Source: Laboratory of Jonathan Flombaum—Johns Hopkins University
Psychophysics is a branch of psychology and neuroscience that tries to explain how physical quantities are translated into neural firing and mental representations of magnitude. One set of questions in this area pertains to just-noticeable differences (JND): How much does something need to change in order for the change to be perceivable? To pump intuitions about this, consider the fact that small children grow at an enormous rate, relatively speaking, but one rarely notices growth taking place on a daily basis. However, when the child returns from sleep-away camp or when a grandparent sees the child after a prolonged absence, just a few weeks of growing is more than perceptible. It can seem enormous! Changes in height are only noticed after an absence because the small changes that take place on a day-to-day basis are too small to be perceivable. But after an absence, many small changes add up. So how much growth needs to take place to be noticeable? The minimal amount is the JND.
Psychologists and neuroscientists measure JND in many domains. How much brighter does a light need to be to be noticed? How much louder does a sound need to be? They often obtain the measurements by employing a forced-choice paradigm. This video will focus on size, demonstrating a standard approach for measuring a JND when the area of a shape changes.
1. Equipment
2. Stimuli and Experiment Design
Figure 1. A schematic depiction of a single forced-choice trial in an experiment to measure the Just-noticeable difference (JND) for circle size. First, a ready screen prompts the participants that a trial will begin. Next, two blue discs appear in the display, side-by-side. They remain present for only 200 ms, at which point the display prompts the participant for a response. The 'L' key is used to indicate the object on the left, and the 'R' key to indicate the object on the right.
Figure 2. A sample output table from a forced-choice JND experiment. The columns report the relevant data from the experimental program.
3. Running the experiment
4. Analyzing the results
Figure 3. Results of a forced-choice experiment to find the JND for circle radius. Plotted is the proportion of time that the comparison stimulus was selected as larger (by the participant) as a function of the size of the comparison stimulus. The constant stimulus always had a radius of 10 px.
The graph in Figure 3 shows the proportion of time in which the comparison stimulus was chosen as a function of the size of its radius. Recall that the constant stimulus always has a 10-px radius in this experiment. This is why with a radius of 5 or 6 px the comparison is almost never chosen, and it is almost always chosen with a radius if 14 or 15 px. However, with a radius of 9 or 11 px, the comparison is difficult. Participants often make mistakes. The JND is defined as follows: The comparison size when it is chosen about 75% of the time minus its size when it is chosen 25% of the time, all divided by 2. Here, those numbers are 12 and 8, respectively. So the JND for circle radius is 2 px.
There are detailed mathematical reasons for why this is the exact calculation of a JND, having to do with statistics and the nature of normal distributions (bell curves). But looking at the graph should make the computation more intuitive. When the radius was only 1 px smaller or bigger than 10, the participant made many mistakes, performing very near 0.5, which is what she would produce if she were just guessing. But performance quickly became far more accurate with a pixel difference of 2, and it was nearly perfect with a pixel difference of 3 or larger. Figure 4 is an annotated version of Figure 3, meant to illustrate the calculation of a JND.
Figure 4. An annotated version of Figure 3.
One of the main applications of the constant stimulus approach to measuring a JND has come in neuroscience, specifically in neurophysiology studies devised to investigate how the firing of individual neurons encodes physical properties about the world. These studies usually involve a monkey with electrodes implanted in their visual cortex. The electrodes penetrate individual cells that respond to visual stimulation by firing or spiking, that is, by conducting a rapid electrical signal. In studies on using JND methods, researchers have discovered that individual neurons are noisy-they respond to the size or brightness or color of a stimulus more or less the same way every time, but with some variability. The result is that two very similar stimuli will elicit the same response some of the time. A circle with a radius of 10 px will sometimes get the same neuronal response as a circle with a radius of 9 px or a circle with a radius of 11 px. This is why JND are just-barely-noticeable: sometimes, in the brain, the relevant stimuli really do produce indistinguishable effects.
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