3e^{-16})$ | (no data) | (no data) | (no data) | $83(3e^{-16})$
25,08h | (no data) | (no data) | (no data) | $60(3e^{-1})$ | $86(4e^{-14})$ | $84(1e^{-13})$ | $84(1e^{-13})$
25,13h | $71(3e^{-2})$ | (no data) | $71(3e^{-2})$ | (no data) | (no data) | (no data) | $71(3e^{-2})$
Total | $74(3e^{-25})$ | $85(78e^{-49})$ | $79(6e^{-69})$ | $86(81e^{-15})$ | $89(3e^{-40})$ | $88(2e^{-53})$ | $82(1e^{-117})$
Table 2. Finer analysis of the first subject’s performance on selecting the
maximal value out of two, separated by display modes (“Dice”, “Heap”, “Disc”
and “Rectangle”), accumulated by the type of display mode (“Discrete” or
“Continuous”) and accumulated over all display modes (“Total”). The sessions
occurred during the month of May 2022 and are identified by the date $d$ and
hour $h$ (e.g. the session which occurred at 17:02 on the 19th of May 2022 is
identified by the tag “19,17h”). Each entry is in the format $a(p)$ where $a$
is the accuracy reported, and $p$ is the probability of achieving such
accuracy or better by selecting answers uniformly at random. Note how the
accuracy percentages are mostly above $80\%$, and that the probability of such
accuracy or a better one to be attained by selecting answers uniformly at
random is smaller than $0.001$ in almost all the cases.

####  5.2.2. Second Subject

The second subject was more reluctant to play, but showed a similar ability.
Overall experimentations requesting to select the maximal value out of two
during the testing phase, the second subject responded correctly $303$ times
out of a total of $409$ trials, corresponding to an average accuracy of
$74\%$. A simple binomial tests indicates that the probability of answering
correctly $383$ or more such binary questions out of $409$ by answering
uniformly at random is $p=2.24\cdot 10^{-23}$: here again, it is very likely
that the subject did _not_ answer uniformly at random. Lacking a bias in the
experimental protocol, this seems to indicate a clear ability to discriminate
between the two values being presented.

Session | Dice | Heap | Discrete | Disc | Rect | Continuous | Total
---|---|---|---|---|---|---|---
21,10h | $84(5e^{-15})$ | (no data) | $84(5e^{-15})$ | (no data) | $73(1e^{-2})$ | $73(1e^{-2})$ | $82(6e^{-16})$
23,15h | $64(5e^{-2})$ | (no data) | $64(5e^{-2})$ | (no data) | (no data) | (no data) | $64(5e^{-2})$
24,08h | (no data) | (no data) | (no data) | $79(5e^{-13})$ | (no data) | $79(5e^{-13})$ | $79(5e^{-13})$
24,17h | $51(5e^{-1})$ | (no data) | $51(5e^{-1})$ | $57(2e^{-1})$ | (no data) | $57(2e^{-1})$ | $55(2e^{-1})$
Total | $74(3e^{-12})$ | (no data) | $74(3e^{-12})$ | $73(2e^{-11})$ | $73(1e^{-2})$ | $73(1e^{-12})$ | $74(2e^{-23})$
Table 3. Finer analysis of the second subject’s performance on selecting the
maximal value out of two, separated by display mode and combined. Note how the
accuracy percentages are in between 51% (not much better than random, on the
last session) and 84% with an average of 74% (both much better than random),
and that the probability of such accuracy to be attained by selecting answers
uniformly at random is $p<0.001$ in almost all the cases.

####  5.2.3. Relation between accuracy and variables

When selecting the maximal value out of two, both subjects showed a lower
accuracy when the two values were close (difference or ratio close to $1$):
see Table 4 for the percentages of correct answers for each subject and each
of the $10$ sets of values presented (ignoring the order). Such results
corroborate those of the three African Grey parrots in Al Aïn et al. (2008)’s
study.

Pearson’s correlation tests for the first subject (see Figure 29 for the
corresponding heat map and Figure 29 for the corresponding scatter plots)
suggest an inverse correlation between the accuracy of the subject’s selection
and the ratio between the two values: for example, for a combination with
small ratio $\frac{1}{5}=0.2$, the subject is more likely to correctly select
the maximal value.

