sensors
ArticleAnalysis of the Correlation between Frontal Alpha Asymmetryof Electroencephalography and Short-Term Subjective
Well-Being Changes
Betty Wutzl 1, * , Kenji Leibnitz 1,2 , Daichi Kominami 1 , Yuichi Ohsita 1,3 , Michiko Kaihotsu 4
and Masayuki Murata 1,2
1
2

3
4

*

Citation: Wutzl, B.; Leibnitz, K.;

Graduate School of Information Science and Technology, Osaka University, Suita 565-0871, Japan
Center for Information and Neural Networks (CiNet), National Institute of Information and Communications
Technology, Suita 565-0871, Japan
Institute for Open and Transdisciplinary Research Initiatives, Osaka University, Suita 565-0871, Japan
Technology Innovation Center, Daikin Industries, Ltd., Settsu 566-8585, Japan
Correspondence: b-wutzl@ist.osaka-u.ac.jp

Abstract: Subjective well-being (SWB) describes how well people experience and evaluate theircurrent condition. Previous studies with electroencephalography (EEG) have shown that SWB can be
related to frontal alpha asymmetry (FAA). While those studies only considered a single SWB score foreach experimental session, our goal is to investigate such a correlation for individuals with a possibly
different SWB every 60 or 30 s. Therefore, we conducted two experiments with 30 participants each.
We used different temperature and humidity settings and asked the participants to periodically rate
their SWB. We computed the FAA from EEG over different time intervals and associated the given
SWB, leading to pairs of (FAA, SWB) values. After correcting the imbalance in the data with theSynthetic Minority Over-sampling Technique (SMOTE), we performed a linear regression and founda positive linear correlation between FAA and SWB. We also studied the best time interval sizes fordetermining FAA around each SWB score. We found that using an interval of 10 s before recording
the SWB score yields the best results.

Kominami, D.; Ohsita, Y.; Kaihotsu,
M.; Murata, M. Analysis of theCorrelation between Frontal Alpha

Keywords: subjective well-being; SWB; frontal alpha asymmetry; FAA; electroencephalography;
EEG; environmental conditions

Asymmetry ofElectroencephalography andShort-Term Subjective Well-Being
Changes. Sensors 2023, 23, 7006.
https://doi.org/10.3390/
s23157006
Academic Editor: Yvonne Tran
Received: 8 June 2023
Revised: 4 August 2023
Accepted: 4 August 2023
Published: 7 August 2023

Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms andconditions of the Creative Commons
Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

1. Introduction
Subjective well-being (SWB) is a subjective condition which everyone perceives differently and describes how people experience their lives in terms of how they think andfeel. Diener et al. described SWB as “a broad category of phenomena that includes people’semotional responses, domain satisfactions, and global judgements of life satisfaction” [1],p. 277. In the past, it was also known under different terms, such as “psychological wellbeing” [2], “quality of life” [3], or “subjective happiness” [4]. There are also discussions
about differences and similarities with other concepts such as “comfort” or “quality oflife”. Pinto et al. [5] summarize this discussion and point out that those terms often refer toeach other in their definitions, e.g., the International Council of Nurses defines comfort as“sensation of physical ease and bodily well-being” [6]. Here, we stick to the term “subjective
well-being”. In recent years, SWB has received more attention as it seems to affect many
areas of our daily life. A worldwide analysis [7] showed that a lot of factors are included
in SWB, such as demographic, institutional, personality, contextual, situational, environmental, and economic factors. There are also many papers focusing on specific aspects,
e.g., psychology and public health [8]. The study of SWB has led to a deeper understanding and to a further subcategorization of SWB, namely into “evaluative well-being”,“experienced well-being”, and “eudaimonic well-being” as, for example, described in [9].

Sensors 2023, 23, 7006. https://doi.org/10.3390/s23157006

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The assessment of SWB is usually done via a questionnaire amongst which the five-item
World Health Organization Well-Being Index (WHO-5) is very popular, see [10] for a systematic review. In addition, as more attention is paid to SWB, a lot of research has been
conducted focusing on psychological interventions to improve SWB, e.g., [11,12].
It is already known that SWB is related to biological phenomena. Some studies focused on metrics extracted from positron emission tomography (PET) [13] or functional
magnetic resonance imaging (fMRI) [14], while others investigated a correlation between
SWB and rapid eye movement (REM) sleep, salivary cortisol, and pro-inflammatory cytokines [15] or the relationship of SWB and neuroendocrine, inflammatory, cardiovascular
activity, cortisol, or plasma fibrinogen [16]. Electroencephalography (EEG) seems to bea promising tool for measuring SWB, especially when focusing on the asymmetry of thefrontal alpha waves. Tomarken et al. [17] measured the EEG of their participants twice,
3 weeks apart. They found that the group of participants who exhibited extreme relativeleft anterior activity compared to the right also reported an increased generalized positive
affect. Wheeler et al. [18] focused on emotional reactivity and concluded that women withhigher frontal activity in the left hemisphere reacted stronger when watching film clips
designed to elicit positive emotions. A review by Davidson et al. [19] showed that the
prefrontal cortex is asymmetrically involved when it comes to experiencing affect. Reznik
and Allen [20] discuss frontal alpha asymmetry (FAA) as a predictor, outcome, mediator, or
moderator for neural and psychological models as well as psychopathology. It was shownthat FAA has a direct correlation to SWB [21,22]. The first of those two studies analyzed
data from 84 right-handed adults and found that higher activity in the left superior frontal
regions compared with the right side was associated with greater self-reported SWB [21].
The second study analyzes the effect of a positive psychological intervention. The authors measured SWB, depression, and anxiety at the beginning of the trial and again after
10 weeks. They found that improvement in SWB and relief of depression and anxiety wereassociated with an increase in FAA [22]. Focusing on other neuroimaging techniques, thefMRI study of Levesque et al. [14] and the PET study of Lane et al. [13] both also reported
that the medial prefrontal cortex plays a crucial role for SWB.
In these studies, either different participants with individual SWB levels are studied,or interventions are conducted that last at least a few weeks when the studies addresschanges in an individual participant’s SWB. In this work, we do not aim for psychologicalinterventions but rather investigate the effect of simple changes in the physical environment.
This means, we assume that the psychological states of the participants stay the sameand that the diverse environmental conditions changed during the experiment are theonly sources for variation in SWB. Moreover, we decided to focus on EEG because it isan easy-to-use and inexpensive measurement technique that can be applied in realistic
indoor environments.
There are studies that discuss the influence of specific EEG sensor locations, e.g., [23],and some studies even report findings for either depression or well-being in EEG frequency
bands other than alpha, or in sensor locations other than the frontal areas [24,25]. However,
we decided to focus on FAA in this paper because it is the most reported measure in theliterature when it comes to finding a correlation between EEG and SWB. We investigate
whether the reported relationship between FAA and SWB also holds when SWB is notchanged by psychological interventions over several weeks, but rather changes in thephysical environment on a minute or second scale. Moreover, we vary the time interval
used for the FAA calculation to find out which intervals give the best results. We try tofind out whether FAA only reflects an individual’s long-term psychological or psychiatricstate or whether it also mirrors subtle short-term changes, such as feeling comfortable in aphysical environment which might vary on a second or minute scale.
In summary, we aim to answer the following two main research questions, (RQ1) and(RQ2), in this paper.
(RQ1) Does FAA also reflect subtle short-term changes in SWB?

