## Lab Session II:  Signal Detection Theory and Magnitude Estimation

### Background:

1. Purpose and Goals
1. To illustrate a different way of thinking about human sensitivity: Signal Detection Theory
2. To illustrate and experience a methodology to examine non-threshold stimuli: Magnitude Estimation procedures
3. To expand your computational horizons.
2. Signal Detection Theory
1. Description of Theory
1. Noise: There are random events in our sensory neurons that happen randomly.  These events are not caused by external events and are called noise.
2. Signal: This is the new name for the stimulus.
3. 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.
4. Measures:
• 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 = ß.  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 signal occurred.
5. See text Chapter 2 for more information.  Look at it all but concentrate on ROC curves which I will not review here.
2. This method argues that there is no such thing as a threshold.  Can you figure out why?
3. Experimental Method
1. 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: Present Absent Participant responds that the signal is: Present Hit False Alarm Absent Miss Correct Rejection
3. Magnitude Estimation
1. 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.
2. 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?
3. 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).
4. Simple basic idea.  Present a stimulus, have participants give the stimulus a number that they they indicates the sensory strength of the that stimulus.
5. 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.
6. More in Chapter 2 of the text.

### Tasks Due for Next Week:

1. Do the following experiments:
1. Signal Detection Experiment from Chapter 2 Media:
1. Stimulus Settings
1. Number of Background Dots : DO NOT CHANGE
2. Relative Speed of Stimulus : Two Levels: 1 and 2.5.
3. Leave rest unchanged
2. Method Settings
1. Number of Trials: 60
2. Percentage of Trials with Signals: three levels: 10, 50, 90, this should change your criterion not your d'
3. So do the experiment 6 times.  As you make your guesses about whether the signal is present, remember how likely it is to be present.
2. Magnitude Estimation: Tone Loudness & Magnitude Estimation: Line Length from Chapter 2 Media
1. Number of Levels to Test: 10
2. Number of Repetitions: 7
3. Use the modulus (leave checked which is the default).  Note the value.
2. Problems:
1. For Signal Detection
1. Report your data tables for each of the 6 conditions
2. Plot ROC Curve with a separate curve for each signal duration (as PDF; for Excel before 2007, PDF)
3. Calculate d' each of the six conditions
• Open Decisions in STD illustration