This article has been accepted for publication in IEEE Transactions on Haptics. This is the author's version which has not been fully edited andcontent may change prior to final publication. Citation information: DOI 10.1109/TOH.2023.3266494

JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2021

1

Pseudo-haptic Heaviness Influenced by The Rangeof the C/D Ratio and the Position of the C/D Ratio
within a given Range
Takahiro Kawabe, Member, IEEE,, Yusuke Ujitoko, Member, IEEE,

Abstract—Pseudo-haptic heaviness refers to the illusory sensation of heaviness caused by a dissociation in amplitudes between
object movements on a screen and users’ motor actions. The
amplitude ratio of object movements to the user’s actions, theso-called C/D ratio, is a powerful determinant of pseudo-haptic
heaviness. According to previous studies, perceptual judgments
for a given stimulus value are influenced by the position of thevalue within a given stimulus range, while no studies have shown
the same to be true for pseudo-haptic heaviness. The present
study examined whether pseudo-haptic heaviness determined by
the C/D ratio was influenced by the range of C/D ratios, andalso, by the position of the C/D ratio within a given range.
Participants were asked to drag and lift a square on the screen
up to a target line and then rate its heaviness; the range of
C/D ratios was controlled as a between-participants factor. We
observed a phenomenon whereby both the range and position of
the C/D ratio influenced the rated heaviness. This phenomenon
was clearly established over 8 experimental trials. We conclude
that both the C/D ratio range and the position of the C/Dratio within a given range are determinants for pseudo-haptic
heaviness.
Index Terms—pseudo-haptic heaviness, the range of C/D ratio,
position in C/D ratio range, human perception, 2D display

I. I NTRODUCTIONPSEUDO-HAPTIC FEEDBACK [1], [2] is an information
presentation technique for providing users with various object-related sensations such as heaviness [3]–[7], softness [8]–[11], texture roughness [12], friction [13], and soforth. Such sensations are generated on the basis of the crossmodal integration of sensorimotor signals from users’ motor
actions with the sensory feedback provided in response tothem [14], [15]. In particular, the space-time relationship of
the sensorimotor signals plays a critical role in determining thestrength of pseudo-haptics as described below. Previous studies[5], [6], [16] have shown that the relative speed of an object’s
movement on a monitor in relation to the motor action appliedin the physical space to cause the object to move determined
the sensation of heaviness for the object. Specifically, lower
ratios of object movement to hand movement tend to produce
an impression that the object is heavier. The relative speed
is often described proportionally by a control-display (C/D)
ratio. However, the precise definition of the C/D ratio varies
across studies; in our definition for this study, the C/D ratio
increases with the relative speed of the cursor (or the object)
T. Kawabe and Y. Ujitoko are with NTT Communication Science Laboratories, 3-1, Morinosato Wakamiya, Atsugi, 243-0033, Kanagawa, Japan
Manuscript received XXX XX, 2022; revised XXX XX, 2022.

on the monitor in relation to the user’s motor action. (Notethat the ratio should more properly be called the D/C ratio,
not the C/D ratio. We refer to it as the C/D ratio, following
the practice of previous studies [16]–[18]).
Although previous studies have repeatedly reported thesignificant role of the C/D ratio in the determination of objectrelated sensations such as heaviness, it was unclear how thesensations were influenced by the position of the C/D ratio
within the given range that users experienced. Previous studies
have shown that perceptual judgments for an identical stimulus
value were biased by the position of the value within its
range. For example, the weight (estimated in grams) of areal object (i.e., not pseudo-haptic heaviness) was judged
to be greater when the object was presented among objects
having lighter weights than when it was presented among
objects with heavier weights [19], [20]. In addition to weight
judgments for a real object, a similar effect of the distributionof stimulus values on perceptual judgment has been reported
for the sweetness of a drink [21], the size of an object [21],the loudness of a tone [22], [23], and so forth. It was still
unclear whether the same effect shown in previous studies[19], [20] could be observed for pseudo-haptic heaviness as
for assessments of the weight of a real object – namely, thatpseudo-haptic heaviness was also influenced by the positionof the C/D ratio within its range.
The purpose of the present study was two-fold. The first
purpose was to examine whether pseudo-haptic heaviness was
influenced by the position of the C/D ratio in its range. In theexperiment, the different groups of participants were tested
with stimulus sets with different ranges of C/D ratios. The
important point was that, as shown in Figure 1, every stimulus
set contained a specific value (0.6) of the C/D ratio. By
employing stimulus sets with different ranges of C/D ratio, wewere able to examine whether pseudo-haptic heaviness with a
C/D ratio of 0.6 was influenced by differences in the ranges of
the C/D ratios among the stimulus sets. It was expected thatas the 0.6 ratio was located at the lower end of the given C/Dratio ranges, the pseudo-haptic heaviness would be greater (seethe caption in Figure 1 for detail). The ratio 0.6 was chosenbecause preliminary observations revealed that this ratio was
the midpoint of the C/D ratio range within which users could
comfortably operate an object with a mouse.
The second purpose was to check whether pseudo-haptic
heaviness was influenced by the difference in the level of the
C/D ratio within the given ranges. Based on previous studies [3]–[7], it was expected that a C/D ratio range involving© 2023 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See https://www.ieee.org/publications/rights/index.html for more information.