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As mentioned above, most of the literature focuses on the correlation between FAA and
SWB when SWB is either seen as a static metric from each participant or when participants
undergo psychological or psychiatric interventions which lead to differences in SWB
scores over weeks, months, or even longer. We are not trying to improve our participants’depression scores or other psychological measures. We assume that these conditions
remain the same during our experiments and, thus, reflect a background state with a static,
unchanged score. We focus on short-term, non-persistent changes in SWB and see if we
can relate changes in FAA to these small SWB changes. We hypothesize that there will be apositive linear correlation between FAA values and the corresponding SWB scores and try
to confirm or deny this in this paper.
(RQ2) Is there an ideal length and position for the time interval used to calculate FAA?
The time interval over which FAA is calculated can vary. We will analyze different
interval lengths and positions to find the interval that best reflects SWB. In other words,
over what interval does FAA show the best correlation with subtle short-term changes
in SWB?
2. Materials and Methods
2.1. Experiments
We conducted two experiments for our study: Experiment 1 in 2020 and Experiment 2
in 2022. Both experiments were approved by the local ethics committee at Osaka University.
Experiment 1 took place in a typical office at the university with dimensions of around
7 m × 3.30 m. The room contained a meeting table and desk with a chair at which ourparticipants were sitting. The main idea for the experiment was to measure brain functionsof the participants during different SWB states. We attempted to influence the SWB statesby changing the room environment to all combinations of temperature (22 ◦ C, 24 ◦ C, and26 ◦ C) and humidity (40%, 60%, and 80%). However, after recording sessions with thefirst seven participants, we realized that the settings with 80% were hard to maintain, so
we changed them to 75%. A tolerance of ±0.5 ◦ C was used for the temperature and ±5% for
the humidity. All the equipment we used in this experiment was off-the-shelf equipment.
For changing the temperature and humidity we used two heaters, two humidifiers, and one
dehumidifier. Temperature and humidity were measured with a combined temperatureand humidity meter. We started each session by bringing the room to the highest of thethree humidity settings as this was the most difficult to achieve and so preparations werestarted before the participant arrived. Then, the humidity was kept stable for three runsof different temperature settings of 22 ◦ C, 24 ◦ C, and 26 ◦ C. After having recorded alltemperature settings at the highest humidity, we lowered the humidity to 60% and kept it
stable while again going through all the three temperatures, from the lowest to the highest.
After these three runs were finished, we lowered the humidity to 40% and performed thelast three runs, with increasing temperature setting.
In Experiment 1 we measured 30 students (29 right-handed, 1 left-handed, 16 males,
14 females, ages 23.4 ± 3.3 years) from Osaka University. After each participant arrived,
we first explained the experimental procedure to them. Then, the participant signed
the consent form and sat on the chair. We used an EEG headset (EPOC+, EMOTIV,San Francisco, CA, USA) for our recording. This device has 14 channels, namely AF3, F7,
F3, FC5, T7, P7, O1, O2, P8, T8, FC6, F4, F8, and AF4, following the standard 10–20 systemwith common mode sense (CMS) and driven right leg (DRL) references at locations P3
and P4, respectively. The device uses sequential sampling with a single analog-to-digitalconverter with an internal sampling rate of 2048 Hertz (Hz), downsampled to either 128 or
256 Hz. In the beginning of our experiment, it was not clear to us which of the sampling
rates would yield better results. Thus, we tried different downsampling rates in different
sessions. We found later that recording at different rates, or downsampling all sessions to
the lower sampling rate at the beginning of the analysis, did not substantially change theresults. Hence, we do not distinguish between sessions having different sampling rates in
the following. The EEG bandwidth is 0.2–45 Hz with a digital notch filter at 50 and 60 Hz.

Sensors 2023, 23, x FOR PEER REVIEW

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4 of 16sessions. We found later that recording at diﬀerent rates, or downsampling all sessions to
the lower sampling rate at the beginning of the analysis, did not substantially change theresults. Hence, we do not distinguish between sessions having diﬀerent sampling rates inDuring the experimental runs all participants were asked to perform the same reading
the following. The EEG bandwidth is 0.2–45 Hz with a digital notch filter at 50 and 60 Hz.
task ofa newspaper
to prevent
distractions
by anyexternal
While
the participant
Duringthe experimental
runs
all participants
were
asked stimuli.
to performthe same
readwassittingonthechair,
theenvironmental
conditions
were
set
to
one
of thespecific
ing task of a newspaper to prevent distractions by any external stimuli. While theparticitemperature–humidity
pairs
mentioned
above.
Oncethesesettings
werereached,thepant was sitting on the chair, the environmental conditions were set to one of the specific EEG
recorded
the brain state
for mentioned
five minutes.
In addition,
theparticipants
were asked
to ratetemperature–humidity
pairs
above.
Once thesesettings
were reached,
the EEG
their
SWB
every
60
s
duringthefive-minuteintervals
on
a
scale
from
1
to
10,
with
1
recorded the brain state for five minutes. In addition, the participants were asked to ratebeing
the
worst
thethebest
SWB. In intervals
other studies,
SWB
is oftenwith 1 beingvia a
their
SWB andevery1060beings during
five-minuteon a scalefrom
1 to 10,determined
questionnaire.
However,feasiblefor usvia
becausethe worst and 10
being theusing
best even
SWB. aInshortotherquestionnaire
studies, SWB is
is notoften
determinedawewant to measurea short-termon questionnaire
a 60 s (or evenscale.
we usequestionnaire.
However,using evenSWB
a shortis shorter)
not feasiblefor Hence,
us because
theform of aan
expandedSWB
Likert[26], namely
verbalwe
ranking
use thefrom
we simplest
want to measure
short-termon ascale
60 s question(or even shorter)
scale. aHence,
1simplest
to 10. Thisapproach
was chosen
it is the[26],fastestwayatoget aranking
responsefromform
of an expanded
Likertbecause
scale question
namelyverbalfrom
1 theto 10. This approach
was chosen
it isforms
the fastest
to get a response from theparticipants
and the Likert
scale because
in various
is wellway
established.
participants
and theSWB
Likerttoscalein various forms
is wellJapaneseestablished.
We described
the participantsin eitheror English, depending on
participantsineitherJapaneseorEnglish,on as
Wedescribed
SWB
to
the
their preference, as follows. An SWB score of 10 corresponds to feeling depending
as comfortable
theirpreference,asfollows.
An
SWB
score
of
10
correspondstofeelingascomfortable
as wellpossible with the physical environment (temperature and humidity) and generally as
possiblewiththephysicalenvironment(temperatureandhumidity)
andgenerallyaswell
as possible. SWB 1, on the other hand, refers to the state of least comfort and not feeling wellasthe
possible.
SWB
1, on therefers situation
to the stateof least comfort
not feelingtopoint ofwanting
to otherleave hand,the current
immediately.
Theandnumbers
between
well
to
the
point
of
wanting
to
leave
the
current
situation
immediately.
The
numbers
be- the10 and 1 represent the gradual change between these states. This rating system and
tween
10
and
1
representthegradualchangebetweenthese
states.
This
ratingsystemandgeneral procedure were explained to the participants before starting the measurement.
the generalprocedure
were theexplained
to the participants
starting themeasurement.
Duringthe EEG
recording,experimenter
reminded before
the participants
every
60 s by saying
During the EEG recording, the experimenter reminded the participants every 60 s by saythe word “number” to report their SWB, which was recorded by the experimenter.
ing the word “number” to report their SWB, which was recorded by the experimenter.
For Experiment 2 we made a few minor changes. We used a newer EEG headset,
For Experiment 2 we made a few minor changes. We used a newer EEG headset, thethe EPOC X (EMOTIV, San Francisco, CA, USA), to measure the EEG signals. The EPOC
EPOC X (EMOTIV, San Francisco, CA, USA), to measure the EEG signals. The EPOC X
X headset has the same technical features as the EPOC+. This time we decided at theheadset has the same technical features as the EPOC+. This time we decided at the beginbeginning to record all sessions at a sampling frequency of 128 Hz. In addition, we usedning to record all sessions at a sampling frequency of 128 Hz. In addition, we used a difaferent
different
experimental room (Figure 1), which was divided by partitions into an area
experimental room (Figure 1), which was divided by partitions into an area of 1.4
of
1.4
m
×
2.1
that the temperature
andwould
humiditywould
be easierm × 2.1 m, withm,
thewithidea thethatidea
the temperatureand humidity
be easierto control
in tocontrolinasmaller
space.
Anotherchangewastheinclusionofcustom-madetemperature–a smaller space. Another change was the inclusion of custom-made temperature–humidhumidity[27].
restequipmentof the equipment
and humidifiers)
was astheinsame
ity sensorssensors[27]. The
restTheof the(heaters (heaters
and humidifiers)
was the sameasthe previous
experiment.
theinprevious
experiment.

