 
Sue Galvin's Theses
Susan Galvin
March 1988
Submitted for the degree of Master of Science in Psychology
Victoria University of Wellington, New Zealand
Abstract
Type II ROC analysis is concerned with the ability of observers to
distinguish between their own correct and incorrect decisions. The Type I task
considered here is to way which of two possible events has occurred during an
observation interval; the Type II task is to decide whether the response made in
the Type I task was correct. Each task can be modelled by a different pair of
overlapping probability functions of an evidence variable. Equations are derived
which give the probability functions for the Type II task in terms of the Type I
functions. Because likelihood ratio may or may not be used as decision axis in
each task, four kinds of Type II probability functions can be obtained. From the
general equations for Type II probability functions the following results
relating the Type I and Type II tasks were found:
 A different pair of Type II probability functions is yielded by each
criterion used in the Type I task.
 Under certain conditions, all the members of a family of Type II ROC
curves lie between the Type I ROC curve and its reflection in the chance line.
 It is not necessary to know the Type I functions underlying an
experimentally obtained Type I ROC curve in order to predict Type II ROC
curves for the associated Type II task. In principle, any pair of probability
functions which yield a Type I curve of the same shape as the obtained curve
can be used.
 If X is used as the Type I decision axis, and the likelihood ratio
of the resulting Type II probability function is used as the Type II decision
axis, then the maximum probability of a correct decision achievable in the
Type II task is equal to the maximum probability of a correct decision
achievable in the Type I task in which likelihood ratio is used as the
decision axis.
Susan Galvin
Submitted for the degree of Doctor of Philosophy
Abstract
This thesis asks what can be learned about the spatial sampling densities of
visual neurons from the motion reversal effect  the apparent reversal of the
direction of motion of a drifting sinusoidal grating when the grating is
spatially undersampled. The motion reversal effect has been attributed to
aliasing by the cone mosaic (Coletta, Williams, & Tiana, 1990) and
postreceptoral layers (Anderson & Hess, 1990). The data and model presented here
suggest that aliasing by at least two sampling stages contributes to the motion
reversal in the peripheral retina. It also indicates that, at some
eccentricities, the densities of both cell populations responsible for aliasing
can be estimated from psychophysical measurements of the motion reversal effect.
The data obtained from human observers indicate that the first sampling layer is
the cone mosaic, and the second sampling layer is a subset of the ganglion cell
population. Although this subpopulation cannot be associated unequivocally with
a class of cell identifiable on morphological or physiological grounds, it
cannot be the parasol cells alone. The is because the sampling density exceeds
estimates of the parasol density at all eccentricities tested. Although aliasing
by the second layer appears to occur at the level of the input to the motion
detectors, it seems to be caused by a substrate as fine as the midget ganglion
cell population.
Last updated
08 Nov 2009 04:37 PM
