Approximate Number Sense Test
Source: Laboratory of Jonathan Flombaum—Johns Hopkins University
A common carnival game is to ask people to guess the number of jellybeans packed into…
1. Stimuli and trials
- Program the experiment in Psychopy, MATLAB, or something similar (a free version can also be downloaded for non-commercial uses at www.panamath.org).
- Design all trials in the experiment to look more or less the same.
- Divide the display in half. Use a grey background.
- One side of the display shows a collection of blue circles.
- The other side shows a collection of yellow circles.
- Draw the circles in different sizes, as shown in the sample trial (Figure 1).
Figure 1. Schematic depiction of a single trial of the approximate number sense test. On each trial, the participant reports whether he saw more blue or yellow dots. - The key manipulation involves the number of yellow and blue circles. There should always be more of one kind than the other. The difference should be characterized in terms of a ratio: 2:1, 1.75:1, 1.5:1, 1.35:1, 1.25:1, and 1.15:1.
- Instruct the program to produce 20 trials with each ratio.
- Randomly select the larger color.
- Randomly select the smaller number of circles.
- Select the larger number to make the desired ratio.
- Draw yellow circles on one side of the display.
- Draw blue circles on the other side.
- Randomly choose the radius of each circle between 1° (of visual angle) and 3.5°.
- On each trial, a display appears for 500 ms. After it disappears, the participant presses the ‘Y’ key if they think they saw more yellow dots, or the ‘B’ key if they think they saw more blue dots.
- Provide feedback after each trial with a screen that displays either “Correct!” or “Incorrect.”
The approximate number sense test is an experimental paradigm for investigating the underlying mechanisms that support the ability to ?guesstimate.?
Guesstimating refers to an intuitive ability to recognize quantity, without knowing the exact number. For instance, in a common carnival game, individuals try to guess the number of jellybeans packed into a jar. The chances are low that anyone will pick the exact number.
Yet everyone can produce a guess in the right ballpark, as no one would guess 20 when there are clearly more than 100. Therefore, estimation is considered a hard-wired ability that individuals possess without relying on mathematical calculations.
This video demonstrates the procedure for investigating nonverbal numerical estimation, including how to design the stimuli, perform the experiment, and how to analyze and interpret data.
In this experiment, stimuli that vary in size and color are randomly and briefly presented on a computer screen. During each trial, two sets are visible: one contains a collection of blue circles, and the other includes a set of yellow circles.
Participants are asked to guess which set contains more. The dependent variable is percent accuracy, or the number of correct responses recorded as a function of the ratios across trials.
Performance accuracy is expected to be near chance when the ratio of circles are very similar?near 1:1?and improve as the ratio differences increase.
In other words, it?s easier to tell apart eight and four versus twelve and eight. In both cases, the subtractive difference is four, but the ratio differences vary, from 2:1 to 1.5:1.
To create the stimuli, generate circles of various sizes in blue and yellow sets. For each set, make sure that the numbers of blue and yellow circles are always different and represent the six ratios.
For each trial, code the program to divide the display to show one set from each color group on a gray background for 500 ms. Note that the color and circle size for the larger amount should be selected at random, and 20 trials with each ratio should be produced.
To begin the experiment, greet the participant in the lab and explain the instructions for the task. Once the participant understands the task rules, load the program.
When the circles disappear in each trial, have the participant press the ?Y? key if they think they saw more yellow dots, or the ?B? key if they think they saw more blue dots.
After each trial, provide immediate feedback via a tone to indicate whether the participant?s response was correct or incorrect.
To analyze the data, average the number of correct responses as a function of the ratio on each trial. Graph the mean accuracy percentage across ratio differences. Note that participants? performances improved as the ratio differences increased.
Approximate number sense positively correlates with arithmetic abilities as measured by standardized tests, even though arithmetic is not about estimating.
In addition, even young children can apply number sense to identify when something is missing from a group of familiar objects.
You?ve just watched JoVE?s introduction to the Approximate Number Sense Test. Now you should have a good understanding of how to design and perform the experiment, as well as analyze results and apply the phenomenon of number estimation.
Thanks for watching!?
View the full transcript and gain access to JoVE Science Education videos
Q1: What is approximate number sense and how does it differ from counting?
Approximate number sense is a hardwired mental ability to estimate quantities without exact calculation or verbal counting. Unlike learned counting skills, it allows people to intuitively recognize quantity and make reasonable guesses. For example, someone can estimate that a jar contains more than 100 jellybeans without counting each one, demonstrating this innate guesstimating ability.
Q2: How does ratio affect performance accuracy in the approximate number sense test?
Performance accuracy improves as ratio differences between compared sets increase. When ratios are similar, like 1:1, accuracy approaches chance level. As ratios diverge—such as 2:1 versus 1.5:1—participants correctly identify the larger set more often. This demonstrates that the visual system relies on proportional differences rather than absolute numerical differences.
Q3: What stimuli are used in the approximate number sense test procedure?
The test uses blue and yellow circles of varying sizes, randomly presented on a computer screen for 500 milliseconds per trial. Each trial displays two sets with different quantities representing six different ratios. Color and circle size for the larger amount are randomized, with 20 trials conducted for each ratio to ensure reliable data collection.
Q4: How do participants respond during the approximate number sense test?
Participants press the 'Y' key if they believe they saw more yellow circles or the 'B' key for more blue circles. After each response, immediate feedback is provided through a tone indicating correctness. This real-time feedback helps participants understand task performance and maintains engagement throughout the experimental session.
Q5: What does data analysis reveal about approximate number sense performance?
Researchers average correct responses as a function of ratio and graph mean accuracy percentages across ratio differences. Results consistently show that performance improves as ratio differences increase, confirming that approximate number sense operates on proportional rather than absolute differences. This pattern validates the underlying mechanisms supporting nonverbal numerical estimation.
Q6: How does approximate number sense relate to mathematical abilities?
Approximate number sense positively correlates with arithmetic abilities measured by standardized tests, despite arithmetic involving precise calculation rather than estimation. Young children also apply number sense to identify missing objects from familiar groups. This suggests that the foundational estimation ability supports broader numerical competence and mathematical development.
Q7: Why is the approximate number sense test considered an important experimental paradigm?
The test investigates underlying mechanisms supporting guesstimation through controlled stimuli and measurable dependent variables like percent accuracy. By systematically varying ratios and analyzing performance patterns, researchers uncover the computational and neural processes enabling nonverbal numerical estimation. This paradigm bridges cognitive psychology with neuroscience to understand fundamental quantitative abilities.