Lab Session II: Signal Detection
Theory and Magnitude Estimation
Purpose and Goals
To illustrate a different way of thinking about human sensitivity:
Signal Detection Theory
To illustrate and experience a methodology to examine non-threshold
stimuli: Magnitude Estimation procedures
To expand your computational horizons.
Signal Detection Theory
Description of Theory
Noise: There are random events in our sensory neurons that happen
randomly. These events are not caused by external events and are
Signal: This is the new name for the stimulus.
Noise and Singal+Noise distributions
So, in looking at a sensory neuron, it fires even when nothing is
present. Sometimes the neuron fires faster, sometimes more slowly.
Still, no stimulus (signal) is present. If you plot a curve where the
x-axis is how strong neuron is firing (often called sensory signal
strength). The y-axis is probability. If you plot a curve for
how likely any sensory signal strength occurs when there is not a signal,
this is called the noise curve.
The noise never goes a way, even when a signal is presented. So,
when presenting a signal to the participant, the noise will not disappear.
There are still different possible sensory signal strengths that will
occur for a given signal. Overall, the curve will move to higher
levels on the x-axis (sensory signal strength axis). Thus, the curve
that is plotted for what can happen when the signal is presented is called
the signal+noise curve.
Sensitivity = d'. The distance between the two curves
(technically in numbers of standard deviations) is call the sensitivity.
The larger d' is the easier to tell noise from signal+noise.
Criterion (one type is called beta). When the noise and signal+noise curve overlap,
there are some sensory signal strengths that could be caused by either
noise alone or signal+noise. So the participant needs to set some
criterion level where below the level, the participant will say only the
noise happened and above this level, the participant will say that the
See text Chapter 2 for more information. Look at it all but
concentrate on ROC curves which I will not review here.
This method argues that there is no such thing as a threshold. Can
you figure out why?
In signal detection experiments, the stimulus is only presented on some
trials. The subjects task is to decide if the stimulus has been
presented. This leads to the following four possible outcomes for each
trial as indicated below:
Stimulus (Signal) is:
Participant responds that the
All of the methods so far have measured something about perception at or
near our limits to either detect a stimulus or a change in the stimulus.
There was a need for a method to try to learn something about stimuli that
are easily detectable or the difference between two stimuli that are easily
told apart, i.e., is one stimulus twice as bright as another stimulus?
Harvard psychologist, S.S. Stevens pondered this question and basically
developed magnitude estimation out of an elevator conversation with another
Harvard professor (not a psychologist).
Simple basic idea. Present a
stimulus, have participants give the stimulus a number that they they
indicates the sensory strength of the that stimulus.
Modulus: In some
versions, a standard stimulus is used, call the modulus. This stimulus
is given a standard number, whatever the researcher wants, say 50. Then
the participant assigns numbers to the other stimulus that takes the modulus
into account. For example, if the participant thinks the stimulus just
presented is twice as strong as the modulus and the modulus is 50 then the
subject should give the stimulus a 100.
Adjust criterion until False alarms match your data
Adjust d' till hits match your data
Read the d' value off of graph
Are your three d's approximately constant for each relative speed of stimulus (1 pixel or 2.5 pixels)? The three d's come from the three signal
probabilities (.1, .5, .9)
Does the ROC curve do a good job of describing your data, i.e., does the
ROC seem to match your expectations?
For Magnitude Estimation
Plot the result from both Magnitude Estimation experiments on the same
Which task seems to generate more accurate results, why? Look at all of
Do these data reflect the same underlying relationship between the
physical dimension studies (sound intensity and line length) and our
psychological experience of that dimension (loudness and perceive line
length)? What do you see in the data that leads to these conclusions.
Worth 25 points
Do figures in Excel and place in a word file and then type the answers
to the questions on the same page. These may not be hand written.
Point: Learn about making graphs and reading them.