This article has been accepted for publication in IEEE Transactions on Haptics. This is the author's version which has not been fully edited andcontent may change prior to final publication. Citation information: DOI 10.1109/TOH.2023.3266494

JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2021

2

higher ratios (e.g., 0.6-1.0) would produce the sensation of alighter object than a C/D ratio range involving lower ratios(e.g., 0.2-0.6). Moreover, Weber’s law and Fechner’s law [24]predict that the variation of rating scores within a range would
depend on the level of the C/D ratio within the given range.
That is, as the level of the C/D ratio increased, the variation
would be smaller because the discriminability of the ratio
would likely be decreased.
Section II describes related previous work. Section III
describes our user experiment. Finally, Section IV describes
the significance and the limitations of the present study andseveral issues that can be assessed in future studies.
II. R ELATED W ORK ON THE E FFECT OF S TIMULUS R ANGEON P ERCEPTUAL J UDGMENTS
It has been shown that a rating score for a certain stimulus
value is influenced by the range of stimulus values in a stimulus set [25], [26]. For example, a previous study [26] showedthat the size of a square or the number of dots presented
was reported to be greater when identical stimulus values
were tested within a stimulus set with low rather than highranges of stimulus values. As described in the Introduction,
similar phenomena have been shown for the weight judgmentof real objects, the sweetness of a drink, and the loudness ofa tone [21], [22]. Another previous study [23] also showedthat even when the mean stimulus value was constant, therange of stimulus values in a stimulus set drastically altered
the slope of the rating scores as a function of the stimulus
value. Specifically, the slope was steeper as the range ofthe stimulus values became narrower. The results of previous
studies indicate that the judgment of magnitude for a specificstimulus value is influenced by the position of the value within
the range of a given stimulus set.
On the other hand, no previous studies have posed the question of whether pseudo-haptic heaviness is influenced by the
position of a C/D ratio within its given range. The followinguser experiment was designed to answer that question.

Pseudo-haptic heaviness(Arbitrary unit)

Range of C/D ratio
0.2-0.6
0.4-0.8
0.6-1.0

A
0.2

B
0.4

0.6
0.8
C/D ratio

1.0

0.2

0.4

0.6
0.8
C/D ratio

1.0

Fig. 1. Schematic figures describing our prediction. If pseudo-haptic heavinessis determined by the position of the C/D ratio within its given range, the result
will be as shown in (A). On the other hand, if it is determined solely by the
C/D ratio irrespective of its range, the result will be as shown in (B).