Figure 1. (a) Overview of the setup of Experiment 2 with heaters and humidifiers, and (b) the layout
Figure1. (a) Overview of the setup of Experiment 2 with heaters and humidifiers, and (b) the layoutof the custom-made temperature-humidity sensors.
of the custom-made temperature-humidity sensors.

We again
again recruitedright-handed,
2 left-handed,
16 males,
14 females,We
recruited30
30students
students(28(28right-handed,
2 left-handed,
16 males,
14 females,
ages
22.3
±
4.2
years)
from
Osaka
University.
None
of
those
students
participatedin Ex- inages 22.3 ± 4.2 years) from Osaka University. None of those students participatedperiment 1. The main procedure, i.e., the participant arriving, giving written consent toExperiment 1. The main procedure, i.e., the participant arriving, giving written consent toparticipate in the experiment, sitting on the chair, and performing a reading task, stayed
participate in the experiment, sitting on the chair, and performing a reading task, stayed
the same. However, we slightly changed the temperature–humidity pairs from absolutethe same. However, we slightly changed the temperature–humidity pairs from absoluteto relative values. Hence, we measured combinations of three different temperatures(high, medium, low) and two different humidity levels (high, low), leading to a total of
6 combinations. See Table S1 in the Supplementary Materials for detailed information on
the mean, standard deviation, and minimum and maximum temperature and humidity
recorded during each run. We focused on changes in temperature and humidity rather thanSensors 2023, 23, 7006

5 of 16absolute values because we do not attempt to correlate absolute temperature or humidity
values with any of the measured quantities, but rather use different temperature–humidity
settings to provoke a change to the participants’ SWB. The frequency of collecting the SWB
scores (again on a scale from 1 to 10) from the participants increased from 1 score every
60 s in Experiment 1 to 1 score every 30 s. The explanation of the experimental protocol
and the SWB rating system were the same as in Experiment 1.
Table 1 below contrasts the two experiments in terms of participant characteristics andthe tools used. Analysis 1, Analysis 2, and Analysis 3 will be described in Section 2.3.
Table 1. Summary of the characteristics of the two experiments performed.

Year performed
Number of total participants
Number of male participants
Number of female participants
Number of right-handed participants
Number of left-handed participants
Mean age (years)
Standard deviation of age (years)
Background of participants
SWB recording interval
EEG headset
Number of EEG sensors
EEG recording downsampling rate
Size of experimental room
Temperature and humidity
measurement devices
Maximum time per session(one participant)Maximum time per run (T-H setting)Different target T-H settings
Number of participants thatcompleted all target T-H settings
Analysis 1 performed
Analysis 2 performed
Analysis 3 performedExperiment 1

Experiment 2

2020
30
16
14
29
1
23.4
3.3
University students
60 s
EPOC+
14
128 or 256 Hz
7 m × 3.30 m

2022
30
16
14
28
2
22.3
4.2
University students
30 s
EPOC X
14
128 Hz1.4 m × 2.1 m
15 custom-madeT-H sensors

1 combined T-H meter
4h

4h

5 min
9

9 min
6

21

28

Yes
No
No

Yes
Yes
Yes

2.2. EEG Processing
To preprocess our data, we wrote a MATLAB [28] pipeline making use of EEGLAB [29],
HAPPE (The Harvard Automated Processing Pipeline for Electroencephalography) [30],and MARA (Multiple Artifact Rejection Algorithm) [31,32]. HAPPE is a standardized
and automated pipeline for EEG recordings of variable lengths and artifact contaminationlevels, which is appropriate for us because we have short recordings from the participants
and an EEG system that easily introduces artifacts. We refer the interested reader to [30]for a detailed explanation of the steps of HAPPE. At the end of our pipeline we turn tothe computation of FAA by adapting the FAA EEGLAB toolbox by Michael Tesar [33],which automatically computes asymmetries of two channels from preprocessed EEG data
following the description given in Section 2.5 in [34].
Our pipeline starts with loading the EEG data as EDF (European Data Format) files.
Each EDF file consists of the data recorded by our EEG headset during one run, i.e.,
one temperature–humidity setting for one participant. If the sampling rate of the recording
is 256 Hz, the first step is to downsample the data to 128 Hz. Then, all non-EEG channels
are explicitly disabled, e.g., motion and other quality control measures that are also stored
in the EDF file. The next step is to set the channel locations that will be needed later fromthe standard layout via sensor names. Then, the pipeline checks if the time series has aduration of at least 15 s to get rid of all runs that had to be stopped due to some problems.

Sensors 2023, 23, 7006

lowing the description given in Section 2.5 in [34].
Our pipeline starts with loading the EEG data as EDF (European Data Format) files.
Each EDF file consists of the data recorded by our EEG headset during one run, i.e., one
temperature–humidity setting for one participant. If the sampling rate of the recording is
256 Hz, the first step is to downsample the data to 128 Hz. Then, all non-EEG channels are6 of 16
explicitly disabled, e.g., motion and other quality control measures that are also stored in
the EDF file. The next step is to set the channel locations that will be needed later from thestandard layout via sensor names. Then, the pipeline checks if the time series has a duraThis
then,
as described[30],
we performtion isof followed
at least 15 bys todetrending
get rid of allthe
runsdatathat andhad tobe stopped
due to insomeproblems.
This thefirst
bad channel
detectionthe
whichuseasofdescribed
the normed
jointweprobability
offirstthe average
is followed
by detrending
datamakes
and then,in [30],
perform thebadlogarithmic
power which(1–125makes
Hz). Ifusea channel’s
probability
is more thanstandard
channel detectionof the normed
joint probabilityof 3theaveragedeviations
logaawayfromthe mean,is considereda badchannel.is Our
also performs
this badrithmic
power(1–125 itHz).
If a channel’s
probability
morepipeline
than 3 standard
deviations
the mean,
it isbadbadchannel.
Our arepipelinealso performs this badaway fromchanneldetection
twice
toconsidered
ensure thata nochannels
missed.
channeldetection
twice theto ensurethatchecks
no badwhether
channelsthe
arechannels
missed. AF3 and AF4, which are
Beforecontinuing,
pipeline
Beforecontinuing,thepipelinecheckswhetherthechannels
AF3caseand further
AF4, whichareneeded to compute FAA, are among the bad channels, in which
processing
neededtocompute
FAA,
are
among
the
bad
channels,
in
which
case
further
processingisis stopped (see Figure 2a for the EEG sensor layout). Then, a wavelet-ICA (independent
stopped(see
Figure
2a
for
the
EEG
sensorlayout).
Then,awavelet-ICA(independent
component analysis) is performed. It removes all types of artifacts including signal discomponent analysis)
is performed.
It removes
types of artifacts
continuities,
high-amplitudeartifacts
such as all
eye-blinks,
and anyincluding
artifacts signal
causeddisby thecontinuities,
high-amplitudeartifactssuchaseye-blinks,
andany
artifacts
causedtheparticipant’s motion. This wavelet-ICA starts with an ICA and then performs bya wavelet
participant’s
This wavelet-ICA
starts withan ICA
then thenperforms
wavelettransform
andmotion.
thresholding
before transforming
back.
Theandpipeline
uses aMARA
to autransform
andthresholding
beforetransforming
back.
The
pipeline
then
uses
MARA
to
tomatically flag and reject independent components if the probability of having an artifact
flag Thisand reject
independent
the probabilityof havingan ar-comisautomaticallylarger than 0.50.
pluginis based oncomponents
the idea thatif neuralactivity andartifactual
tifact is larger than 0.50. This plugin is based on the idea that neural activity and artifactual
ponents are generated independently and, thus, it carries out an automatic independent
components are generated independently and, thus, it carries out an automatic independcomponent classification by making use of a linear pre-trained classifier [31,32].
ent component classification by making use of a linear pre-trained classifier [31,32].

