Scaling

1
Scaling
2
Scaling seeks to discover how varying the
physical parameters of the stimulus affects the
psychological parameters. In general, scaling is
concerned with the question "How does subjective
magnitude (perception) vary with changes in
physical magnitude?" e.g. If we double the
intensity of a light does it look twice as
bright? Investigators have attempted to
determine the functional form of this
relationship - basically to find functions to
describe the relationship between psychological
and physical variations in suprathreshold stimuli.
3
Some Terminology
The type of scaling with which we are concerned
here, usually called unidimensional scaling
Two different types of dimensionsprothetic and
metathetic. Prothetic - dimensions of
quantity - how much? Metathetic - dimensions of
quality - what kind?
Unidimensional scaling is generally concerned
with prothetic dimensions
4
Indirect Scaling

Weber's law This law states that the smallest
difference in intensity that can be detected is
directly proportional to the background intensity.
Ernst Weber (1795-1878)
5
Suppose we want to want to find the just
noticeable difference (jnd) needed to detect an
increment in light intensity
We would find that the increment needed was a
constant proportion of the background intensity
6
(No Transcript)
7
Webers Law
DI/I K
where K is a constant DI small incremental
intensity I background intensity
8
This law holds fairly well over a wide range of
background intensities.
But, Weber's does not hold for all values of
I. In fact, it's often the case that for very
small values of I, Weber's law starts to break
down, but if we add Generalize Law to ?I K( I
Io) where Io is the absolute threshold--the
smallest intensity of a given physical dimension
we can reliably detect.
9
Weber Fraction
Rough Index of Sensitivity
10
Webers law suggests that standard physical
scales are not appropriate for representing
perceptual experience
The physical difference between 1 and 2 mm in
length is the same as between 101 and 102 m
But Webers law tells us that while we could
readily discriminate the first difference
(between 1 and 2 cm), we couldnt the
second (between 101 and 102 cm)
Fechner wished to construct a psychological scale
that would reflect such differences
11
Fechner's Law
Fechner used Webers law to help understand the
relationship between changes in physical
intensity and the psychological experience of
those changes - scaling Fechner argued that our
subjective experience of intensity changes is
related in a logarithmic fashion to changes in
physical intensity
12
Fechner needed a measurement unit that could be
used to describe the quantity of the sensory
experience. 1) He assumed Weber's Law was
correct. ( It does hold over a wide range of
stimuli) 2) He assumed that the subjective
impression of the difference between 2 stimuli
separated by one JND was the same regardless of
the absolute magnitude of the 2 stimuli - JND -
atom of sensation. 3) Absolute threshold was 0
point. 4) One can add and subtract JND's.
13
Key Assumption
Fechner was saying that regardless of its size in
physical units the JND is the standard unit of
sensation magnitude because it is the smallest
detectable increment in a sensation and therefore
always psychologically the same.
14
How does one determine the number of JND's above
threshold corresponding to values of the physical
stimulus. Empirically Measure first DI above
threshold - gives first JND. This is starting
point for the measurement of the next DI - gives
second JND.
15
(No Transcript)
16
However, Fechner assumed the validity of Weber's
Law. Hence, e.g. if ?I/I1/5 and the absolute
threshold is 10, the first JND is 101/51012.
Next is 121/51014.4 of JNDs Stim.
intensity Log stim. intensity 0
10.0 1.00 1
12.0 1.079 2
14.4 1.158 3
17.28 1.238 etc...
17
Fechner's Law S k log I S subjective
magnitude k a constant number appropriate for
the modality (like the Weber fraction) I
physical intensity
18
Fechners law means that as the magnitude of
the physical intensity increases, the magnitude
of our subjective intensity increases rapidly at
first, but then slows.
19
Does doubling intensity double brightness? set k
1 I 10 ---gt S 1 I 20 ---gt S 1.3 If I
100, P 2
20
Problems with Fechner's law 1) All JNDs are
not equal --gt e.g. sound 20 JND's above threshold
is more than twice as loud as one 10 JND's
above. 2) problems with Weber's law at low
intensities --gt generality of Fechner's law
restricted to certain ranges. 3) S.S. Stevens
proposed an alternative equation that describes
the relationship between sensation and stimulus
intensity for a wide range of senses more
accurately than Fechner's law.
21
Stevens Law
Stevens used a technique called magnitude
estimation - direct method in that one assign
numerals to reflect perception For example, in
judging the length of lines first given a
standard length (e.g. 10 unit length) Variety of
stimuli then presented and task is to assign
numerals to these other stimuli in relation to
the one with a value of 10. e.g. if you see a
line that appears twice as long, you should
assign it a number 20. If you see a line that
appears 1/5 as long, you should assign it a
number 2.
S. S. Stevens (1906-1973)
22
Brightness - response compression - e.g. doubling
intensity causes less than doubling
brightness. Shock - response expansion - e.g.
doubling intensity cause more than doubling of
sensation. Line Length - linear - e.g. doubling
line length doubles observer's estimate.
23
Steven's Power Law
P kIn Perceived magnitude, P, equals a
constant, k, times the stimulus intensity, I,
raised to a power, n.
24
What about all these curves? Does the
relationship between the intensity of a stimulus
and our perception of its magnitude follow
different rules for different senses?
25
No! Replot data On log-log paper gives straight
lines Such data are called power functions
26
Take log of power function - P kIn
Log P n Log ILog k estimate n
?y/ ?x (slope) (intercept) Any
systematic deviation of the data points from a
straight line on log-log graph indicates that the
function is not a power function (yaxb)
27
A little demo of Magnitude Estimation
Take out a piece of blank paper and label the
lines from A to H Judge the area of each circle
relative to the standard Do not measure, simply
write down your subjective impression
28
Standard circle. Call its area 1
29
A
30
B
31
C
32
D
33
E
34
F
35
G
36
H
37
(No Transcript)
38
What is the correct law Fechners or
Stevens? Most present day psychophysicists would
likely opt for some more direct method of
measuring the psychophysical function than the
indirect method used by Fechner. Fechners
assumptions seem to have been wrong in at least
one very fundamental respect his assumption
that jnds of different physical size have the
same subjective size. There is still
controversy over which formulation may be correct
and whether the two 'laws' can be reconciled. It
is even possible that both the power function and
the logarithmic function are valid under
different conditions - or maybe neither is
valid! An important feature is shared by both
laws - the relationship between stimulus and
sensation is a downward curve, so larger
increments are needed to have similar effects at
higher stimulus levels.