III. U SER E XPERIMENT
A. Participants
In total, 187 people participated in the experiment. The
participants were recruited online by a crowdsourcing researchcompany in Japan and were paid for their participation. Only
people who could participate in the experiment using their own
personal computers with a computer mouse were recruited andthey were unaware of the specific purpose of the experiment.
Ethical approval for this study was obtained from the ethics
committee at Nippon Telegraph and Telephone Corporation(Approval number: R02-009 by NTT Communication Science
Laboratories Ethics Committee). The experiment was conducted according to principles that have their origin in theHelsinki Declaration. Written informed consent was obtained
from all participants in this study.
B. Design and Condition
Using a between-participants design, we tested the effect of
C/D ratio range on pseudo-haptic rating scores. The participants were assigned to one of three groups that were tested
with different C/D ratio ranges. The group assigned to the0.2-0.6 C/D ratio range condition [0.2, 0.3, 0.4, 0.5, and0.6] consisted of 63 participants (31 females) whose mean
age was 35.95 (SD: 8.76). The group assigned to the 0.40.8 C/D ratio range condition [0.4, 0.5, 0.6, 0.7, and 0.8]
consisted of 62 participants (32 females) whose mean age was
35.57(SD: 8.73). The group assigned to the 0.6-1.0 C/D ratio
range condition [0.6, 0.7, 0.8, 0.9, and 1.0] consisted of 62
participants (32 females) whose mean age was 35.10 (SD:9.17).
C. Procedure
1) Apparatus: This experiment was conducted online. Participants were required to use a personal computer with acomputer mouse for the experiment. It was not possible toparticipate in our experiments using either smartphones ortablet PCs because our experimental script would not workon those devices. The mean frame rate of the participants’
computer monitors was was 58.42Hz with a standard deviation of 6.38 Hz. We assembled our experimental websiteby using p5js (https://github.com/processing/p5.js). Although
we did not measure network speeds in each participant’s
environment, it was not expected that the latency for stimulus
presentation would be large since our experimental program
was assembled with the Java scripting language, which ran
locally on the participant’s computer and thus the program did
not communicate with our server during the experiment. For
this reason, network communication states in the participant’s
environment did not affect the performance of our program.
We provided the participants with a URL link to our experimental website. The participants visited the website andperformed the experimental task.
2) Card Size Matching: Before performing the practice andmain trial sessions, participants conducted a card size matchingtask in which they adjusted the size of a rectangle on theirdisplay so that the rectangle had the same size as a credit cardor any other identically-sized card. By asking the participant
to do this, we could account for the pixel size of the monitor
that the participant used for the experiment, as reported inprevious studies [27]–[29].

© 2023 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See https://www.ieee.org/publications/rights/index.html for more information.

This article has been accepted for publication in IEEE Transactions on Haptics. This is the author's version which has not been fully edited andcontent may change prior to final publication. Citation information: DOI 10.1109/TOH.2023.3266494

JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2021

D. Measures
Our aim was to analyze how the rating scores for pseudohaptic heaviness with the C/D ratio 0.6 differed among theparticipant groups. We also wanted to check the effect of trial
blocks on the variation in pseudo-haptic heaviness to understand how quickly the observed effect occurred. Additionally,
we wanted to examine the mean rating scores as well as thevariation of rating scores within a given C/D ratio range.
E. Results and Discussion
1) Effect of the Position of the 0.6 C/D Ratio: The rating score for each condition was averaged across the four
repetitions for each participant. Figure 3 shows the mean
rating scores for pseudo-haptic heaviness as a function of the
C/D ratio for each C/D ratio range. We checked whether the
rating scores were determined by the position of the C/D ratio
within its given range. Specifically, we analyzed whether the
rating score for the condition with a C/D ratio of 0.6 differedamong the C/D ratio range conditions. Since rating scores
do not follow a normal distribution, it is not appropriate toparametrically assess the statistical aspect of the scores intheir raw form. Hence, we transformed the rating scores byTarget line

SquareRepresentative
trajectory ofsquareCursorInitial position ofsquareFig. 2. Schematic descriptions of stimuli. Stimuli consisted of a square, thecursor (a pink disk), and a target line. The square, which was 1.1 cm (width)
× 1.1 cm (height), had an RGB intensity of [64, 64, 64]. At the initiationof each trial, the square was positioned so that its center was 4.4 cm below
the center of the monitor. The target line, which was 11.6 × 0.1 cm, wascentered at 2.2 cm below the center of the display. The RGB intensity of thetarget line was [192, 192, 192] when the square did not overlap the target
line but changed to an RGB intensity of [192, 255, 192] when this overlap
occurred. While being clicked/dragged, the square was bordered by a 1-pixel
white line with an RGB intensity of [192, 192, 192]. The cursor had a circularshape with an RGB intensity of [246, 186, 187]. The background had an RGB
intensity of [128, 128, 128]. The RGB intensities and shapes of the visual
stimuli were chosen to ensure high visibility of the components even when
they were superimposed on each other.
Range of C/D ratio
0.2-0.6