Value Set | Total | Difference | Ratio | Accuracy
---|---|---|---|---
$(x,y)$ | $x+y$ | $y-x$ | $y/x$ | 1st Subject | 2nd Suject
{1,2} | 3 | 1 | 0.5 | 81% | 69%
{1,3} | 4 | 2 | 0.33 | 90% | 70%
{1,4} | 5 | 3 | 0.25 | 93% | 78%
{1,5} | 6 | 4 | 0.2 | 94% | 94%
{2,3} | 5 | 1 | 0.66 | 82% | 57%
{2,4} | 6 | 2 | 0.5 | 81% | 68%
{2,5} | 7 | 3 | 0.4 | 96% | 76%
{3,4} | 7 | 1 | 0.75 | 67% | 45%
{3,5} | 8 | 2 | 0.6 | 73% | 70%
{4,5} | 9 | 1 | 0.8 | 55% | 71%
Table 4. Both subject’s Accuracy for each pairs of values from the domain
$\\{1,2,3,4,5\\}$. Total is the total value of the representation shown to the
test subject, Difference is the difference between the two values presented,
Ratio is equal to the smallest quantity divided by the largest quantity. For
the first subject, note how the lowest _Accuracy_ ($55\%$) corresponds to the
highest _ratio_ ($0.8$), while for the second subject the lowest _Accuracy_
($45\%$) corresponds to the second highest _ratio_ ($0.75$), suggesting a
trend confirmed by the Pearson’s correlation tests.

Heat map correlation plot between the variables described in Table 4 for the
first subject.

Figure 28. Heat map correlation plot between the variables described in Table
4 for the first subject. Notice the strong negative correlation ($-0.9$)
between _Accuracy_ and _Ratio_ one one hand, and the strong positive
correlation ($0.74$) between _Accuracy_ and _Difference_ on the other hand.

Scatterplot between the variables described in Table 4 for the first subject.

Figure 29. Scatter-plot of the variables described in Table 4 for the first
subject. The diagonal plots show the distribution of the values of each
variable. Note the uniform distribution of the _Total_ and _Ratio_.

There is a strong negative correlation ratio of $r=-0.9$ between the accuracy
and the ratio, and a positive correlation ratio of $r=0.74$ between the
accuracy and the difference (see the heat map in Figure 29). The scatter plots
(in Figure 29) show a decreasing relationship between the accuracy and the
ratio, and an increasing relationship between the accuracy and the difference.

There is a similar correlation between accuracy and ratio in the results of
the second subject (see the heat-map in Figure 31 and the scatter plots in
Figure 31). There is a strong negative correlation ratio of $r=-0.74$ between
the ratio and the accuracy. The correlation ratio of $r=0.52$ between the
difference and the accuracy is much weaker.

Heat map correlation plot between the variables described in Table 4 for the
second subject.

Figure 30. Heat map correlation plot between the variables described in Table
4 for the second subject. Notice the negative correlation ($-0.74$) between
_Accuracy_ and _Ratio_.

Scatter plots correlation plot between the variables described in Table 4 for
the second subject.

Figure 31. Scatter plots for the variables described in Table 4 for the second
subject.

###  5.3. Selecting the maximal value out of three and four values

Only the first subject was tested on selecting the maximal value out of three
and four values: the second subject chose to stay in the “Nest” aviary or to
play the digital piano for the remaining sessions. The subject a lower
accuracy when asked to select the maximal value out of 3 or 4, than out of 2:
on average the achieved an accuracy of $70\%$ for selecting the maximal out of
three and $62\%$ for the maximal out of four, but still much better that what
would be expected ($33\%$ and $25\%$ respectively) if the subject chose
uniformly randomly among the values proposed (see Tables 5 and 6 for the
detailed performances separated by display mode and sessions).

