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Abstract

Studies of visual size perception with the method of magnitude estimation have shown a linear relationship between actual sizes and magnitude estimates [1]. Similar studies for touch do
not yield unequivocal evidence for a linear relationship; in some cases, a positively accelerated
power function described best the relationship between stimulus sizes and estimates [2].
We have investigated haptic magnitude estimation for length in two haptic experiments with
different methods of haptic exploration (whole hand, nger span).
The haptic stimuli consisted of 15 rectangular shapes. The only difference from one shape
to another was the length of the horizontal side, which ranged from 40 mm to 68 mm in equal
intervals. For all shapes, the depth and height were 10 mm and 40 mm, respectively.
In the Multiple cues Experiment, blindfolded participants used their dominant hand to feel
each shape freely. The shape was presented xed at onto a support, so they could feel the
entire shape under their hand. The participants' task was to give a modulus-free magnitude
estimate for the horizontal side. All shapes were presented once in random order in each block.
In the Single cue Experiment, blindfolded participants were restricted to grasping the horizontal
side of a shape between the thumb and index nger of their dominant hand. Their task
was to give a magnitude estimate for the length of that side.
Magnitude estimates for side length could be tted by a two-parameter linear function with
a high goodness-of-t statistic in both experiments (R2
'
.97). Thus, when participants were
given a size range of 40 to 68 mm, their magnitude estimates increased linearly with each
physical increment, independently of the exploration method used.
Because of the small range of total size variation present in the shape set, we do not conclude
from our results that haptic magnitude estimation of unidimensional size is generally
linear. It should be noted that the present linear functions had a negative y-intercept and that
when a power function was t to the data, the exponent was greater than 1.0 in both experiments,
and goodness-of-t was also high. Our results suggest, however, that haptic perception
of size can safely be considered linear within this small part of the size continuum. These results
are important for considering further psychophysical studies with shapes within this size
range.