0.4-0.8

0.6-1.0

5.0
Mean rating scores for object heaviness3) Practice Session: After completing the card size matching task, the participant moved on to a practice session. Thissession consisted of two trials each with the lowest and highest
C/D ratios in the given C/D ratio range. The participant was
asked to drag and lift a square up to a target line using
the computer mouse (see Figure 2). We believe this task
represents a typical behavior for users dragging an object ina graphical user interface. After the square reached the target
line, the participant was asked to release the button of themouse. Immediately after the participant released the square,
the stimuli disappeared, and instead, five buttons appeared.
The participant was asked to rate the strength of the heavinesssensation for the square on a 5-point scale. The next trial began
after they had clicked one of these rating buttons.
While the participant was not dragging the square, the cursor
speed was determined by the default setting of the operating
system of the participant’s computer. We refer to the cursor
speed based on the setting in the operating system as the“default speed”. While dragging the square, the cursor position
relative to the square was fixed at the location within it where
the participant clicked to start dragging it. Moreover, the cursor
speed while dragging the square was set at the default speed
multiplied by the C/D ratio. Thus, when the C/D ratio was
1, the cursor speed was identical to the default speed of the
cursor. When the C/D ratio was below 1, the cursor speed was
lower than the default speed of the cursor.
4) Main Session: After the participant had completed thepractice session, the main session was initiated. The participant’s task in the main session was identical to the one
in the practice session. Each participant performed 20 trials
consisting of the four repetitions of the 5 levels of the C/Dratio. The order of the trials was not blocked, but rather
randomized within and across the participants. The experimentlasted 5 to 10 minutes depending on the participant.

3

4.0

3.0

2.0

1.0
0.2

0.4

0.6

0.8

1.0

C/D ratio

Fig. 3. Results of our user experiment. Rating scores for object heaviness areplotted as a function of the C/D ratio. Error stripes denote 95% confidence
intervals.

using an aligned rank transformation (ART) [30], and thenconducted an analysis of variance (ANOVA) with the C/Dratio range as a between-participant factor. The main effectof the C/D ratio range was significant [F(2,184) = 37.335, p< .0001, ηp2 = 0.289]. Using the ART-C [31], we conducted
multiple comparison tests, which showed that the rating scoresfor the C/D ratio of 0.6 in the 0.2-0.6 range were significantly
greater than those in the 0.4-0.8 and 0.6-1.0 ranges, while thedifference in the rating scores between the 0.4-0.8 and 0.6-1.0
ranges did not reach a significance level, p = .05 (Table I).
The results showed that the position of a C/D ratio within
its given range significantly influenced the rating scores forpseudo-haptic heaviness. Specifically, rating scores for pseudo-© 2023 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See https://www.ieee.org/publications/rights/index.html for more information.

This article has been accepted for publication in IEEE Transactions on Haptics. This is the author's version which has not been fully edited andcontent may change prior to final publication. Citation information: DOI 10.1109/TOH.2023.3266494

JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2021

TABLE IT HE RESULTS OF MULTIPLE COMPARISON TESTS FOR MEAN RATINGSCORES WITH A C/D RATIO OF 0.6 AMONG PARTICIPANT GROUPS TESTEDWITH DIFFERENT C/D RATIO RANGES .
Pair
0.2-0.6 v.s. 0.4-0.8
0.2-0.6 v.s. 0.6-1.0
0.4-0.8 v.s. 0.6-1.0

DF
184
184
184

t-ratio
6.052
8.357
2.296

p value<0.0001<0.0001=0.0684

Cohen’s d
1.082
1.495
0.412

2) Effect of Trial Blocks: It is important to establish when
during the 20 trials the position of the C/D ratio within its
given range began to have an effect. To answer this question,
we divided the rating scores with the 0.6 C/D ratio into five
trial blocks, each of which involved four sequential trials. The
variation of the rating scores among the trial blocks is shownin Figure 4. Using the rating scores, we conducted a twoway ANOVA with the C/D ratio range and the trial block as
between-participant factors. The main effect of the C/D ratio
range was significant [F(2,541) = 56.848, p < .0001, ηp2 =0.173]. Multiple comparison tests (Table II) showed that eachC/D ratio was significantly different from the others. On theother hand, the main effect of the trial block was not significant[F(4,541) = 2.106, p = .0787, ηp2 = 0.015]. Interaction between
the two factors was significant [F(8,541) = 3.664, p = .0003,
ηp2 = 0.051].
We further analyzed the simple main effect of the significant
interaction. Since the volume of the results is large, we provide
the details of this analysis in the section Supplementary data
1. Here we briefly describe the significant results. The simple
main effect of the trial block was significant only with the
0.2-0.6 C/D ratio range. Multiple comparison tests showedthat with this range, trial block 1 was significantly different
from blocks 3 and 4. The simple main effect of the C/D ratio
range was significant with blocks 2, 3, 4, and 5. According tomultiple comparison tests, the 0.2-0.6 range was significantly
different from the 0.4-0.8 and 0.6-1.0 ranges. Uniquely withblock 3, the 0.4-0.8 range was also significantly different fromthe 0.6-1.0 range.
The results showed that the effect of the position of the
C/D ratio within its given range was not observed in the initial
four trials. The effect became significant in the following trial
blocks. The results indicate that the brain establishes internal
response criteria for a stimulus range quickly (with less thaneight samples) and uses the criteria to perceptually judge eachstimulus value.
3) Effect of C/D Ratio Range on Overall Rating: We examined whether the mean rating scores were different among
participant groups tested with different C/D ratio ranges. The
main effect of the C/D ratio range was significant [F(2,184)= 18.653, p < .0001, ηp2 = 0.168]. Using the ART-C [31],we conducted multiple comparison tests with the Bonferroni
correction, which showed that the rating scores for a certain

