thresholds, weber’s law, fechner’s three methods research methods fall 2010 tamás bőhm
TRANSCRIPT
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Thresholds, Weber’s law, Fechner’s three methods
Research Methods
Fall 2010
Tamás Bőhm
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Introspection
• Method applied by early psychologists (Wundt)• Self-observation of conscious thoughts and
sensations– Do I perceive this light brighter than that? Why?
• Inherently subjective rejected as a scientific method
• But it provides useful intuitions when designing experiments (helps forming hypotheses)– I realized that it is hard for me to hear very high and
very low tones. Thus the frequency of a tone may be a factor in its perceived loudness/audibility. Let’s test this in an experiment!
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Formal methods
• Quantifying the sensations evoked by physical stimuli
• Gustav Fechner (1860): established 3 formal psychophysical methods
• Fechner’s methods have been (and are being) widely used
• More reliable and accurate than introspection
• Results from different experiments are comparable
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Thresholds
If a linear relationship is assumed, two values determine the function:
– X-intercept: minimum stimulus value that evoked any sensation;absolute threshold
– Slope: the rate at which sensation grows as we increase intensity;difference threshold(inversely proportional to slope)
Stimulus intensity
Sen
satio
n m
agni
tude
Linear psychophysical
equation
X-intercept
slope
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Thresholds
General definitions (not assuming linearity):– Absolute threshold:
intensity that the observer can just barely detect• Intensities below absolute threshold: undetectable• Intensities above absolute threshold: detectable
– Difference threshold (aka. just noticeable difference /JND/ and difference limen):minimum intensity difference that is noticeable to the observer
• A change in intensity that is smaller than the difference threshold: undetectable
• A change in intensity that is larger than the difference threshold: detectable
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Difference thresholds• Linear function
difference threshold (slope) is constant
• An observer able to detect the difference between intensities 100 and 110 should also be able to detect the difference between 1000 and 1010. This is not the case: the observer is able to detect the difference only between 1000 and 1100
• 500 & 550 Hz tones• 5000 & 5050 Hz tones• 5000 & 5500 Hz tones• Difference threshold is not
constant!Stimulus intensity
Sen
satio
n m
agni
tude
Linear psychophysical
equation
constant slope
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Difference thresholds
• Difference threshold is not constant (changes with intensity) function is nonlinear
• Weber’s law: difference threshold is a constant proportion of the initial stimulus value
ΔI / I = c• Previous
examples:c=10%
• Weber’s lawholds only approximately!
Stimulus intensity
Sen
satio
n m
agni
tude
Nonlinear psychophysical
equation
slope changes with intensity
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Absolute thresholds
• Even in the absence of stimulation, there is some random firing on sensory nerves
• This inner noise can even vary from moment to moment• Observers cannot distinguish inner noise from the effect
of a weak stimulus• Even when there is no light (perfect darkness),
observers may experience a dim light (dark light, intrinsic light)
• Observers in an anechoic chamber often report hearing a whistling sound
Measuring truly „absolute” thresholds is problematic: observers may confuse inner noise with the real thing
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Psychophysical methods• Threshold measurements: detection of small intensities (absolute thr.) and
discrimination of small intensity differences (difference thr.)Is it intense enough to see? How small a difference can you see?
– Fechner’s 3 methods• Method of constant stimuli• Method of limits• Method of adjustment
– Modifications of Fechner’s methods• Staircase method• Modifications of the method of constant stimuli (adaptive, no standard)
– Forced choice, objective methods– Sensory decision theory (SDT)– Psychophysical functions from psychometric data
• Direct scaling: growth of sensation with intensityHow bright do you see a light?
– Magnitude estimation and the power law• Multidimensional scaling: degree to which stimuli are comparable along
some dimensionsAlong which dimensions do you judge the similarity of two stimuli?
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Fechner’s three methods
• Presenting one stimulus at a time
• The stimulus is very weak
• Possible responses:“Yes, I see it.” /“No, I don’t see it.”
Absolute threshold Difference threshold
Method of constant stimuli
Method of limits
Method of adjustment not used
• Presenting two stimuli at a time:
– Standard: fixed, easily detectable
– Comparison: either more or less intense than the standard
• Possible responses:“Comparison is stronger.” /“Comparison is weaker.”
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Method of constant stimuli for measuring absolute thresholds
1. Select a range of light intensities from certainly invisible to certainly visible
2. Pick a few (4-7) points uniformly in this intensity range; this will be the constant stimulus set
Weak Strong
Light intensity
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Method of constant stimuli for measuring absolute thresholds
3. Test each stimulus many times (20-25) in random order
…
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Method of constant stimuli for measuring absolute thresholds
4. Present the stimuli one at a time and ask the observer if it was visible or not
Visible?YES NO
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Click to start
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Could you see the spot of light?
