The Psychophysics Psyber Lab




Sue Galvin's Theses

The Theory of Type II ROC Analysis

Susan Galvin

March 1988

Submitted for the degree of Master of Science in Psychology
Victoria University of Wellington, New Zealand


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:

  1. A different pair of Type II probability functions is yielded by each criterion used in the Type I task.
  2. 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.
  3. 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.
  4. 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.

The spatial grain of motion perception in human peripheral vision

Susan Galvin

Submitted for the degree of Doctor of Philosophy


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 sub-population 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.

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