Range of C/D ratio
0.2-0.6
Mean rating scores for pseudo-haptic heavinesshaptic heaviness rose as the position of a C/D ratio within its
range became lower. The results indicate that in addition to aheaviness sensation for real objects [19], [20], pseudo-haptic
heaviness for a virtual object is also affected by the positionof a C/D ratio within its given range.

40.4-0.8

0.6-1.0

5.0

4.0

3.0

2.0

1.0
1
(1st-4th)2(5th-8th)3
4
5(9th-12th) (13th-16th) (17th-20th)
Trial block

Fig. 4. The variation of rating scores with the 0.6 C/D ratio among trial blocks
for each C/D ratio range. Error stripes denote 95% confidence intervals.
TABLE II
T HE RESULTS OF MULTIPLE COMPARISON TESTS FOR MEAN RATINGSCORES WITH A C/D RATIO OF 0.6 AMONG PARTICIPANT GROUPS TESTEDWITH DIFFERENT C/D RATIO RANGES WHEN TRIAL BLOCKS ARECONSIDERED .
Pair
0.2-0.6 v.s. 0.4-0.8
0.2-0.6 v.s. 0.6-1.0
0.4-0.8 v.s. 0.6-1.0

DF
541
541
541

t-ratio
7.263
10.4973.571

p value<0.0001<0.0001=0.001

Cohen’s d
0.812
1.199
0.386

C/D ratio range were significantly different from those in theother ranges (Table III).
The results indicate that the overall rating scores for pseudohaptic heaviness vary with the level of C/D ratio within its
range, consistent with the findings in previous studies [5], [6],[16].
TABLE IIIT HE RESULTS OF MULTIPLE COMPARISON TESTS AMONG THE
PARTICIPANT GROUPS FOR MEAN RATING SCORES .
Contrast
0.2-0.6 v.s. 0.4-0.8
0.2-0.6 v.s. 0.6-1.0
0.4-0.8 v.s. 0.6-1.0

DF
184
184
184

t-ratio
2.543
6.083
3.527

p value=0.0355<0.0001=0.0016

Cohen’s d
0.45481.0882
0.6333

4) Variation of Pseudo-haptic Heaviness within Each
Range: As described in the Introduction, the Weber ratio
predicted that the variation in rating scores within each range
would be smaller for higher levels of the C/D ratio within
the given range. To quantify the variation in each range, we
calculated the “variation index” (Figure 5) by subtracting therating scores for the highest C/D ratio within a range fromthe scores for the lowest one in that range. We conducted an
ANOVA with the C/D ratio range as a between-participant
factor. The main effect of the C/D ratio range was significant© 2023 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See https://www.ieee.org/publications/rights/index.html for more information.

This article has been accepted for publication in IEEE Transactions on Haptics. This is the author's version which has not been fully edited andcontent may change prior to final publication. Citation information: DOI 10.1109/TOH.2023.3266494

JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2021

[F(2,184) = 32.607, p < .0001, ηp2 = 0.262]. As shown in
Table IV, multiple comparison tests showed that the variationindex for a certain C/D ratio range differed significantly fromthat for the other C/D ratio ranges.
The results indicate that pseudo-haptic heaviness withineach C/D ratio range is influenced by the discriminability of
the C/D ratio.

Variation index

3.0

2.0

1.0

0.0

0.4-0.8

0.2-0.6

0.6-1.0

Range of C/D ratio

Fig. 5. Variation index (i.e., the variation of rating scores within each rangeof the C/D ratio). Error bars denote 95% confidence intervals.