Session | Dice | Heap | Discrete | Disc | Rect | Continuous | Total
---|---|---|---|---|---|---|---
19,17h | $55(4e^{-3})$ | $75(2e^{-4})$ | $61(7e^{-6})$ | $6(1e^{-2})$ | $85(3e^{-6})$ | $72(5e^{-7})$ | $66(3e^{-11})$
22,09h | $51(4e^{-3})$ | $65(4e^{-4})$ | $56(1e^{-5})$ | $78(1e^{-10})$ | (no data) | $78(1e^{-10})$ | $64(2e^{-13})$
22,11h | $57(1e^{-4})$ | $64(9e^{-6})$ | $60(6e^{-9})$ | $90(1e^{-16})$ | $89(6e^{-31})$ | $89(3e^{-46})$ | $77(2e^{-47})$
25,16h | $67(6e^{-12})$ | (no data) | $67(6e^{-12})$ | (no data) | (no data) | (no data) | $67(6e^{-12})$
Total | $59(1e^{-17})$ | $66(1e^{-11})$ | $61(2e^{-27})$ | $80(1e^{-25})$ | $88(7e^{-36})$ | $84(2e^{-59})$ | $70(3e^{-77})$
Table 5. Finer analysis of the first subject’s performance on selecting the
maximal value out of three, separated by display mode and combined. Note how
the average accuracy of random position selection in this case is 33%, so an
accuracy between 51% and 84% is a reasonable measure, as well as the
probability to achieve such accuracy or above when choosing one of the value
between 3 options uniformly at random

Two simple binomial tests give a more formal measure of how much better the
subject performed compared to someone choosing uniformly at random: the
probabilities of obtaining an accuracy equivalent or superior by randomly
choosingthe same number of answers is $p=3.479\cdot 10^{-77}$ with probability
$0.33$ of success (for selecting the maximal out of 3 values $588$ times) and
$p=2.549\cdot 10^{-31}$ with probability $0.25$ of success (for selecting the
maximal out of 4 values $136$ times): with very high probabilty, the subject
showed their ability to discriminate between three and four values.

Session | Dice | Heap | Discrete | Disc | Rect | Continuous | Total
---|---|---|---|---|---|---|---
25,16h | $59(7e^{-20})$ | (no data) | $59(7e^{-20})$ | (no data) | (no data) | (no data) | $59(7e^{-20})$
26,09h | (no data) | $72(1e^{-12})$ | $72(1e^{-12})$ | $53(2e^{-2})$ | (no data) | $53(2e^{-2})$ | $68(2e^{-13})$
Total | $59(7e^{-20})$ | $72(1e^{-12})$ | $62(2e^{-30})$ | $53(2e^{-2})$ | (no data) | $53(2e^{-2})$ | $62(3e^{-31})$
Table 6. Finer analysis of the first subject’s performance on selecting the
maximal value out of four, separated by display mode and combined. Note how
the average accuracy of random position selection in this case is 25%, so an
accuracy between 53% and 72% is a reasonable measure, as well as the
probability to achieve such accuracy or above when choosing one of the value
between 4 options uniformly at random

##  6\. Conclusion

We conclude with a summary of what the project achieved to the date (Section
6.1), a discussion of the potential issues with the results presented (Section
6.2) and some perspective for future research (Section 6.3).

###  6.1. Achievements

Whereas Al Aïn et al. (2008)’s protocol requested the subject to choose
between two pieces of cardboard holding distinct amount of food, for discrete
and continuous types of food material; we proposed a protocol which requests
the subject to choose the largest among a set of values (of parameterized
size) on a visual display, using discrete and continuous representations of
values, by touching a touchscreen on the representation of the largest value.
By developing a simple but extensively parameterized web application
requesting the user to select the largest among two to four values chosen at
random, using discrete and continuous representations of values and providing
visual and audio feedback about the correctness of the answer, we achieved a
solution with various advantages, which we tentatively list as follows.

####  6.1.1. Better guarantees against subjects reading potential cues from
the experimenter

In the context of the measurement of the discrimination abilities between
discrete and continuous quantities of subjects, we designed a variant of Al
Aïn et al. (2008)’s experimental protocol which presents better guarantees
against subjects reading potential cues from the experimenter. Whereas their
protocol is performed in presence of a human experimenter who know the
complete set-up of the experiment, in our variant the experimenter can ignore
the options offered to the subjects and receive audio feedback to indicate
whether to reward or not the subject (see Section 2.5 for the definition of a
masked experimental set-up).