Figure 2. (a) EEG sensor layout. The frontal sensors AF3 (purple) and AF4 (orange) are the sensors

Figure 2. (a) EEG sensor layout. The frontal sensors AF3 (purple) and AF4 (orange) are the sensors
used for the FAA calculation. (b) Overview of determining four pairs (FAAi, SWBi), i = 1, …, 4, fromused
for the FAA calculation.
(b)data.
Overviewof determining
pairs (FAA
, SWB
. . .,the4, fromi ), i = 1,and
the pre-processed
EEG channel
The purple
time seriesfour
represents
the iAF3
channelthepre-processedchannelThe series
purpletime inseriesthe AF3
channeland theorangetime series EEG
standsfor AF4.data.
The timeshown
grayrepresents
symbolize thoseof otherunused1), namely
60 s, 120channels.
SWB
scoreswereforgiven
byThe
the time
participants
every 60insgray(Experimentorangetime
seriesstandsAF4.
series shown
symbolize
those ofatotherunuseds, 180 s, andso scoreson (only
the given
first 270
areparticipants
shown in theevery
drawing).
These time instants
are indicatedchannels.
SWB
were
bysthe60 s (Experiment1), namely
at 60 s, 120 s,by the dashed vertical lines. The 60 s intervals were chosen so that the SWB scores were given in the180s, and so on (only the first 270 s are shown in the drawing). These time instants are indicated bymiddle of these intervals. The lower part of (b) shows the frequency spectra that result in FAA values
the dashed vertical lines. The 60 s intervals were chosen so that the SWB scores were given in thecorresponding to each SWB score.
middle of these intervals. The lower part of (b) shows the frequency spectra that result in FAA values
corresponding
to each
SWB score.steps, the pipeline selects time segments, e.g., for 60 s long
After thesepreprocessing

intervals, interval 1 from 30 to 90 s of the EEG time series, interval 2 from 90 to 150 s,

After these preprocessing steps, the pipeline selects time segments, e.g., for 60 s longintervals, interval 1 from 30 to 90 s of the EEG time series, interval 2 from 90 to 150 s,interval 3 from 150 to 210 s, interval 4 from 210 to 270 s, and so on. Then, the frontal
channels AF3 and AF4 are selected. Following [33,34] a Fast Fourier Transform with aHanning window of 50%, overlap is applied and the mean power density within the alphaband (8–13 Hz) is computed for both channels and for each interval. FAA is then calculated
by subtracting the natural logarithm of the power density of the left side from that of
the right side. Unlike [33], we decided not to use the absolute value of the difference ofthe log-transformed power spectra to also see the direction of the difference. Hence, theformula we used is
FAA = mean(log pow R − log pow L )(1)

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with log standing for the natural logarithm, pow R being the power density of the signal on
the right side, and pow L the power density of the left side. Figure 2b shows the selection of
the channels and the time intervals, as well as the computation of the FAA values for thecorresponding SWB scores.
2.3. Time Intervals for Determining FAA
In order to verify the stability of our results and also to see how using different timeintervals for the FAA calculation will affect our results, we will perform the same analysis
but calculate the FAA over different time intervals. In this section, we present three different
analyses: Analysis 1, Analysis 2, and Analysis 3.
In Analysis 1, we use a 60 s interval for Experiment 1 and a 30 s interval for Experiment
2 around the given SWB (Tables 2 and 3, second column). In Analysis 2, we investigate how
different time intervals affect the results. We do not have a smaller time interval than 30 s
for the SWB scores, but we shrink the interval over which we calculate the FAA, namely, we
use intervals of lengths L = 5 s, 10 s, and 15 s. Moreover, we check two different approaches:(i) we calculate the FAA over the interval from L prior to the time tSWB when the SWB score
was recorded, i.e., [tSWB —L, tSWB ], and (ii) we calculate the FAA of an interval over bothsides of the time tSWB when the SWB score was recorded, i.e., [tSWB —L/2, tSWB + L/2]. In(i), the time of reporting the SWB score is at the end of the interval, see columns 3–6 inTable 3, and in (ii), the time of reporting the SWB score is in the middle of the interval, seecolumns 7–9 in Table 3.
Table 2. Overview of the time intervals used for determining the FAA for Analysis 1 and Experiment 1.
The SWB score from 1 to 10 is denoted as SWBi for i = 1, . . ., 4. Time intervals are given in seconds
after the start of the EEG recording.
SWB

Interval

SWB1
SWB2
SWB3
SWB4

[30, 90][90, 150][150, 210]
[210, 270]

Table 3. Overview of the time intervals used for determining the FAA in Analysis 1 and 2 forExperiment 2. The SWB score from 1 to 10 is denoted as SWBi for i = 1, 2, . . .. Time intervals are
given in seconds after the start of the EEG recording. L denotes the length of the time interval. The
parameter side = 1 if the time of the SWB recording was at the end of the interval and side = 2 stands
for an interval where the SWB was recorded in the middle of the interval.
SWB

Interval

Side = 1L=5sside = 1
L = 10 s

Side = 1
L = 15 s

Side = 2
L=5sSide = 2
L =10 sSide = 2
L = 15 s[25, 30][55, 60][85, 90][115, 120]
[145, 150]
[175, 180]

[20, 30][50, 60][80, 90][110, 120]
[140, 150]
[170, 180]

[15, 30][45, 60][75, 90][105, 120]
[135, 150]
[165, 180]

[27.5, 32.5][57.5, 62.5][87.5, 92.5][117.5, 122.5][147.5, 152.5][177.5, 182.5][25, 35][55, 65][85, 95][115, 125]
[145, 155]
[175, 185]

[22.5, 37.5][52.5, 67.5][82.5, 97.5][112.5, 127.5][142.5, 157.5][172.5, 187.5]

... .

... .

... .

... .

... .

[15, 45][45, 75][75, 105][105, 135]
[135, 165]
[165, 195]
... .

... .

SWB1
SWB2
SWB3
SWB4
SWB5
SWB6

Analysis 2... .

