
The Psychophysics Symposium 1993The Psychophysics Symposium was held in August 1993 as part of the New Zealand Psychological Society's Annual Conference. Papers were presented by John Whitmore, Vit Drga, Brian Scurfield, and Judi Lapsley. The following links are abstracts for these papers; more details are available from the authors. AbstractsWhy group operating characteristic (GOC) analysis?John WhitmoreIt is understood widely that experimental technique and research design
reduce data varaibility or error, and that statistics measures the error which
remains. The remaining error almost always confounds the comparison of data to
theory. In psychoacoustics, GOC analysis statisically reduces data error
further, providing a more precise and powerful way of testing theories of
hearing. Group operating characteristic (GOC) analysis of Type II decisionsJohn Whitmore and Susan GalvinA few years ago, one of us (Susan Galvin) presented to the NZPS a theoretical
analysis of Type I and Type II detection tasks in the theory of signal
detectability. Type I tasks are concerned with how observers distinguish between
environmental events, and Type II tasks are concerned with how observers
distinguish between their own correct and incorrect decisions about those Type I
events. We generated complete families of Type II ROC curves for strict, medium,
and lax Type I criteria. Human GOC curves from Type II tasks are found to be in
excellent agreement with their appropriate theoretical ROC curves. A diotic amplitude discrimination experiment replicated 100 timesJohn Whitmore, Vit Drga, and Alan TaylorThe impact of large numbers of replications on the reduction of error in GOC
analysis demonstrates the way in which substantive problems can be analysed.
Individual and mean ROC curves are shown to be dramatically inferior to GOC
curves for two observers. Both the locations and shapes of the GOC curves
conform to the theoretical model for the discrimination task, whereas the ROC
curves do not. Theory of group operating characteristic (GOC) analysisVit DrgaUp to now, it has not been clear why a GOC curve should tend toward the appropriate theoretical ROC curve, nor has it been clear why a transformaveraged GOC curve should tend toward the theoretical ROC curve regardless of the particular transform chosen for calculation. A theory of GOC analysis will be presented which covers both transformaverage GOC analysis and transferfunction analysis within the same theoretical framework. An ideal observer is modelled as a system consisting of a black box discriminator, a unique noise source, an additive unique and common noise mixer, followed by a transfer function onto a rating scale. The theory allows the unique noise distribution to vary as a function of common noise evidence value. The theory assumes strict stochastic ordering of the distributions of unique and common noise mixed together. It allows the specification of conditions under which GOC analysis will and will not work. Transformaveraged group operating characteristic (GOC) analysisVit DrgaTransformaveraged GOC analysis is a new form of emperical ROC analysis based
on the mean rating per stimulus across replications. Here, mean rating refers to
a generalised, transformaveraged mean, which is calculated as follows: A
strictly monotonic transform is applied to the set of ratings, the arithmetic
mean (y) of the transformed ratings per stimulus is calculated, and the
inverse transform is applied to y. This generalised GOC analysis can be
interpreted in either of two equivalent ways: 1) as GOC analysis based on
transformaveraged mean ratings, or 2) as GOC analysis based on arithmeticmean
ratings following a rescaling of the rating scale. Transformaveraged GOC curves
from a simple frequency discrimination experiment will be presented along with
their theoretical ROC curve. Each GOC curve is based on the same data set, but
relies on a different choice of transform. Some transformaveraged GOC curves
lie at least as close to the theoretical ROC curve as the arithmeticmean GOC
curve, implying there is nothing inherently special about the arithemeticmean
rating. GOC analysis based on the sum of ratings is seen to be a special case of
transformaveraged GOC analysis. Transferfunction analysis of rating scales in the theory of signal detectabilityVit DrgaIn the context of signal detection and discrimination experiments, the
transfer function is a onetoone mapping between a decision axis variable and a
rating scale. This concept is implicit in any theoretical interpretation of
empirical ROC analysis. Given a pair of eventconditional theoretical
distributions, a transfer function is estimated by pairing the theoretical
criteria and empirical rating cutoffs that result in the same values of
cumulative probability and cumulative proportion. Data from a frequency
discrimination experiment will be used to illustrate the estimation of transfer
functions. Given a transfer function, ratings can be converted into estimated
decision axis pseudovalues. This allows estimation of the distribution of
unique noise under the assumption that unique noise is additive with common
noise on the decision axis. The meaning of the area under the Receiver Operating Characteristic curveBrian ScurfieldMany applications of the Theory of Signal Detectibility (TSD) use the
parametric measure d' to determine observer sensitivity. This Measures of sensitivity in singleinterval forcedchoice and twointerval forcedchoice tasksJudi Lapsley, Brian Scurfield, Vit Drga, Susan Galvin, and John WhitmoreThe relationship between the area under the ROC curve for the singleinterval
forcedchoice (SIFC) task, A_{SIFC}, and the proportion
correct in the twointerval forcedchoice (2IFC) task, P(C)_{2IFC},
is well known. However A_{SIFC}=P(C)_{2IFC}
has only been derived for the case of continuous probability functions. We have
derived the relationship for discrete probability functions as well as relaxing
a number of assumptions in the continuous case. To date, experimental research
that tests the relationship has been equivocal, mainly because of observer
inconsistency. Empirical results that are degraded by observer inconsistency
cannot be used to justify theoretical relationships. We have overcome this by
using a detection task with known, discrete, probability functions. By using
known functions, the theoretical measures of sensitivity are also known.
Observer inconsistency in our experimental data was removed by using group
operating characteristic (GOC) analysis. The measures of sensitivity based on
the GOC curves closely approximated the theoretical measures of sensitivity,
whereas the measures based on mean ROC curves were poor approximations to the
theoretical measures. The results indicated that A_{SIFC}=P(C)_{2IFC}
empirically, once unique noise had been removed from the data. The implications
of this result will be discussed. The Acoustical Uncertainty Principle & WTJudi LapsleyAcoustic signals can be represented in both the time domain and the frequency domain. The Fourier transform is used to swap from one domain to the other. In modelling human hearing it is desirable to use input signals that are finite in both domains for they are more like naturally occurring sounds. However, it is theoretically impossible for a signal to have both a finite bandwidth (W) and a finite duration (T), for as resolution is increased in one domain, it is lost in the other. This tradeoff is analogous to the Heisenberg uncertainty principle of quantum physics. Many mathematical models of human hearing assume that the bandwidthduration product, WT, is the important parameter and not the actual bandwidth or duration. This means that a detector's performance would still be the same no matter how resolution in time, and in frequency, was tradedoff. Due to physiological limitations of the human ear, this tradeoff is likely to break down for very large, or very small, bandwidths and durations. Last updated 08 Nov 2009 04:37 PM 
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