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. The codes were as follows:
After the 15 screens were presented to the participant, they were debriefed.
The mean estimation increased when arrangement became more random. When there are 79 dots onscreen, in a random arrangement the mean estimation was 53.4, whereas on a regular arrangement the mean estimation was 48.6, indicating that participant would predict that there were more dots on a random arrangement. However studying the same participants shows that there was a wider deviation from the mean for the random dots than those of the regular dots, showing that mean may have been influenced by extreme estimations; there was a mean estimation of 110 by one participant, which would skew the rest of the result by drawing them towards that extreme estimation.
There wasn’t much of a difference between the initial estimations by both participant groups. When presented with 31 dots both groups had a mean estimation of approximately 25 dots, and a similar deviation as well.
As the estimations for dots seem to be higher when the dots are arranged in a random arrangement, than the dots arranged regularly, it seems that the experiment doesn’t agree with Ginsburg’s RRNI theory. The results also disprove the hypothesis put forward at the beginning of the experiment.
It was expected that there would be a larger estimate for dots in a regular arrangement than those arranged randomly, however the results indicated the reverse. However for estimations with few dots the arrangement didn’t make a difference, and this can be supported by work done by Woodworth and Schlosburg (1954) who claim that small number of objects can be ‘directly perceived’.
There were a lot of flaws with the experiment and reasons why the outcome disproves the RRNI theory. A major error with the experiment is that the sample was chosen as an opportunity sample and by means of independent measures. Having an opportunity sample is convenient, but gives very unrepresentative samples and is often biased, due to the fact that psychology students took part in the experiment. Also as it was psychology students that took part there is the possibility that some of the estimations are a result of demand characteristics. Also as different participants took part in the different condition, or being independent measures, suggests that individual differences become a major factor, as they turn into confounding variables and become difficult to control. The only way to overcome this is to test the participants under both conditions and reduce the individual difference factor, however it does give rise to demand characteristics and consumes more time.
The experimental environment wasn’t ideal for the experiment, and there were a lot confounding variables that affect the test and the experimenter had little control over. As the experiment took part in an open computer room, there were many participants subjected to the experiment at the same time. As the room was very noisy and many participants giving their estimation, it would have been unavoidable that other participants didn’t influence a few of the estimations given.
Also it was mentioned that the screens were coded to aid the experimenter, however if the participant noticed the coding and gave their estimation based on the coding, it could result in estimates influenced by other factors apart than their judgement in numerosity.
There have been many studies that have tried to measure judgement in numerosity, and many have provided factors that affect the estimations of the objects. If the experiments were taken to another dimension and see whether factors like depth or colour would affect judgement. A simple experiment to see whether the distance objects are presented to the participant affects Folk’s subutizing effect.
Folk, C L, Egeth, H and Kwak, H-W. Subutizing: Direct Apprehension or Serial Processing? Perception and Psychophysics, 1988, 44, 313-320.
Frith, C D and Frith, U. The Solitaire Illusion: An Illusion of Numerosity. Perception and Psychophysics, 1972, 11, 409-410.
Ginsburg, N. Effect Of Item Arrangement On Perceived Numerosity: Randomness vs Regularity. Perceptual and Motor Skills, 1976, 43, 663-668.
Ginsburg, N. The Regular-Random Numerosity Illusion: Rectangular Patterns. General Psychology, 1980, 103, 211-216.
Krueger, L E. Perceived Numerosity. Perception and Psychophysics, 1972, 11, 5-9.
Woodsworth, R S and Scholsburg, H. Experimental Psychology, 1954, London, Methuen.