####  6.1.2. Generalization of results to Monk Parakeets

Using such protocol, we replicated and generalized the results obtained by Al
Aïn et al. (2008) on the discrimination abilities of three African Grey
(_Psittacus erithacus_) parrots to that of of two Monk Parakeets (_Myiopsitta
Monachus_) parrots. Concerning the ability to discriminate the largest between
2 values chosen randomly in a domain of 5 distinct values, in discrete or
continuous quantities, the two Monk Parakeets parrots performed as well as the
three African Grey parrots from Al Aïn et al. (2008)’s study, with global
accuracies of $82\%$ for the first subject and $74\%$ for the second one (see
Section 5.2 for the detailed results). Similarly to the results described by
Al Aïn et al. (2008), we found a strong correlation between the ratio between
the smallest and largest values and the accuracy of the subject: close values
are harder to discriminate than others.

####  6.1.3. Increased agency of the subject

A subject’s sense of _agency_ , defined as the faculty for the subject to take
decisions and to act upon them, was proven to be an important factor in the
well-being of captive nonhuman animals (Mancini, 2017; Perdue et al., 2012;
Kohn, 1994). In addition to features from the experimental protocol aiming to
promote the subject’s sense of agency, the web application itself provides
various means for the subject to exert its agency, from the ability to choose
the mode of display of the values to the ability to interrupt the game at any
time and to choose a different mode of display.

####  6.1.4. Extension to tuples

Taking advantage of the extensive parametrization of the web application, we
slightly extended the settings of Al Aïn et al. (2008)’s study from pairs to
tuples: whereas their protocol requested the subject to choose between only
two quantities, we were able to study the discrimination abilities not only
between pairs of values, but also between triple and quadruple sets of values,
showing a reduction of accuracy when the size of such set increased.

####  6.1.5. Diversifying Discrete and Continuous Representations

Furthermore, we refined the analysis by diversifying the types of discrete and
continuous representations of values (Section 5.2), again with the subjects
showing an accuracy similar to that of the study of Al Aïn et al. (2008).

####  6.1.6. Increased Number of Experiments

The web application used in the experiments is similar to other digital life
enrichment applications made available to nonhuman animals by their guardians.
Similarly to the behavior described by Washburn (Washburn, 2015; Richardson et
al., 1990) of apes presented with digital life enrichment applications serving
as cognition tests, the subjects often chose to play such web application over
other toys made available to them, and often asked to continue playing after
the end of a game. This allowed for multiple repetitions of the experiments,
and to gather a large amount of data points without incommoding the subjects:
the two subjects of this study voluntarily answered a total 2429 tests in one
week (see Table 1 for a summary), without any observable negative consequences
during nor after the end of the testing phase.

####  6.1.7. True Randomness

The web application generates the instances presented to the subjects
uniformly at random, whereas the high organisational cost of Al Aïn et al.
(2008)’s protocol limited it to testing the exhaustive enumeration of pairs
between values from a specific domain, in a random order. The later could
yield some issues if the domain is sufficiently small that a subject could
deduce the answer to some questions by an elimination process, based on
previous answers. As Al Aïn et al. (2008) considered a domain of values of
size $5$, the amount of distinct unordered pairs is $\frac{5\times 4}{2}=10$,
a list which subjects with working memory abilities similar to humans might be
able to manage. Beyond the fact that the web application allows the use of a
domain of size up to $10$ (which brings the amount of distinct unordered pairs
to $\frac{10\times 9}{2}=45$), and of sets of values of size larger than two,
the fact that the sets of values presented to the subject are generated at
random completely suppresses the possibility of a subject to deduce the answer
to some questions by an elimination process, based on previous answers.

####  6.1.8. Automatic generation of the experimental logs

The web application automatically generates locally a log of the subject’s
interactions with it. This greatly reduces the generation cost of such log,
reduces the probability of errors in it, and increases the amount of
information captured by it, such as the exact time of each answer, allowing
for instance the computation of the amount of time taken to answer each
question or studies between the time and/or whether of the day and performance
(albeit we did not take advantage of such information in the present study).

