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.
- For this experiment, use a computer and experiment implementation software such as E-Prime, or a programming environment such as MATLAB or PsychoPy.
2. Stimuli and Experiment Design
- This experiment will involve repeated trials with the same basic design. Two discs will appear on the screen simultaneously, one on the left side and one on the right. One will always be bigger than other, and the task will be to use a keypress to select the larger one. The details are as follows:
- Program the experiment to draw a blue disc with a radius of 10 px. The disc will appear in each trial of the experiment, centered in the display vertically, and centered horizontally in either the left or right half of the display. Using one stimulus that appears unchanged in every trial is sometimes called the method of constant stimulus. It just refers to the fact that one of the two stimuli in each trial is always the same. The 10-px blue disc is thus the constant stimulus.
- Opposite the constant stimulus in each trial, display another blue disc. This disc is called the comparison stimulus. It will have a radius between 5 and 9 and between 11 and 15 px. That is 10 total possibilities. In the experiment, include 10 trials each for each of the 20 possible comparison stimuli. So the experiment will involve 200 trials.
- Display the two stimuli on the screen for 200 ms, followed by a screen which reads only 'Which was bigger L/R?' Figure 1 schematizes the sequence of events in each trial.
- 'L' key responses will indicate that the left object was bigger, and 'R' key responses will designate that the right one was perceived as bigger.
- Be sure that the program outputs the following important data into a table: the trial number, the size of the comparison stimulus, the screen position of the comparison stimulus, the correct response, and the response given by the participant. Figure 2 shows a sample of such a data table.
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
- Recruit a participant, and when she arrives in the lab tell her that she will do a simple experiment on the perception of shape. Then have her complete informed consent.
- Seat the participant in front of the testing computer, and explain the task as follows:
- Every trial of this experiment will involve the same basic sequence of events. First, you will see the word 'Ready?' on the screen. Press spacebar when you are ready to begin the trial. At that point, two blue discs will appear on either side of the screen very briefly. When they disappear, the display will read 'Which was bigger, L/R?' Your job is to report which of the two discs looked bigger to you, the one on the right or the one on the left side of the screen. There are 200 trials in the experiment, but they are short. The whole experiment should take under five minutes. Do you have any questions?
- After answering any questions, launch the experimental program, and let the participant begin. Leave her in the quiet testing room until the experiment is complete.
4. Analyzing the results
- To analyze the results, the first thing to do is determine which responses were correct and which were incorrect. Add a column to the data output table for these purposes. Compare the response given and the correct response, marking the final column with a 1 when the response given was correct and 0 when it was not.
- Quickly look to make sure that performance was sensible-that the participant was at or near perfect accuracy when the comparison was 5 and 15 px, differences large enough compared to 10 that no errors should have been made.
- Now add another column to the data table, called 'Proportion of C Responses.' In the column, note whether the comparison or the constant was chosen by the participant. If the comparison object was chosen, mark a 1 in the column. If the constant was chosen, mark a 0.
- Now, for each comparison size, compute the fraction of the time that the comparison was selected as larger by the participant. For comparison stimuli of 5, the number should be close to 0, and for comparison stimuli of 15 it should be close to 1.
- To visualize the results, graph them as follows: Make scatter plot, with the size of the comparison on the x-axis and the proportion of times it was chosen on the y-axis. It will look something like the one in Figure 3.
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.
Exactly how much does something need to change for a difference to be perceived?
Think of, for instance, young children who grow rapidly—getting taller on a daily basis. However, it’s often difficult to notice subtle changes, especially if they still struggle to reach a basketball.
Over a much longer span, their growth spurt becomes more than perceptible; in fact, the amount can seem enormous! These changes in height are only noticed after a lapse because the small day-to-day differences are too small to be perceivable.
The minimal yet perceived amount is the just-noticeable-difference, which, for this example, is the smallest amount of growth noticed.
This video demonstrates a standard approach for measuring a just-noticeable-difference in shape size. Not only do we discuss the steps required to design and execute an experiment, but we also explain how to analyze the data and interpret the results describing just how small of a change in area is necessary to be perceived.
