Part 1 Psychometric Functions Psychometric Functions A function

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.

Part 4: Psychometric Functions Linear Function = Sigmoidal Function = (Slope * X) + “Y-Intercept” 1_________ 1 + {( exp^ - Slope )^ - ( X - “X-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)

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).

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.

Class Data From A Lab Exercise 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).