TABLE IV
T HE RESULTS OF MULTIPLE COMPARISON TESTS AMONG THE
PARTICIPANT GROUPS FOR THE VARIATION INDEX .
Pair
0.2-0.6 v.s. 0.4-0.8
0.2-0.6 v.s. 0.6-1.0
0.4-0.8 v.s. 0.6-1.0

DF
184
184
184

t-ratio
3.943
8.075
4.116

p value=0.0003<0.0001=0.0002

Cohen’s d
0.705
1.444
0.739

IV. G ENERAL D ISCUSSION
A. SignificanceThe main significance of the present study has been to showthat the pseudo-haptic heaviness sensation was influenced
concurrently by the C/D ratio range and the position of the C/Dratio within a given range. Consistent with previous studies, a
C/D ratio range involving higher ratios produced lower ratingscores for pseudo-heaviness. Moreover, as expected, a C/Dratio range involving higher ratios showed lower variations ofrating scores within the range than those involving lower ratios. Importantly, the position of the C/D ratio within its given
range also influenced the mean rating scores. Specifically, alower position in the range produced higher rating scores forpseudo-haptic heaviness. Due to the concurrent involvement of
the C/D ratio range and the position of the C/D ratio withinthat range, the obtained results did not match the predictions
in either Figure 2A or Figure 2B, but instead fell into a pattern
in between.
The results of the present study may be an importantsource of information for engineers who wish to provide
users with certain specific levels of pseudo-haptic heavinessfor several different objects. Conventionally, engineers assume

5

that a specific level of the C/D ratio will produce a specificlevel of pseudo-haptic heaviness. However, according to our
results, this assumption is not always valid because, among
multiple objects being compared, pseudo-haptic heaviness will
be influenced by the position of the C/D ratio within its given
range.
B. Limitations and Future Issues
Finally, we would like to mention several limitations of thepresent study and some issues to be addressed in future studies.
Because the present study adopted a between-participant
design, it is unclear whether similar results would be obtained
when different ranges of the C/D ratio were tested over timewith a single participant. Future studies may check whether
the pattern of rating scores changes with the range of the
C/D ratio when the different ranges are tested in different
sessions but with the same participant. Moreover, since we
did not investigate any condition in which the cursor speed
was higher than the default speed, it is difficult to knowwhat effect this would have. We did not measure the cursor
speed for each participant’s computer individually, and it isunclear how individual differences in cursor speed might haveinfluenced the determination of the heaviness sensation. Thisis one fascinating issue for future investigation.
Though we manipulated the C/D ratio range, an interesting
direction for further study would be to examine how the sizeof the range influences the results. As described earlier, aprevious study [23] has shown that the size of the range ofstimulus values altered the slope of the rating scores as afunction of the stimulus value, even when the mean stimulus
value was constant. In future studies, it will be possible tocheck how the size of a C/D ratio range influences the slopeof the rating scores of pseudo-haptic heaviness as a functionof the C/D ratio.
As we have already mentioned, differences between themonitors used by the participants are unlikely to have influenced the participants’ performance because we matched
the stimulus sizes across the environments of the different
participants, as described above. That said, it is neverthelessa critical limitation that we did not control the experimental
apparatus among the participants. Moreover, though we recruited participants who would use a personal computer with acomputer mouse to perform our task, we did not verify whether
they actually used a mouse or a trackpad (common in laptop
computers) in the experiment. We also did not control theviewing distance.
It is also one of the limitations of the present study that
we did not check each participant’s previous experience ofthe pseudo-haptic effect. Past experience with the pseudohaptic effect might cause a difference in the discriminabilityof the effect. For example, it might be easier for experienced participants to interpret the difference in the cursor
speed as an indication of a difference in heaviness. Indeed,a previous study [32] has reported individual differences inthe discriminability of the pseudo-haptic effect. Thus, futurestudies may require checks as to whether individual differences
have affected the results and how these differences can be
explained.

© 2023 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See https://www.ieee.org/publications/rights/index.html for more information.

