part 1 psychometric functions. a function is a rule for turning one number into another number. in a...
TRANSCRIPT
Part 1
Psychometric Functions
Psychometric Functions
• A function is a rule for turning one number into another number.
• In a psychometric function, we take one number (e.g. a quantified stimulus) and turn it into another number (e.g. the probability of a behavioral response).
• By convention, the physical quantity is represented on the abscissa, and the behavioral response is represented on the ordinate.
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Relative Stimulus Value (Physics)
The Axes of a Psychometric Function
Part 4: Psychometric Functions
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1 + {( exp^ - Slope )^ - ( X - “X-Intercept”)}
Sigmoidal Function =
Linear Function = (Slope * X) + “Y-Intercept”
Psychometric Functions
About Slope
About Slope• Psychometric functions vary from each other in slope.
• Steeper slopes, better discrimination, lower thresholds: Shallower slopes, worse discrimination, higher thresholds.
• If your slope is infinite (i.e., a step function), you have a “ceiling effect”. Your task is too easy for the subject.
• If your slope is zero (i.e., a flat function), you have a “floor effect”. Your task is too difficult for the subject.
• Intermediate slopes are desirable, and allow you to dismiss objections that your subjects didn’t understand the task. (Perceptual limits, not “Conceptual” limits)
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Relative Stimulus Value
Slope Indicates Discriminability
Step Function
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Relative Stimulus Value
Slope Indicates Discriminability
Flat Function
Step Function
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Relative Stimulus Value
Slope Indicates Discriminability
Intermediate Slope
Flat Function
Step Function
Psychometric Functions
About X-Intercept
About X-Intercept
• Psychometric functions vary from each other in X-intercept.
• The X-intercept is an index of bias, and an index of the Point-of-Subjective-Equality (PSE).
• To the extent that the X-intercept departs from the center of the abscissa (i.e., the center of the range of stimuli being tested), there is bias.
• The PSE is equal to the abscissal value (i.e., the stimulus quantity) that is associated with the 50% ordinal value (the 50% response rate).
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Relative Stimulus Value
Mid-Point Indicates Bias (or PSE)
No Bias
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Relative Stimulus Value
Mid-Point Indicates Bias (or PSE)
Liberal Bias
No Bias
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Relative Stimulus Value
Mid-Point Indicates Bias (or PSE)
Conservative Bias
Liberal Bias
No Bias
Psychometric Functions
About Goodness-of-Fit
About Goodness-of-Fit
• Psychometric functions vary from each other in “goodness of fit”.
• To the extent data points (or their error bars) fall on or near the psychometric function, the fit is good.
• The goodness of fit can be indexed by the correlation ( “r” statistic) between the data and the function.
• If the fit (that is, the “r” statistic) is statistically greater than the would be expected by chance ( p < 0.05 ), we can be confident in estimating thresholds and P.S.E.’s from them.
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"r" Statistic Indicates Goodness-of-Fit
Perfect Fit ( r(8) = 1, p < 0.01 : r^2 = 1 )
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Relative Stimulus Value
"r" Statistic Indicates Goodness-of-Fit
Acceptable Fit ( r(8) = 0.72, p < 0.05 : r^2 = 0.53 )
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"r" Statistic Indicates Goodness-of-Fit
Unacceptable Fit ( r(8) = 0.57, n.s. : r^2 = 0.33 )
Class Data From A Lab Exercise
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Relative Duration (Seconds)
When in doubt, say “Longer”: slope = 1.8 arbitrary units mid-point (PSE) = -0.23 secs r statistic = 0.99
When in doubt, say “Shorter”: slope = 2.4 arbitrary units mid-point (PSE) = +0.13 secs r statistic = 0.99
Learning Check
• On one plot, draw two psychometric functions that differ from each other only in slope (i.e., discriminability).
• On another plot, draw two psychometric functions that differ from each other only in mid-point (i.e., PSE).
• On a third plot, draw two psychometric functions that differ from each other only in ‘goodness of fit” (r stat).