Re: identification task...negative d' values

[Richard Pastore <pastore@xxxxxxxxxxxxxx>]

Dear List:

silvadmr first
wrote:  

?I have some few small negative
values of d' obtained from an identification task in which
subjects label vowel sounds from a continuum with three phoneme labels.
?

silvadmr
then wrote:
?I have imagined two
solutions: 
?1. take only the d's obtained from the probabilities of
responding with the label corresponding to the category in the
middle of the continuum - "o". 
?2. simply split the results in two at an arbitrary point
in the middle of the '"o" category' 

Looking over the many responses illustrates the problems in trying to do research through internet discussion.

First look at what is being asked:
    silvadmr has a few small negative values.  Note the words ?few? and ?small negative.? Keep in mind that there is not a rigid threshold at d? = 0.  If subjects cannot do the task, the average value of d? may be 0, but some subjects will exhibit small positive and some small negative values of d? .   Thus, the extensive discussion about the negative values seems to miss one of many greater concerns.  

Doug Creelman is right on in pointing out some considerations, then concluding, 
?This is only the beginning of what could be an extensive discussion. Is your continuum really unidimensional??


silvadmr, and some of the others responding, seem to want to simply  force fit analyses of the superficially described research with impoverished notions from the detection version of the Gaussian Equal Variance Model of SDT.  I?ve seen, cringed at, and done some modeling with data from others who have tried using silvadmr?s two solutions.  As Doug implies, more than a simple, force-fit is needed.  What follows simply points out a few of the problems.

Let?s assume (not necessarily valid) that the stimulus set maps into a unidimensional decision continuum.   Our goal, then, is to compute a z-score based descriptive statistic (d') that reflects the statistical separation of perceptual categories for each subject.  Think about what one is doing when looking up a z-score value.  One can look up the z-score distance for a probability that represents the logical bisection of a distribution; the z-score is the distance from the mean to the logical partition point of the distribution.  

Now apply this idea.  Let?s assume that we use 4 ordinal response categories, where 1 and 4 are used to indicate the decision reflecting strong judgment of the two extremes of the unidimensional continuum, with 2 & 3 representing the partitioning of those intermediate values in terms of ordered relationship to the end points of the continuum.   This is essentially the Rating Task that sometimes is used to generate ROC curves.  One thus has 3 ordered criteria:  1  vs (2+3+4), (1+2) vs (3+4), and (1+2+3) vs 4.  One can compute the z score distances for any given stimulus (i.e., repeated presentations of stimulus n), and thus the z-score distances between the means for statistical distributions for any given pair of stimuli (stimuli n and n+j), and this latter gives us d?.  

Does it make sense, however, to try to look up the ?z-score? value for the area under a Normal distribution that is between two arbitrary points located somewhere within the distribution (e.g., those that represent response 2, or the grouping of responses 2 and 3)?   Note that I puts quotes around ?z-score?, since what I have just described has no logical meaning.  Yes, the probability of response ?1? specifies a meaningful z-score, as does the probability of response ?4?, but the probability of responses ?2 or 3? can have any value between minus and plus infinity.  If what one computes as a nominal z-score is invalid, then so is any nominal descriptive statistic based upon that computation.  What I have just described is equivalent to using the middle of three ordered categories, and this is what silvadmr has described as the first solution (see above).

Does it make any more sense to arbitrarily partition the data in the middle of this middle category  - silvadmr?s alternative solution.  

I have provided an explanation of a logical problem with what silvadmr has proposed.  However, as Doug noted, this is only the beginning of what would need to be an extensive discussion - one that is far too complex for a few simple statements on a web chat site, when an understanding is needed of the material in one of the books by Macmillan & Creelman, Wicken, McNichol, or Green & Swets.

Dick Pastore

Richard E. Pastore
  Professor of Psychology
  Psychology Department
  Binghamton University (SUNY)
  Binghamton, NY 13902-6000
   http://bingweb.binghamton.edu/~pastore