Analysis 1

For Analysis 2 described above, we do not use the data of the entire EEG time series,
but only data from some intervals. This results in omitting some data. It is not clear whether
a larger interval would lead to better results. Therefore, we perform Analysis 3, in which
we take the entire time series and divide it into intervals of length L = 5 s, 10 s, and k × 15 s,

SWB4
SWB5
SWB6
⁞
Sensors 2023, 23, 7006

[105, 135] [115, 120] [110, 120] [105, 120] [117.5, 122.5] [115, 125] [112.5, 127.5][135, 165] [145, 150] [140, 150] [135, 150] [147.5, 152.5] [145, 155] [142.5, 157.5][165, 195] [175, 180] [170, 180] [165, 180] [177.5, 182.5] [175, 185] [172.5, 187.5]
⁞
⁞
⁞
⁞
⁞
⁞
⁞

For Analysis 2 described above, we do not use the data of the entire EEG time series,8 of 16
but only data from some intervals. This results in omitting some data. It is not clear
whether a larger interval would lead to better results. Therefore, we perform Analysis 3,
in which we take the entire time series and divide it into intervals of length L = 5 s, 10 s,
for k = 1, . . ., 20, i.e., we divide the time axis into as many intervals of length L as possible.
and k × 15 s, for k = 1, …, 20, i.e., we divide the time axis into as many intervals of length
Figure 3 shows an illustration of a full time series of 300 s and an interval length of 45 s
L as possible. Figure 3 shows an illustration of a full time series of 300 s and an interval
when SWB scores were recorded every 30 s (Experiment 2). Considering a time series oflength of 45 s when SWB scores were recorded every 30 s (Experiment 2). Considering a
300 s, six full intervals of length 45 s can fit into it. We start at 15 s and add the six intervals
time series of 300 s, six full intervals of length 45 s can fit into it. We start at 15 s and add
continuously
until
we reach 300
What
also
to be
this approach
the six intervals
continuously
untils.we
reach300needss. Whatalsoconsideredneeds to beinconsidered
in is
that
different
original
SWB
scoresmay
fallwithinthesameinterval.
We
assumethat
this approach is that diﬀerent original SWB scores may fall within the same interval. We theoriginal
SWBthegiven
at time= 30 satistime
constant
t = 15 froms until= 45s, afterthatt = 45s, weassume thatoriginal
SWBt givent = 30 sfrom
is constantt =t 15s untilassumea different
SWB
from time= 45 stime
until
= 75
s, anduntillast originalafter that
we assume
a diﬀerent
SWBt from
t =t45s untilt = so75 ons, andso theon untilthe
SWB.
To associate
an associate
SWBInt with
theIntFAA
the giveninterval,
we take wethe takeaveragelast original
SWB. Toan SWB
withfrom
the FAA
from thegiven interval,
over
the originalscores givenin thatgiven
interval
weighted
the numberof numberseconds thisthe averageover SWB
the original
SWB scoresin thatintervalbyweighted
by theSWB
represents.
This
method resultsin having
non-integer
values for the
SWB
which
of seconds
this SWB
represents.
This method
resultsin having non-integer
valuesforIntthewethenroundwetothentheirroundnearestvalue,
so that
we canuse wethecansame
Int which
to integer
their nearest
integervalue,
so thatuseanalysis,
the sameas in
SWB
Analysisanalysis, 1asorin2.Analysis 1 or 2.

Figure 3.
3. Illustration
Illustration of
forforAnalysis
3. Thetimetime
seriescontinues
until untilaFigureof choosing
choosingtime
timeintervals
intervals
Analysis
3. Theseriescontinuesamaximum ofof 300300 ss and3030
s (Experiment2). 2).
A diﬀerent
colorcolor
representsamaximumand SWB
SWBisisrecorded
recordedeveryeverys (Experiment
A different
representsapossibly diﬀerent original SWB score SWBk for k = 1, …, 10. The gray boxes show how the six 45 s
possibly different original SWB score SWBk for k = 1, . . ., 10. The gray boxes show how the six 45 s
intervals are aligned within the 300 s and the corresponding associated SWBintk with k = 1, …, 6.
intervals are aligned within the 300 s and the corresponding associated SWBintk with k = 1, . . ., 6.

2.4. Correlation between FAA and SWB
2.4.
Correlation between FAA and SWB
After determining the FAA values and their corresponding SWB scores, we now aim
After determining the FAA values and their corresponding SWB scores, we now aim toto find a relationship between those (FAA, SWB) pairs. We test our hypothesis that there
find a relationship between those (FAA, SWB) pairs. We test our hypothesis that there will
will be a positive linear correlation between FAA values and the corresponding SWB
be a positive linear correlation between FAA values and the corresponding SWB scores (seescores (see RQ1). Looking at the dataset, we see that our data samples are not uniformly
RQ1). Looking at the dataset, we see that our data samples are not uniformly distributed.
distributed. Typically, participants would report an SWB score of 6, 7, or 8 more often
Typically,
participants would report an SWB score of 6, 7, or 8 more often than 1, 2, 3, orthan 1, 2, 3, or 10. Therefore, running a linear regression on the given data would result in
10.
Therefore,runninga lineargiven
data we
would
overfitting the central
valuesand regression
underfittingon
thetheothers.
Hence,
makeresult
use ofinanoverfitting
existthevalues and underfitting
others. Hence,
make usedataset,of an existinging central
and well-establishedapproach forthe
overcoming
such anweimbalanced
namely andwell-establishedapproach
overcomingTechnique)such an imbalanced
namely SMOTE
SMOTE (Synthetic
Minorityfor
Over-Sampling[35]. We usedataset,the implementation(Synthetic
Minority Over-Sampling
Technique)[35]. Weuse
thesource
implementationin thein the imbalanced-learn[36] python [37]package, which
is an
open
library underimbalanced-learn[36]
python[37]
package,
which
is
an
open
sourcelibrary
under
the
MIT
the MIT license and relies on scikit-learn [38].

license and relies on scikit-learn [38].
Before running SMOTE on each participant’s data individually, we make sure thateach SWB score was given at least three times, so that we have at least three (FAA, SWB)
pairs for each SWB reported by this participant. Otherwise, we remove all (FAA, SWB)
pairs that contain this specific SWB score. This step is needed because SMOTE relies ona minimum number of nearest neighbors to produce new artificial data. We then checkif there are at least three unique SWB scores among the given data in order to be able toperform a meaningful linear regression.
After these exclusion criteria, we apply SMOTE to the remaining data, resulting inthe same number of (FAA, SWB) pairs per SWB score for each individual participant.
Then, we perform a linear regression by making use of scikit-learn [38]. In Figure 4, weshow a comparison of the linear regression of the data of an example participant with andSensors 2023, 23, 7006