This article has been accepted for publication in IEEE Transactions on Haptics. This is the author's version which has not been fully edited andcontent may change prior to final publication. Citation information: DOI 10.1109/TOH.2023.3266494

JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2021

It would also be interesting to investigate whether, in
addition to heaviness, other pseudo-haptic sensations such as
stiffness and roughness are also determined based on the C/Dratio range and the position of the C/D ratio within its range.
Finally, one could point out a problem in the fact that we
did not test whether the effect on pseudo-haptic heaviness ofthe position of the C/D ratio in its range could be observed
even when participants were asked to judge the heavinessby using an external reference such as the weight of a real
object. Since we examined pseudo-haptic heaviness using only
a rating scale, we must admit that the scope of the resultsin the present study is limited to situations where users are
expected to internally establish some response criteria withina given C/D ratio range. We believe that any application
implementing pseudo-haptic heaviness among several objects
requires the internal establishment of response criteria about
which feedback corresponds to a light or heavy sensation.
Thus, we believe it was valid for the present study to use
a rating scale. Nevertheless, it would be interesting to check
whether similar results are observed when the participant isasked to report the degree of pseudo-haptic heaviness bycomparing the sensation with the heaviness of an actual object,
whereby the participants would not seem to require a numberof attempts to establish internal response criteria for a given
range of stimuli. On the other hand, even if similar results are
not observed when the heaviness of an actual object is used
as a response criterion, that does not affect the interpretationof our results, because the main contribution of this study is
to show that the internal establishment of the response criteria
for the pseudo-haptic heaviness occurred without an externalreference.
R EFERENCES[1] A. Lécuyer, “Simulating haptic feedback using vision: A survey ofresearch and applications of pseudo-haptic feedback,” Presence: Teleoperators and Virtual Environments, vol. 18, no. 1, pp. 39–53, 2009.
[2] Y. Ujitoko and Y. Ban, “Survey of pseudo-haptics: Haptic feedback design and application proposals,” IEEE Transactions on Haptics, vol. 14,
no. 4, p. 699–711, 2021.
[3] P. Issartel, F. Guéniat, S. Coquillart, and M. Ammi, “Perceiving mass in
mixed reality through pseudo-haptic rendering of Newton’s third law,”in 2015 IEEE Virtual Reality (VR). IEEE, 2015, pp. 41–46.
[4] S. Kaneko, T. Yokosaka, H. Kajimoto, and T. Kawabe, “A pseudohaptic method using auditory feedback: The role of delay, frequency,
and loudness of auditory feedback in response to a user’s button
click in causing a sensation of heaviness,” IEEE Access, vol. 10, p.
50008–50022, 2022.
[5] T. Kawabe, Y. Ujitoko, and T. Yokosaka, “The relationship between
illusory heaviness sensation and the motion speed of visual feedback
in gesture-based touchless inputs,” Frontiers in Psychology, vol. 13, p.
811881, 2022.
[6] M. Samad, E. Gatti, A. Hermes, H. Benko, and C. Parise, “Pseudohaptic weight: Changing the perceived weight of virtual objects bymanipulating control-display ratio,” in Proceedings of the 2019 CHI
Conference on Human Factors in Computing Systems, 2019, pp. 1–13.
[7] R. Yu and D. A. Bowman, “Pseudo-haptic display of mass and mass
distribution during object rotation in virtual reality,” IEEE Transactions
on Visualization and Computer Graphics, vol. 26, no. 5, pp. 2094–2103,
2020.
[8] M. Achibet, B. Le Gouis, M. Marchal, P.-A. Leziart, F. Argelaguet,
A. Girard, A. Lécuyer, and H. Kajimoto, “Flexifingers: Multi-finger
interaction in vr combining passive haptics and pseudo-haptics,” in 2017
IEEE Symposium on 3D User Interfaces (3DUI). IEEE, 2017, pp. 103–106.