In this experiment, participants are briefly shown two different circles that vary in size and are forced to choose which one is larger.
During each trial, one is always presented with the same circumference, whereas the other is varied. This approach is referred to as the method of constant stimulus.
In this case, the constant stimulus is designed to have a radius of 10 px and located randomly on either the left or right side of the screen. In contrast, the other circle, called the comparison stimulus, will have a radius that varies between 5 and 9 and between 11 and 15 px.
Given these 10 possibilities, the comparison stimulus is shown 10 times on each side, for a total of 200 trials. The dependent variable is recorded as which stimulus was chosen to be the larger one.
Participants are expected to choose correctly if they perceived a difference in size between the two stimuli. However, when the shapes are closer in circumference and below the just-noticeable difference, performance is predicted to decline.
To begin the experiment, greet the participant in the lab. With them sitting comfortably in front of the computer, explain the task instructions: The screen will have the word "Ready?" on it until they press the space bar.
Watch as two blue stimuli appear and instruct the participant to indicate which stimulus they thought was larger by pressing the 'L' key for left- and 'R' for right-side responses. Remind them that they should guess if they are not sure which one is larger.
After answering any questions the participant might have, leave the room. Allow them to complete all of the 200 trials over a 5-min period. When they finish, return to the room and thank them for taking part in the experiment.
To analyze the data, first retrieve the programmed output file that captured each participant’s responses. Quickly glance at the data to make sure that performances were sensible—namely, that when the sizes of the comparison stimuli were 5 and 15 px, accuracy was near perfect.
Next, add a column to the output table called 'Accuracy' to determine whether the recorded answers are correct or not. Compare those given to the correct responses for all trials. Use the following IF statement to register a 1 when the response given was correct and 0 when it was incorrect.
Now, add another column to the table, labeled 'Proportion of Comparison Responses'. Compare the column 'Comparison Position' with 'Response' and use a new IF statement to mark a '1' when the comparison stimulus was chosen or a '0' if the constant circle was chosen.
To visualize the results, make a scatter plot with the size of the comparison on the x-axis and the proportion of times it was chosen as being larger on the y-axis. Recall that the constant stimulus always had a 10-px radius, which is why stimuli with 5 or 6 px radii were almost never chosen and those with 14 or 15 were always chosen.
With a radius of 9 or 11 px, the comparison was more difficult and participants often made mistakes. In fact, performance was at chance level, suggesting that differences were not being perceived.
To calculate the just-noticeable-difference, take the comparison size that was chosen 75% of the time, in this case a radius of 12, minus the comparison size that was chosen 25% of the time—radius of 8—and divide the result by 2 for an answer of 2 px.
In other words, the radii of the circles need to differ by at least 2 px for their sizes to be accurately perceived.
Now that you are familiar with just-noticeable differences in the perception of visual objects’ sizes, let’s look at how this paradigm is used in neurophysiological studies to explore how the brain responds and in other behavioral situations, such as distinguishing between fat levels in food.
Researchers have investigated how individual neurons in the visual cortex encode the physical properties of the world, like objects’ sizes.
Using electrophysiological recording techniques that measure firing patterns in conjunction with stimuli presentation, researchers found that neurons that are sensitive to size will sometimes respond in the same way to objects that are actually different sizes.
This is why JND are just-barely-noticeable: sometimes, in the brain, the relevant stimuli really do produce indistinguishable effects.
In addition, researchers have used a just-noticeable-differences task to characterize individual thresholds for detecting fat concentrations in food.
They found that individuals with a higher body mass index required a higher just-noticeable difference, or higher threshold, before tasting fatty acids in the samples. These results could lead to new approaches to limit excess fat consumption.
You’ve just watched JoVE’s introduction to just-noticeable differences. Now you should have a good understanding of how to design and run the experiment, as well as how to analyze and assess the results.
Thanks for watching!
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.
Applications and Summary
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.