pairs for each SWB reported by this participant. Otherwise, we remove all (FAA, SWB)
pairs that contain this specific SWB score. This step is needed because SMOTE relies on aminimum number of nearest neighbors to produce new artificial data. We then check if
there are at least three unique SWB scores among the given data in order to be able toperform a meaningful linear regression.
After these exclusion criteria, we apply SMOTE to the remaining data, resulting in9 of 16
the same number of (FAA, SWB) pairs per SWB score for each individual participant.
Then, we perform a linear regression by making use of scikit-learn [38]. In Figure 4, weshow a comparison of the linear regression of the data of an example participant with andwithout
SMOTE.Without
WithoutSMOTE,
SMOTE,
canthat
middlevalues,in thiswithout applying
applying SMOTE.
wewe
canseeseethatthethemiddlevalues,in thiscase,
SWB
scores
of
4
or
5,
are
favored,whereas,after
applying
SMOTE
we
do
not
see
case, SWB scores of 4 or 5, are favored, whereas, after applying SMOTE we do not see that thatphenomenon.
is random,
we runrun thethe samesame analysis
analysis1010timestimes perphenomenon. Since
Since thethe output
output ofof SMOTE
SMOTE israndom, weparticipant
to
get
an
averageresult.
Runningthesameanalysis
one
or
even
100
times,
per participant to get an average result. Running the same analysis one or even 100 times,does
notchangethe results
much,much,
but itbut
turns
out that
the analysis
10 timesis enoughdoes
not change
the results
it turns
out runningthat running
the analysis
10 timesistogetstableresults.
We
end
up
with
10
slopesandintercepts
perindividual
participant,enough to get stable results. We end up with 10 slopes and intercepts per individual parwhich
wewhichthen averagefor further
processing.
The statisticalsignificanceof theofmean
ticipant,
we then averagefor further
processing.
The statisticalsignificancethe ofthese
slopes fromallfromparticipantsis testedwith awith
one-sided
t-test.t-test.
The Thep-valuemeanaveragedof these averaged
slopesall participantsis testeda one-sided
andthe 95%
confidence
intervalinterval(CI) are(CI)calculatedusingusing
SciPySciPy[39]. [39].
p-valueand the95% confidence
are calculated

Figure 4.4. Comparison
Comparison ofExperiment
2 andAnalysis
1. Thedots dots
in eachFigureofthethelinearlinearregression
regressionofof
Experiment
2 andAnalysis
1. Thein eachsubplot represent the (FAA, SWB) pairs of an example participant used for calculating the linear
subplot represent the (FAA, SWB) pairs of an example participant used for calculating the linear
regression which is shown as a straight line. On the upper left-hand side, the linear regression ofregression
whichis shown
asisagiven.
straightOn
the plots
uppereachleft-handside,
the oflinearregression
imbalanced
data
Theline.
other
three
show theresultlinearregressionof thethe original
original
imbalanceddata
is given. The
otherthreeSMOTE.
plots eachtheof
resultof SWB)linearpairs
regression
after correcting
for theimbalanced
datasetusing
Theshownumber(FAA,
in the after
original dataset#(FAA, 3) =dataset
3, #(FAA,
4) =SMOTE.
11, #(FAA,5) number= 12, andof#(FAA,= 3 andafterinSMOTE
correcting
for theare:
imbalanced
using
The
(FAA,6)SWB)
pairs
the original#(FAA,are:SWB)= 12 forof 3, 4,4)5,=and
The diﬀerencein thenumber(FAA,
SWB)
pairs #(FAA,isdataset#(FAA,
3) =SWB
3, #(FAA,
11, 6.
#(FAA,
5) = 12, and#(FAA,
6) = of
3 and
after
SMOTE
SWB) = 12 for SWB of 3, 4, 5, and 6. The difference in the number of (FAA, SWB) pairs is highlighted
for SWB = 3, see circled areas in all four subplots. When considering the original data, we can see thatthe linear regression favors values of SWB = 4 or 5. The results after SMOTE all show, while being
numerically slightly different, a regression that does not favor the values in the center anymore andthus has a steeper line.

3. Results
Analysis 1 of Experiment 1 did not yield any statistically significant results. There is atendency toward a positive linear correlation between FAA and SWB, but this correlation
does not have a statistically significant p-value (p > 0.05). Hence in the following, we justfocus on Experiment 2.
The first statistically significant result that we present is the analysis of the whole timeseries when FAA was calculated over 30 s intervals with SWB being in the middle of theSensors 2023, 23, 7006

10 of 16

time intervals (Analysis 1). Two participants were excluded because they were left-handed,
and it is not clear how FAA measures of left-handed participants differ from measuresfrom right-handed participants (see [25] for further information). A third participant was
excluded because less than three different SWB scores were given. We got p = 0.016 with
26 degrees of freedom (df) and a CI of [0.26, Inf) with an average number of 66.37 (FAA,
SWB) pairs per participant.
In the next parts, we present the results using different time intervals, i.e., Analysis 2 and 3
described in Section 2.3. In Analysis 2, intervals of length L = 5 s, 10 s, and 15 s were consideredwith the option that the SWB score was given at the end of the interval (marked as side = 1 inTable 3) or in the middle of the analyzed interval (marked as side = 2 in Table 3). The same
three participants as before were excluded. Table 4 gives the p-value, df, and CI of each of
the six analyses. One can see that if the interval of the FAA is taken before the SWB score is
asked (side = 1 in Table 4), the p-value is lower, and the left endpoint of the CI is higher thanfor the side = 2 cases. All results are statistically significant (p < 0.05). The 10 s interval withside = 1 gives the best result with p = 0.0016, 26 df, a CI for the slope of the linear correlationof [0.52, Inf), and an average number of 66.48 (FAA, SWB) pairs per participant.
Table 4. Results of Analysis 2 of Experiment 2. The first column shows the chosen time interval
length, i.e., L = 5 s, 10 s, or 15 s. The second column shows the sidedness of the interval, namely 1 if
the SWB score was reported at the end of the chosen time interval or 2 if the SWB score was given in
the middle of the time interval. The third column gives the corresponding p-value of a one-sided
t-test, with df given in the fourth column. The next column gives the CI of the slope of the linear
correlation. The hash symbol (#) in the last column stands for the average number of (FAA, SWB)
pairs per participant. The analysis with the best fit (i.e., lowest p-value and highest value of the left
endpoint of the CI) is given for a one-sided interval of 10 s and is marked in bold in the table.
L

Side

p-Value

df

CI

#

5
10
15
5
10
15

1
1
1
2
2
2

0.00170.00160.0056
0.03390.01980.0140

26
26
26
26
26
26

[0.32, Inf)
[0.52, Inf)
[0.35, Inf)
[0.05, Inf)
[0.14, Inf)
[0.23, Inf)

72.55
72.55
72.55
72.55
68.48
66.81

Analysis 3 uses the entire time series and also includes longer time intervals, see
Section 2.3. Table 5 gives an overview of the determined p-values for the one-sided t-test,
df, CI of the slope of the linear regression, and the average number of (FAA, SWB) pairs per
participant for a chosen length of the intervals. The presented intervals of length L = 5 s,
10 s, and k × 15 s for k = 1 to 10 are shown in Table 5. The same three participants as
before were excluded in all settings. However, the longer the interval length L, the moreparticipants were excluded (see df in Table 5). For intervals longer than 150 s, analysis
could not be performed because there were too few participants who would have met theinclusion criteria. In this analysis, we do not have a parameter “side” as in Analysis 2
because the time intervals can encompass more than one SWB score. Thus, it is not possible
to center the interval around one value. The interval of 15 s gives the lower endpoint of the
CI with the highest value and the interval of 10 s has a slightly lower p-value. These values
are marked in bold in Table 5.
We also looked at the results of the two left-handed participants. The first participant
had a negative slope of −0.91 in Analysis 1, whereas the same analysis for the second lefthanded participant resulted in an average slope of 6.11 for the linear fit over all 10 SMOTE
repetitions. A similar result was found for Analysis 2 and 3, namely, a slightly negative
slope for the linear fit between FAA and SWB for the first of the two left-handed participants
and a positive slope for the second left-handed participant.