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Could you see the spot of light?
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Could you see the spot of light?
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Could you see the spot of light?
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Could you see the spot of light?
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Could you see the spot of light?
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Could you see the spot of light?
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Could you see the spot of light?
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Could you see the spot of light?
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Could you see the spot of light?
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Could you see the spot of light?
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Could you see the spot of light?
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Could you see the spot of light?
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Could you see the spot of light?
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Method of constant stimuli for measuring absolute thresholds
5. Calculate the proportion of “yes” and “no” responses at each light level
+ - + + + - - - + + + - - - - +
0% 5% 20% 50% 80% 95% 100%
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Method of constant stimuli for measuring absolute thresholds
6. Plot the percentages against stimulus intensity psychometric function
Stimulus intensity
Per
cent
age
“see
n”
0%
100%
50%
75%
25%
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Psychometric function for absolute thresholds
Ideal
FIG (Sekuler)
• Fixed absolute threshold• Step function
Actual
FIG (Sekuler)
• Absolute threshold varies somewhat from trial to trial (due to constant fluctuations in sensitivity)
• Conventionally, the intensity corresponding to 50% is considered to be the threshold
sigmoid function
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Method of constant stimuli for measuring difference thresholds
1. Standard stimulus has a fixed intensity
2. The intensities of comparison stimuli bracket the standard
Light intensity
Standard stimulus:
Comparison stimuli:
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Method of constant stimuli for measuring difference thresholds
3. All pairs of standard and comparison stimuli are tested many times
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Method of constant stimuli for measuring difference thresholds
4. For each pair, the observer judges if the comparison stimulus was stronger or weaker than the standard
http://www.yorku.ca/psycho
STRONGER WEAKER
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Method of constant stimuli for measuring difference thresholds
5. For each comparison level, the percentage of “stronger” responses is calculated and results are plotted as a psychometric function
Light intensity of comparison stimuli
Per
cent
age
“str
onge
r”
0%
100%
50%
75%
25%
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Psychometric function for difference thresholds
• When the observer cannot see a difference, he/she chooses randomly between “stronger” and “weaker”; this corresponds to 50% on the psychometric function point of subjective equivalence (PSE)
Light intensity of comparison stimuli
Per
cent
age
“str
onge
r”
0%
100%
50%
75%
25%
PSE
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Psychometric function for difference thresholds
• By convention, the intensity at 75% is considered to be just noticeably stronger than the standard DS
• A comparison intensity at 25% is just noticeably weaker than the standard DW
• Difference threshold = the average of DS and DW
Light intensity of comparison stimuli
Per
cent
age
“str
onge
r”
0%
100%
50%
75%
25%
DW DS
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Method of limits for measuring absolute thresholds
1. On each trial, the observer reports if she/he could see the light or not.
2. Start with presenting a light intensity well above the expected threshold (the observer can certainly see it)
3. Decrease the intensity until the observer cannot see it
4. Threshold estimate: the intensity at which the response changes
+
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+
+
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Ligh
t in
tens
ity
Trials
• Descending series: start from above the expected threshold and decrease intensity
• Ascending series: start from below the expected threshold and increase intensity
threshold estimate
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Click to start
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Method of limits for measuring absolute thresholds
• Ascending and descending series may yield different results use both
• Even in the same direction, there is variability in the threshold (inner noise, etc) average many measurements
• Measured threshold corresponds to 50% point in a psychometric function (method of constant stimuli)
+
-
+
+
+
+
+
-
-
-
- -
+
+
+
+
+
-
-
-
-
Ligh
t in
tens
ity
Trials
pure-tone audiometry
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threshold estimate
Method of limits for measuring difference thresholds
• Intensity of the comparison stimulus is decreased (descending) or increased (ascending) until the response changes
• Threshold estimate: intensity difference between the standard and comparison stimuli where the response changes
• Average results from multiple series in both directions
+
-
+
+
+
+
Ligh
t in
tens
ity o
f co
mpa
rison
stim
ulus
Trials
+ comparison brighter
- comparison weaker
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-
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Method of adjustment for measuring absolute thresholds
• Observer can vary the stimulus intensity
• Instructed to adjust it so that it is just visible or just invisible
• Initial intensity is set to be far from the expected threshold value
adjustment device
stimulus with adjusted intensity
observer
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Method of adjustment for measuring absolute thresholds
• Threshold estimate: final intensity value
• Descending: initial intensity is well above expected threshold; adjusted to just visible
• Ascending: initially well below threshold; adjusted to just invisible
• Ascending and descending task repeated several times and results averaged
• Similar to method of limits but observers find it easier
threshold estimate
descending ascending
• Adjustment: by a real or a software device (e.g. knob, slider)