####  6.1.9. Reduction of Experimental Cost

As the web application can be run on a simple pocket device, this reduces the
cost of running such experiments to the extreme that it can be run on the
experimenter’s shoulder while the device is hold by hand (at the cost of some
accuracy in the results of such experiment). Such lowered cost might prove to
be key in the design of citizen science projects extending this work.

###  6.2. Discussion

Our digital adaptation of Al Aïn et al. (2008)’s experimental protocol present
some other key difference, which might the result of our study relatively
difficult to compare to that of Al Aïn et al. (2008). We attempt to list such
difference as follows:

####  6.2.1. Non proportional rewards and reward withdrawal

The protocol defined by Al Aïn et al. (2008) instructs to reward the subject
with the content of the container they chose: the importance of the reward is
proportional to the value being selected. The protocol we defined instructs to
reward the subject with a single type of reward each time it does select the
maximal value of the set, and to withdraw such reward when the subject fails
to do so. Such a difference might alter the experiment in at least two
distinct ways:

  * •

The proportionality of rewards could result in a larger incentive to select
the maximal value when the difference between the two values is the largest,
and a reduced incentive when the difference is small, and Al Aïn et al. (2008)
indeed noticed a correlation between the gap between the two values and the
accuracy of the answer from the subjects of their experiment. The absence of
such proportionality in our experiments might have reduced such an incentive,
but we observed the same correlation than they did (described in Section
5.2.3).

  * •

The withdrawal of rewards when the subject fails to select the largest value
of the set is likely to affect the motivation of the subject to continue to
participate in the exercise on the short term, and in the experiment in the
long term. To palliate the frustration caused by such withdrawal, extensive
care was taken to progressively increase the difficulty of the exercises
(first through the size of the domain from which the values were taken, then
through the size of the set of values from which to select the maximal one).
No frustration was observed, with both subjects often choosing to continue
playing at the end of a game.

Implementing the proportionality of rewards is not incompatible with the use
of a digital application. For instance, it would be relatively easy to extend
the web application to vocalize the value selected by the subject, so that the
experimenter could reward the subject with the corresponding amount of food.
Such an extension was not implemented mostly because it would slow down the
experimentation, for relatively meagre benefits.

####  6.2.2. Irregular pairs and tuples

The web application generates the sets of value presented to the subject
uniformly at random (without repetitions) from the domain of values set in the
parameter page. While such a random generation yields various advantages, it
has a major drawback concerning the statistical analysis of the results, as
some sets of value might be under-represented. An unbalanced representation of
each possible set of values is guaranteed only on average and for a large
number of exercises; whereas Al Aïn et al. (2008)’s protocol, using a
systematic enumeration of the possible sets of values (presented in a random
order to the subject), does not yield such issues. Such issue was deliberately
ignored in order to develop a solution able to measure discrimination
abilities on values taken from large domains (assuming that some nonhuman
species might display abilities superior to that of humans in this regard),
and presenting the subject with a systematic enumeration of the possible sets
of values is practical only for small domains (e.g. values from 1 to 5), not
for large domains. For a domain of size $5$ (as that of Al Aïn et al. (2008)),
enough datapoints were generated that no pair was under represented (see Table
4).

####  6.2.3. Extension to sensory diverse species

The colors displayed by digital displays and the sound frequencies played by
devices are optimized for the majority of humans. It is not always clear how
much and which colours and sound can be seen and heard by individual of each
species. The web application presents extensive parameters to vary the colours
displayed and the sounds played to the subject. Even less intuitively, species
can differ in their Critical Flicker Fusion Frequency (CFFF) (ND et al.,
2021), the frequency at which they perceive the world and can react to it (in
some species, such frequency even vary depending on the time of the day or of
the season (Reas, 2014; Healy et al., 2013)). For instance, dogs have higher
CFFF while cats have lower ones, and the CFFF of reptiles vary with the
ambient temperature. Such variation might affect not only their ability to
comprehend the visual display and sound play from devices, but might also
affect how they comprehend some application designs over others. The web
application presents extensive parameters to vary the time between each
exercise and which game, so that part of the rhythm of the application can be
adjusted by the experimenter to the CFFF of the subject, but more research is
required in order to automatically adapt the rhythm of such applications to
the CFFF of individuals from a variety of species.