Sensors 2023, 23, 7006

11 of 16

Table 5. Results of Analysis 3 of Experiment 2. The first and sixth columns show the selected interval
length in seconds. The second and seventh columns show the corresponding p-values, followed by
df and CI for the slope. The highest lower endpoint of the CI is given for a 15 s long interval andthe lowest p-value for an interval length of 10 s, both are marked in bold in the table. The first seveninterval lengths, i.e., 5, 10, 15, 30, 45, 60, and 75 s, all are statistically significant with p < 0.05. The hashsymbol (#) in the last column stands for the average number of (FAA, SWB) pairs per participant.
L

p-Value

df

CI

#

L

p-Value

df

CI

#

5
10
15
30
45
60

0.01000.00830.00850.02090.01340.0493

26
26
26
26
26
26

[0.192, Inf)
[0.280, Inf)
[0.311, Inf)
[0.200, Inf)
[0.301, Inf)
[0.004, Inf)

419.22207.44138.96
66.37
45.48
32.89

75
90
105
120
135
150

0.0332
0.21880.2707
0.06120.42830.2183

24
23
22
6
5
4

[0.111, Inf)[−0.444, Inf)[−0.568, Inf)[−0.112, Inf)[−2.938, Inf)[−1.033, Inf)

26.44
20.33
18.87
15.14
13.33
13.25

4. Discussion
4.1. Experiment 1
In the analysis of Experiment 1, in which SWB was recorded every 60 s, we did not
find any statistically significant results. Looking more closely at the data, we conclude that
one reason for not finding statistical significance for this experiment could be the amount ofavailable data. The number of available (FAA, SWB) pairs per participant for the analysis,
when FAA was calculated over 60 s, was 36.26 with two participants having only 17 pairs.
Since these numbers are very small, we expect that, if our hypothesis is correct, we willfind statistically significant results when more data are available. Another reason for not
finding a statistically significant correlation between FAA and SWB could be that there isno correlation and that our hypothesis is wrong. However, it may also be due to the timeinterval, i.e., a 60 s interval for the FAA calculation may be too long to correctly reflect
subtle changes in SWB. These two possible reasons were improved in Experiment 2, in
which the frequency of the recorded SWB scores was increased from 1 per 60 s to 1 per 30 s.
This gives a higher temporal resolution of the SWB and thus might be more sensitive tocapture slight changes in SWB, but it also increases the number of available (FAA, SWB)
pairs per participant.
4.2. Experiment 2, Analysis 1
Focusing on Experiment 2, Analysis 1, where we calculated FAA over a 30 s intervalwith the SWB score recorded in the middle, showed a positive linear correlation between
FAA and SWB with p = 0.016, df = 26, and CI = [0.26, Inf). This shows that the correlation
between FAA and SWB also holds even when SWB is varied over environmental conditions
and measured every 30 s, which means that we can answer our first research question (RQ1)
from the Introduction: Yes, FAA does reflect subtle short-term changes in SWB. If we compare
this result with the analysis of Experiment 1, we find that the average number of (FAA,
SWB) pairs almost doubled from 36.26 to 66.37. This means that the lack of data could
be the reason for not finding statistically significant results with the data of Experiment 1.
However, we also increased the frequency of SWB which could also influence the result.
4.3. Experiment 2, Analysis 2
In the next part, we analyzed the influence of the chosen time interval on the results
to find the best interval size and alignment. We tested several approaches. In Analysis 2,
we focused on small interval lengths, namely 5 s, 10 s, and 15 s, and two different analysis
methods, (i) with the SWB score reported at the end and (ii) in the middle of the analyzed
time interval. All of those six different settings resulted in p < 0.05 and the lower bound for
the CI was greater than 0. Going into more detail, we found that the worst result with thehighest p-value and the lowest left endpoint of the CI was for the 5 s interval with the SWB
score reported in the middle of the interval. The first reason for this is that it is a two-sided
interval, which means that there are distortions in the time series due to the participants’Sensors 2023, 23, 7006

12 of 16

head movements when reporting their SWB. We preprocessed the raw data and tried to
get rid of all artifacts, including movement artifacts, but it seems that we could not fully
correct them, because all two-sided intervals give worse results than the one-sided intervals.
Therefore, the artifacts, due to talking, affected the analyses, especially in the shortest timeinterval of 5 s. The other conclusion we can draw from this analysis is that a one-sided 10 sinterval gives the best results, namely CI = [0.52, Inf) and p = 0.0016. Thus, it seems thata 10 s interval is ideal for our analysis in the absence of motion by the participant. Since
all of these approaches yield statistically significant results, we can confirm the findingsof Analysis 1 and also conclude that the relevance of this correlation can be improved bychoosing shorter intervals before the time of reporting the SWB score.
4.4. Experiment 2, Analysis 3
In our final Analysis 3 we focused on time intervals of up to 300 s. Here, we assumed
that the SWB score was stable for 30 s around the time when reported by the participant.
We took the weighted average of all SWB scores in the chosen interval. The linear correlation between the FAA calculated over intervals of 5, 10, 15, 30, 45, 60, and 75 s andthe corresponding averaged SWB scores all show a statistically significant positive linear
correlation (p < 0.05, lower endpoint of CI > 0). The interval lengths of 60 and 75 s seemto mark a boundary between statistical significance and non-significance. Both of theseintervals are still statistically significant, but their p-values are already close to 0.05 andthe lower endpoint of the CI is close to 0. This is the same length of the time interval as
in Experiment 1 with a similar number of (FAA, SWB) pairs per participant. Since theresults were not statistically significant in Experiment 1 and are just below the cut-off inthis analysis, we conclude that this interval length with the corresponding average numberof (FAA, SWB) pairs is a boundary between statistical significance and non-significance.
Longer interval lengths, namely 90, 105, 120, 135, and 150 s, are all not statisticallysignificant, and intervals longer than 150 s did not yield any results at all due to the
exclusion criteria. There could be diverse reasons why the analysis of the interval length
between 90 s and 150 s did not yield statistically significant results. The first reason is thatsuch an interval is already too long to capture the small changes in brain functions that
correlate with short-time SWB changes. However, we cannot fully confirm this because
there are two other variables that contribute to having statistically significant results, andin our case, these are, first, the number of (FAA, SWB) pairs for each participant that go
into the analysis, which probably also influenced the analysis of Experiment 1, and second,the df of the analysis. We can clearly see that the number of average (FAA, SWB) pairs
per participant in the analysis decreases drastically as the interval length increases, startingwith 419.22 for 5 s and ending with 13.25 for 150 s. Similarly, we can observe that the df
decreases. For shorter interval lengths it remains quite stable with 26 for 5 s until 60 s and24 for 75 s. Then it drops and so does the relevance of the results.
To see if these two factors are the main causes of the poor performance of the longer
intervals, we limited the analysis of the shorter interval length to an input sample sizeof 20 (FAA, SWB) pairs and/or a df of eight by random sampling. In this case, even theanalyses of the shorter intervals cannot maintain their statistically significant results. Thus,
we cannot be sure which of the mentioned factors is the main reason for the lack of statisticalsignificance. This means that intervals with a length of >75 s for the FAA calculation might
already be too long to clearly represent the changes in SWB, but we cannot be sure because
the small number of (FAA, SWB) pairs included in the analysis and the low df clearly
influence the result. To further analyze this influence, we performed the same analysis with
100 randomly sampled (FAA, SWB) pairs per participant for interval lengths of 5 s, 10 s,
and 15 s. When comparing the three results, there was no clear tendency for any of thethree interval lengths to be superior to the other two. Therefore, the actual interval length
over which we calculate the FAA does not seem to affect the result as long as the sample
size and df are the same.

