On Fri, 29 Jan 2016 07:47:20 -0800, Paul Brandon wrote:
The main point I liked to make about Signal Detectability is
that there is no such thing in the sense that a given stimulus
has a given strength below which it cannot be detected.
Exactly right, The old idea of an absolute threshold is
shown to be wrong because it is not the threshold that
varies and produces a normal distribution (or other
probability distribution) of sensations but there is an
intrinsic background level of "noise" (be it neural or
a combination of factors) that exists and is used as a
reference level that the new distribution of "signal+noise"
is compared to. Thus, the ratio of the signal+noise
distribution to the noise distribution (i.e., the likelihood ratio),
serves as the basis for making a decision. The
comparison of this ratio L(S+N/N) to Beta (criterion or
a fixed value of L(S+N/N) for the combination of payoffs,
probabilities of signals/stimuli, distributions, etc.) is what
serves as the person's/organism's decision rule:
If L(S+N/N) > Beta, say "Yes" or "Stimulus present"
if L(S+N/N) < Beta say "No" or "Stimulus absent"
If L(S+N/N) = Beta guess. ;-)
So, unlike the old absolute threshold notion that there is
an energy level that cannot be detected, we have sensations
that are produced even by weak stimuli and the only question
is do they produce a S+N distribution of sensations that differs
from noise alone. Of course, our willingness to say "Yes" is
only partly determined by this because the pay-off matrix
(costs of being wrong, benefits of being right) and probability
of the stimulus) play important roles.
First you must define the response being controlled by the
stimulus. We are really talking about changes in the likelihood
of occurrence of a specified response given the presence of
a certain stimulus situation. A particular change in the strength of
f a stimulus may increase the likelihood of one response enough
for it to be emitted, while not a different response.
Don't forget the effect of context on underlying noise distribution.
Detecting the presence of a weak flash of light through a pinhole
or a small area of a computer screen will be affected by whether
you do the task in a room with bright lighting or completely dark.
David Krantz & Co have estimated that it might take a single
quantum of light to activate a rod in the eye under conditions of
pure darkness for the dark adapted eye (remember the commercials
that said one could see the light of candle several thousand feet
away on a dark night [assuming no light pollution]) but under ordinary
light conditions, a stimulus, even a weak one, will require many more
quanta in order to produce a sensation that leads to detection or,
in other words, a d-prime not equal to zero or a Hit rate not = False
Alarm rate (or AUC = .50).
So SDT is really about behavior under stimulus control, not just
stimuli.
for my own experimental application:
Your behavioristic tendencies are showing. ;-)
"Brandon, Paul K.
A Signal Detection Analysis of Counting Behavior (1981).
in Quantitative Analysis of Behavior vol.I, Michael Commons and John
A. Nevin,
eds., Ballinger"
Remember Skinner's comparison of his approach to that of Tolman
that I mentioned in a previous post? Tolman asserted that certain
variables operated within the organism while Skinner argued that
those variables operated in the environment. The latter gives rise to
notions like "stimulus control" while the former gives rise to the
evaluation of evidence, an internal process. This then raises the
question of whether SDT is correctly specified or even the correct
model (perhaps Luce's choice axioms provide a better description).
-Mike Palij
New York University
m...@nyu.edu
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