###  6.3. Perspective on future work

Some issues with the results presented in this work are not related to any
difference with Al Aïn et al. (2008)’s experimental protocol, but rather with
limitations of the current one. We list them along with some tentative
solutions, to be implemented in the future.

####  6.3.1. Random Dice and Heap representations

The discrete representation modes Dice and Heap associate each value with a
fixed representation of a number of points corresponding to the value being
represented. This differs from what happens in Al Aïn et al. (2008)’s
experimental protocol, where the seeds are in no arranged configuration on the
cardboard. This might affect the results of the experience in that a subject
could learn to select a particular symbol (e.g. the one corresponding to the
largest value of the domain) anytime it is present, without any need for any
comparison between the presented values. Check in the results if value sets
including the largest value of the domain have a better accuracy ratio than
others: this could be an indication that the subjects learned to select the
corresponding symbol anytime it is present, without any need for comparing
values. The development and evaluation of their impact on the discrimination
abilities of human and nonhuman subjects will be the topic of a future study,
once the corresponding randomized representations have been added to the web
application. FABIAN: should you want to work on a second article after this
one, this topic might be either to study than the campaign mode, and the
random display should be quick enough to program…

####  6.3.2. Systematic logs

The easiness with which logs are generated tends to make one forget about it,
to the point that the bottleneck could become the transfer of the logs from
the device used to perform the experience to a central repository. As one
guardian might get more excited to transfer the logs of sessions where the
subjects excelled at the activities than that of less positive sessions, this
might create a bias toward positive results in their report. While not an
issue while implemented by personal with a scientific training, such risk of a
bias might become more problematic in the context of a citizen science project
(Association, 2021). The development of a website serving as a central
repository of experimental data sent by web applications such as the one
presented in this work will be the topic of a future study. The roles of such
a central “back-end” website could include the automatizing of the most
frequent statistical tests on the data received; a greater ease of separation
between the roles of experimenter and researcher, which will be an important
step toward a true citizen science generalisation of this project; and the
aggregation of sensory and cognitive data from distinct applications,
individuals and species.

####  6.3.3. Adaptive Difficulty

The great amount of parameters available in the settings page of the web
application makes it possible to adapt the difficulty of the activities to the
level of abilities of the subject. Such abilities evolve with time, most often
advancing and only rarely receding (such as after a long period without using
the web application). Choosing which values of the parameters is the most
adequate to the current level of abilities of the subject requires an
extensive understanding of the mechanisms of the application. An extension of
the web application presenting the subject with a sequence of parametrization
of increasing difficulty, along with a mechanism raising or lowering the
difficulty of the activities presented to the subject would greatly simplify
the task of the experimenter, and will be the topic of a future study.

####  6.3.4. Cardinal Discrimination

Pepperberg (2006) recounts how the African Grey parrot (_Psittacus erithacus_)
Alex, after being trained to identify Arabic numerals from 1 to 6 (but not to
associate Arabic numbers with their relevant physical quantities) was able to
label which of two Arabic numerals is the biggest, having inferred the
relationship between the Arabic number and the quantity, and having understood
the ordinal relationship of his numbers. Modifying the web applicationInCA-
WhatIsMore so that to replace the graphical representations of values by
ordinal numbers would/will be easy. Testing ethically the ability or inability
of subjects to replicate Pepperberg (2006)’s results without frustrating those
subjects might require more sophistication in the design of the experimental
protocol. Such protocols concerning the measurement of skills that subject
might lack is the topic of the next section.