Sensors 2023, 23, 7006

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4.5. Comparing all Analyses Performed
When comparing the p-value and CI of all our analyses, it appears that the analysis of
a 10 s interval before the time of the SWB recording yields the best results. We conclude that
it is not the length of the interval that contributes to this result, but rather its location. Since
the interval is located before the SWB score was reported, it eliminates all sorts of motion
artifacts from saying the SWB score. We tried to get rid of such artifacts via preprocessing,but it seems that some are still present. In addition, the 10 s before the recorded SWB
seems to be the most accurate time to be in a specific SWB state. If we select 10 s intervals
continuously over the time series and associate an averaged SWB score with the computed
FAA values, the result is still statistically significant, but has a higher p-value and a lower
left endpoint of the CI. The reason may be that our assumption that SWB is stable for 30 s
and then changes immediately is only an approximation. We can say that an analysis ofabout 70 (FAA, SWB) pairs with accurate SWB performs better than using 200 pairs withapproximated SWB scores. This leads us to the answer of our second research question(RQ2) presented in the introduction: The length for the time interval to compute the FAA seems
to be less important than its temporal location. An interval over the 10 s prior to the SWB recording
yielded the best results. However, intervals of 5 s or 15 s prior to the SWB recording perform
similarly well. When considering all possible 5 s, 10 s, or 15 s intervals in the time series,
we get worse results than when just considering the ones before the SWB was recorded.
When it comes to left-handedness, we cannot draw any statistically significant conclusions because we only had two participants. We cannot even make an educatedguess because the two participants we analyzed had contradictory results. This meansthat left-handed participants could also have a tendency towards positive linear correlation, and we just happened to measure a particular participant who does not show it.
However, the opposite could also be true. A third possibility is that there is no tendency for
either a positive or negative linear correlation between FAA and SWB when all left-handed
participants are considered.
All things taken together, we were able to answer both of our questions (RQ1) and(RQ2). We found that the correlation between FAA and SWB holds for small time intervals,
with the specific interval location having the major influence on the performance of themodel. Thus, we can say that the positive linear correlation between FAA and SWB holds
not only on large time scales, when SWB is changed by psychological interventions over,e.g., weeks, as shown in the previous studies, but also when measured on small time scales,such as 30 s, when SWB is influenced by environmental conditions.
FAA is a relative measure. The higher FAA, the higher the activity in the left hemisphere also is. Affect is considered to be lateralized in the brain, with positive affect being
predominantly in the left hemisphere and negative affect predominantly in the right hemisphere [40,41]. Greater activity in the left than in the right prefrontal cortex was found to be
associated with dispositional positive affect [17]. Such an imbalanced activity is also related
to a higher reaction to positively rated emotional stimuli [18,42]. Greater left than rightprefrontal cortex activity also plays a role when it comes to suppressing or overcoming
negative affect [43,44]. The first finding of our study, that FAA is high when SWB is also
high, indicates higher left frontal activity when participants have higher SWB. Such an
asymmetry was also reported by [21,22]. We would also like to point out that our study
now indicates that this correlation also holds true when measuring short-term changes in
SWB, namely on a 30 s scale, and when only the physical environment is changed. Thismeans that the lateralization of brain activity adapts fast. This leads us to conclude thatthe correlation between FAA and SWB is not just a static phenomenon, but that it also
follows slight short-term SWB changes in a given physical environment. This allows us tothink about FAA not only as a measure in psychological or psychiatric studies, but also asa measure for everyday use that may one day find an application in smart homes, where
FAA could be used to control the physical environment.
It should be noted that the results presented in this paper are group-level evaluations,which means that they do not automatically hold at the individual participant level. In

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fact, there were participants who did not show this specific correlation at the individual
participant level. This may be partly due to the fact that SWB means something different
to each individual. We have tried to be as clear as possible in our explanation to theparticipants, but we cannot be sure that we have completely eliminated these individual
differences in interpretation in our participants. Especially in neuroscience, we see a highvariability between individuals, e.g., in the localization of language processing areas orwhenever the participant is left-handed [23]. The specific localization of the sensors used
for the FAA computation also seems to be important, see [23] for a discussion. We decided
to use an EEG headset in our study that was easy to use and quick to set up. This resulted ina trade-off between EEG preparation time and sensor density. Thus, an EEG headset with ahigher sensor density might provide results with a higher accuracy. This also needs to beconsidered when thinking about a smart home application. The specific sensors and bands
used in this study may not have been ideal choices for controlling the physical environment
or may vary from person to person. However, our research shows that FAA calculated
from the EEG sensors AF3 and AF4 could definitely be a candidate for such an application.
5. Conclusions
In this study we focused on short-term changes of SWB under different environmental
conditions. We aimed to find a correlation between EEG recordings, more specifically thederived FAA, and SWB. Such a correlation has been described in the literature. However,
we wanted to investigate whether such a correlation also holds for SWB in the sense of
feeling comfortable and well in the physical environment, or if it can only be considered as a
psychological or psychiatric measure. The results presented in this paper show that there isa positive linear correlation between FAA measured by EEG and short-term changes in SWB
when reported every 30 s on a scale from 1 to 10 and varied by environmental conditions.
This correlation was found to be strongest when FAA was calculated over a 10 s interval
before the SWB was reported. This means that changes in FAA in correlation with SWB canalso be seen on time scales of seconds. As mentioned in the previous sections, our results
are at the group level and do not automatically apply to each individual participant. Thus,
a future point of interest will be to discuss inter-subject variability as well as intra-subject
variability. Furthermore, we plan to investigate different frequency bands in combination
with all available EEG sensors to see if other combinations of frequency bands and EEG
sensors might also correlate with short-term SWB changes.
Supplementary Materials: The following supporting information can be downloaded at: https://www.
mdpi.com/article/10.3390/s23157006/s1. Table S1. In the first column we give the Part-Temp-Hum-Trialvariable, where Part stands for the participant number, Temp for the temperature (L = low, M = medium,H = high), Hum for the humidity (L = low, H = high), and Trial for the trial number (some trials had tobe repeated). The numbers in the first columns of the first seven rows are the intended absolute values.
From row 8 on we started using relative values. The temperature and humidity recordings for 28-M-L-1
were accidentally deleted. This is marked as ‘-‘ in the table. Tmean stands for the mean temperature
over the whole session and all used sensors. Tstd gives the standard deviation and Tmin and Tmax theminimum and maximum value measured during the session. Hmean is analogously the mean humidity
over the whole time of the session and all used sensors. Hstd stands for the standard deviation and
Hmin respective Hmax represent the minimum and maximum humidity values measured during thisone session. Tmean , Tstd , Tmin , and Tmax are given in units of degree Celsius [◦ C] and Hmean , Hstd , Hmin ,and Hmax in percent [%].
Author Contributions: Conceptualization and Methodology, B.W., K.L., D.K., Y.O., M.K. and M.M.;
Software, B.W. and K.L.; Validation, B.W.; Formal Analysis, B.W. and K.L.; Investigation, B.W.,
K.L., D.K. and Y.O.; Resources, D.K., Y.O., M.K. and M.M.; Data Curation, B.W., K.L. and D.K.;
Writing—Original Draft Preparation, B.W. and K.L.; Writing—Review and Editing, B.W., K.L., D.K.,
Y.O., M.K. and M.M.; Visualization, B.W. and K.L.; Supervision, M.K. and M.M; project administration, D.K., Y.O., M.K. and M.M. All authors have read and agreed to the published version of
the manuscript.

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Funding: This research received no external funding.
Institutional Review Board Statement: Our experiments received approval from Osaka University
Research Ethics Committee and permission from the head of our research institution.
Informed Consent Statement: Informed consent was obtained from all participants involved in
the study.
Data Availability Statement: The datasets generated during and/or analyzed during the current
study are available from the corresponding author on reasonable request.
Conflicts of Interest: The authors declare no conflict of interest.

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