6[9] I. Jang and D. Lee, “On utilizing pseudo-haptics for cutaneous fingertip
haptic device,” in 2014 IEEE Haptics Symposium (HAPTICS). IEEE,
2014, pp. 635–639.
[10] T. Kawabe, “Mid-air action contributes to pseudo-haptic stiffness effects,” IEEE Transactions on Haptics, vol. 13, no. 1, pp. 18–24, 2019.
[11] P. Punpongsanon, D. Iwai, and K. Sato, “Softar: Visually manipulating
haptic softness perception in spatial augmented reality,” IEEE Transactions on Visualization and Computer Graphics, vol. 21, no. 11, pp.
1279–1288, 2015.
[12] K. Watanabe and M. Yasumura, “Visualhaptics: Generating haptic sensation using only visual cues,” in Proceedings of the 2008 International
Conference on Advances in Computer Entertainment Technology, 2008,
pp. 405–405.
[13] Y. Ujitoko, Y. Ban, and K. Hirota, “Modulating fine roughness perception of vibrotactile textured surface using pseudo-haptic effect,” IEEE
Transactions on Visualization and Computer Graphics, vol. 25, no. 5,
pp. 1981–1990, 2019.
[14] K. Collins and B. Kapralos, “Pseudo-haptics: Leveraging cross-modal
perception in virtual environments,” The Senses and Society, vol. 14,
no. 3, pp. 313–329, 2019.
[15] S. Luo, N. F. Lepora, U. Martinez-Hernandez, J. Bimbo, and H. Liu,
“Vitac: Integrating vision and touch for multimodal and cross-modal
perception,” Frontiers in Robotics and AI, vol. 8, 2021.
[16] Y. Ban and Y. Ujitoko, “Enhancing the pseudo-haptic effect on thetouch panel using the virtuual string,” 2018 IEEE Haptics Symposium(HAPTICS), p. 278–283, 2018.
[17] A. Lécuyer, J.-M. Burkhardt, and L. Etienne, “Feeling bumps and holes
without a haptic interface: the perception of pseudo-haptic textures,” inProceedings of the SIGCHI conference on Human factors in computing
systems, 2004, pp. 239–246.
[18] L. Dominjon, A. Lécuyer, J.-M. Burkhardt, P. Richard, and S. Richir,“Influence of control/display ratio on the perception of mass of manipulated objects in virtual environments,” in IEEE Proceedings. VR 2005.
Virtual Reality, 2005. IEEE, 2005, pp. 19–25.
[19] A. Parducci, L. M. Marshall, and M. Degner, “Interference with memory
for lifted weight,” Perception & Psychophysics, vol. 1, no. 2, p. 83–86,
1966.
[20] A. Parducci and R. Haugen, “The frequency principle for comparative
judgments),” Perception & Psychophysics, vol. 2, no. 2, p. 81–82, 1967.
[21] A. Parducci, S. Knobel, and C. Thomas, “Independent contexts for category ratings: A range-frequency analysis,” Perception & Psychophysics,
vol. 20, no. 5, p. 360–366, 1976.
[22] G. R. Lockhead and J. Hinson, “Range and sequence effects in judgment,” Perception & Psychophysics, vol. 40, no. 1, p. 53–61, 1986.
[23] S. Namba, T. Yoshikawa, and S. Kuwano, “Effects of range andphysical intensity of stimuli on category judgment function,” Japanese
Psychological Research, vol. 10, no. 2, p. 95–103, 1968.
[24] F. W. Nutter Jr, “Weber-Fechner Law,” Encyclopedia of research design,
vol. 3, pp. 1612–1615, 2010.
[25] N. E. Cohen, “The relativity of absolute judgments,” The American
Journal of Psychology, vol. 49, no. 1, pp. 93–100, 1937.
[26] A. Parducci, “Range-frequenpseucy compromise in judgment,” Psychological Monographs: General and Applied, vol. 77, no. 2, p. 1–50, 1963.
[27] Q. Li, S. J. Joo, J. D. Yeatman, and K. Reinecke, “Controlling forparticipants’ viewing distance in large-scale, psychophysical online
experiments using a virtual chinrest,” Scientific Reports, vol. 10, no. 1,
p. 904, 2020.
[28] M. Adolphe, M. Sawayama, D. Maurel, A. Delmas, P.-Y. Oudeyer, and
H. Sauzéon, “An open-source cognitive test battery to assess humanattention and memory,” Frontiers in Psychology, vol. 13, p. 880375,
2022.
[29] T. Yokosaka and T. Kawabe, “Delay and speed of visual feedback
of a keystroke cause illusory heaviness and stiffness,” Frontiers in
Neuroscience, vol. 16, p. 761697, 2022.
[30] J. O. Wobbrock, L. Findlater, D. Gergle, and J. J. Higgins, “The aligned
rank transform for nonparametric factorial analyses using only ANOVA
procedures,” in Proceedings of the SIGCHI conference on human factors
in computing systems, 2011, pp. 143–146.
[31] L. A. Elkin, M. Kay, J. J. Higgins, and J. O. Wobbrock, “An aligned rank
transform procedure for multifactor contrast tests,” in The 34th Annual
ACM Symposium on User Interface Software and Technology, 2021, pp.
754–768.
[32] H. Kim and W. K. Chung, “Experimental study of pseudo-haptic perception for consistent pseudo-haptic rendering,” in 2013 10th International
Conference on Ubiquitous Robots and Ambient Intelligence (URAI).
IEEE, 2013, pp. 241–242.

© 2023 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See https://www.ieee.org/publications/rights/index.html for more information.