####  6.3.5. Ethical Measurement of Inabilities

The frustration potentially caused by the withdrawal of rewards (described in
Section 6.2.1) when measuring skills that a subject might lack (an example of
which was given in Section 6.2.1) points out to another issue, of ethical
dimensions: how can one ethically demonstrate the inability of subjects to
perform a given action through experimentation, without hurting the well-being
of the subject by exposing them to the frustration of failing to performed the
requested action? Note that such issue is not specific to the action of
withdrawing rewards when a subject fails: as proportional rewards can also
generate frustration. One solution could be to mix potentially “difficult”
requests with other, similar but known to be “easy”, requests, in such a way
that the proportion and frequency of the former to be a fraction of the
proportion and frequency of “easy” requests that the subject fail (for
inattention or other reasons). One can hypothesize that 1) the frustration
generated by such questions would be minimum; that 2) a statistical analysis
of the correction of the difficult requests would yield useful information
about the ability or inability of the subject to answer those; and that 3) a
small proportion of “difficult” requests helps to further motivate the
subject, making the exercise more of a challenge.

####  6.3.6. Citizen Science Extensions

The term “ _Citizen Science_ ” refers to scientific projects conducted, in
whole or in part, by amateur (or nonprofessional) scientists (Gura, 2013). It
is sometimes described as “public participation in scientific research”, with
the dual objectives to improve the scientific community’s capacity, as well as
improving the public’s understanding of science and conscience about the
research’s themes (Association, 2021). Citizen Science has become a means of
encouraging curiosity and greater understanding of science whilst providing an
unprecedented engagement between professional scientists and the general
public.

Such methodology must be used with care, in particular about the validity of
volunteer generated data. Projects using complex research methods or requiring
a lot of repetitive work may not be suitable for volunteers, and the lack of
proper training in research and monitoring protocols in participants might
introduce bias into the data (Thelen and Thiet, 2008). Nevertheless, in many
cases the low cost per observation can compensate for the lack of accuracy of
the resulting data (Gardiner et al., 2012), especially if using proper data
processing methods (McClure et al., 2020).

Scientific researchers in comparative psychology could definitely benefit from
some help, with many cognitive aspects to explores for so many species. In the
process of defining the _anecdotal method_ of investigation for creative and
cognitive processes, Bates and Byrne (2007) mentioned that “ _collation of
records of rare events into data-sets can illustrate much about animal
behaviour and cognition_ ”. Now that the technology is ready to analyze
extremely large data-sets, what is lacking in comparative psychology are the
means to gather such large data-sets.

Delegating part of the experimental process to citizens without proper
scientific training is not without risk. Given the conflicted history of
Comparative Psychology (Pepperberg, 2020) in general and Animal Language
Studies (Pepperberg, 2016) in particular, the challenge of avoiding “Clever
Hans” biases and related ones will be of tremendous importance. Could
applications and experimental protocols such as the one described in this work
help to design citizen science projects for the study of sensory and cognitive
abilities in nonhumans species living in close contact with humans?

## Contributions

Jérémy Barbay programmed the first versions of the software, managed the
interactions with the subjects during the development, training and testing
phases, obtained the approval of the _Institutional Animal Care and Use
Committee_ , structured the article and supervised the work of Fabián Jaña
Ubal and Cristóbal Sepulveda Álvarez. Fabián Jaña Ubal improved and maintained
the software, and described it (Sections 3.1 and 3.2). Cristóbal Sepulveda
Álvarez reviewed the experimental results, performed their statistical
analysis, and described the log structure (Section 3.3), the statistical
analysis process (Section 4.3) and the results (Section 5). All authors are
aware of the submission of this work and of its content.

###### Acknowledgements.

We wish to thank Joachim Barbay for his suggestion of using Svelte and his
mentoring in the development of the various versions of the application;
Jennifer Cunha from Parrot Kindergarten for sharing images and video of
parrots using touchscreens, suggesting the (Al Aïn et al., 2008)’s study and
for helping during the design and test of the preliminary versions of the
software InCA-WhatIsMore (as well as other software projects); Corinne
Renguette for her help concerning the bibliography and the ethical aspects of
the experiments and of its description; Cristina Doelling for pointing out
some of the existing literature about the use of touchscreens by apes in zoo;
and Francisco Gutierrez and Jenny Stamm for suggesting alternative names to
the problematic term “blind” in expressions such as “blind setup”, and for
pointing out some bibliography supporting such replacement.

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