Judgements of numerosity

Dustin Hoffmann received an Oscar for his portrayal of an autistic character, Raymond, in the film Rainman. In one memorable scene, Hoffmann counts the exact number of toothpicks on the floor at a glance, much to the amazement of his brother, Charlie (Tom Cruise). This scene poses the question of what would be the amount an ‘ordinary’ person would give, just by glancing at the toothpicks, or any other stimulus. There has been research carried out to see people’s capability to estimate the number of objects presented to them for a few seconds.

Initial research was conducted to see the attention span of people. Woodworth and Schlosburg (1954) conducted research based on an experiment by Jevons, who had found that participants could estimate the amount of objects (beans randomly dispersed on a tray) accurately until 8 beans, after which there would be errors in judgement. This ability to observe the correct amount of objects until about eight has been defined as ‘subutizing’. (Folk et al (1988).) Accuracy is still reasonable above eight, according to Woodworth and Schlosburg, who found that there were different factors that could affect the accuracy of object estimation. These processes would predict the amount of objects presented without counting them. So even though amount of objects could be large or small, the processes can perceive to make a rough estimation.

Other factors do affect the accuracy of the estimation. Experiments found that the density of the distribution of objects affects the estimation of the objects. Participants viewed circles, either filled or empty, randomly arranged, and were asked to predict the number of filled circles. When the number of empty circles increased, the estimation for filled circles decreased. ((Granburg and Aboud (1969)).

According to Krueger (1972), when participants where presented with distribution of dots, ranging from 25 to 200 dots, and varied the dispersion, so that the dots would be clustered close together or spread far apart, Krueger found an increase in estimation when dots were spread over a large area. Frith and Frith (1972) conducted experiments on ‘solitary illusions’, whereby participants were shown 2 sets of 12 dots. One set was distributed into a single cluster and the other arranged into a few clusters. The single cluster appeared to have more dots.

So if the arrangement of the dots has a large effect on the estimation, would there be a difference if the dots were arranged randomly or in a regular pattern? Ginsburg (1980) conducted work on ‘Regular-Random Numerosity Illusion’. (RRNI.) Ginsburg had found that participant were presented with dots in a regular pattern, arranged in a circular arrangement, they would estimate a higher number of dots than if the dots were presented in a random arrangement (Ginsburg 1978). He repeated the experiment using rectangular arrangement instead of a circular one and the findings were similar to experiments he had conducted with circular arrangement and that by Frith and Frith. The regular arrangement appeared to have a larger estimate than that of the random arrangement.

The experiment conducted was to see whether Ginsburg RRNI theory would still be obtainable. The hypothesis was that when participants were asked to estimate the number of dots presented to them for a few seconds, there would be a larger estimate for dots in a regular arrangement than those arranged randomly. Participants 28 participants of mixed backgrounds, race and gender. The participants are of an opportunity sample that was all First Year Psychology Students.

Apparatus A computer program, PowerPoint, was used to present the participants with dots for a brief period of time. The software was programmed to display the dots for one second, followed by a blank screen, which is displayed until the participant is ready to be presented with the next stimulus. The stimulus was a screen of dots, consisting of 20, 31, 44, 55 or 79 dots, arranged either randomly or regularly.

Procedure With the participant seated before the computer, they were presented with each stimulus for 1 second, before estimating the amount of dots onscreen. It had been predetermined whether the participant would be presented by the random or regular arrangement. Each screen was presented 3 times during the experiment, so the participant gave 15 estimations overall. After the participant was shown their stimulus, they would give their estimation to the experimenter, after which the experimenter presented them with their next stimulus. Each screen had its own code so it would be easy for the experimenter to identify while taking the participants estimates.

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