Past studies have found that our visual systems can not only be influenced by visual illusions, but that the observation of a numbers magnitude can also lead us to make errors of judgement.
A study by Fischer, Castel, Dodd & Pratt (2001) where participants were asked to estimate the midpoint of a string of digits provided data which suggests that a numbers magnitude has an effect on spatial response codes. Fischer et al. (2001) presented participants with different digit strings, consisting of 1’s, 2’s 8’s or 9’s, and asked them to estimate the midpoint of the digit string. They found that depending on the magnitude of the numbers presented in the strings, participants would either be biased to the left of the centre (for digit strings containing 1’s and 2’s) or to the right of the centre (for those strings containing 8’s and 9’s). This suggests that a number’s meaning is automatically activated by perceiving the number, and that our spatial representations are associated with a numbers magnitude.
A further study by Fischer (2003) also found evidence for this theory using a simple detection experiment which suggested that there are similar structures controlling internal spatial representations and external space, and that these are connected – we appear to map external events to our internal representations of the world.
These experiments provide support for the theory that people show a bias depending on a numbers magnitude, and that this will affect their perception and estimation abilities, and this is the issue the following experiment will address.
Following results from previous research, the hypothesis is that digit strings consisting of 9’s will be perceived as longer than the reference line more often than digit strings consisting of 1’s. The null hypothesis states that there will be no significant difference between the perceived lengths of the digit strings in relation to the reference line, regardless of their numerical value.
Method
Participants
54 students in the third year of their psychology course at the University of Dundee took part. Their average age was 22.7 years, with the maximum age being 39 and the minimum being 19. 48 participants were right-handed, with the remaining 6 left-handed. 19 were male and 35 female, and they were all taking part due to a course requirement.
Materials
All stimuli were made with 26 point boldface Courier Font and presented in black on a white background (see appendix 1). The digit strings were presented in a straight, horizontal line, a string made of the digit 1 and a string made of the digit 9. Each stimulus was either 12 or 14 characters long, i.e. either short or long respectively. Stimuli were projected onto a white wall. Participants’ responses and information about their age, gender, handedness and viewing distance were collected on a response form.
Design
The independent variables were: Reference Line Length: 2 levels (12 char, 14 char); Probe Identity: 2 levels (digits 1, digits 9); and Probe Length: 2 levels (12 char, 14 char). Their combination resulted in 8 experimental conditions which were presented randomly in each block. The dependant variable was the response of “longer” or “shorter” from the participants, and the design of the experiment was within-subjects.
Procedure
Before the experiment began, the experimenter explained to participants how the stimuli would be presented and then gave their informed consent. On this consent sheet, gender, handedness, and the position of participant (i.e. the number of the row they were sitting in) were also recorded. They were then given response sheets to record their judgements. In each experimental trial, participants were presented firstly with a single straight line (the reference stimulus), followed by a blank screen. A digit string (the probe) then appeared, consisting of either 1’s or 9’s. Participants were then asked “was the last item longer or shorter?” and instructed to record their response (L or S) on the response sheet. There were short breaks after each set of 16 trials, with a total of 48 trials or 6 blocks.
Analysis
Data was downloaded as an SPSS file from Blackboard, containing the responses from each participant. The trials recorded in SPSS were in chronological order of presentation, so the first data column contained the first trial etc. These were coded as “1” if the participant had answered “longer” and “0” if the participant had responded “shorter” for each trial. The probability of a “longer” response for each of the probes (i.e. 1’s or 9’s) was calculated, giving the mean probability of “longer” responses for each participant. These means were then compared using a two-tailed paired samples t-test.
Results
Table 1 shows the means and standard deviations (SD’s) for the probabilities of probes consisting of 1’s and probes consisting of 9’s to be perceived as longer than the reference line.
Table 1: Probability of probes being perceived as longer than the reference line
Graph 1: Means of Probability of Probe Length being Perceived as Longer than Reference Line
This graph shows the means of probability of probe length being perceived as longer than reference line for both probes consisting of 1’s, and those consisting of 9’s.
A two-tailed paired samples t-test analysing the probability of longer responses in relation to differing probe identity was carried out on the data gathered. The probability of probes with identities of 9 being perceived as longer than the reference line was found to be significantly greater than the probability of probes with identities of 1 being perceived as longer (t (53) = 6.86; p<0.01).
This finding provides support for the experimental hypothesis and allows us to reject the null hypothesis.
Discussion
Examining the results obtained from this experiment, it can be seen that they provide support for the theory that number magnitude has an effect on the perceptual system, which can be likened to the effect of a visual illusion such as the Muller – Lyer. The fact that the probability of perceiving the 9’s probe as longer than the 1’s probe is significantly different supports the theory that the mere observation of numbers automatically activates our internal spatial representations associated with the numbers magnitude. This finding, in turn, suggests that our mental representations are closely related to our external visual experiences, so if our internal representations are “tricked” then our behaviour in the real, external world will be altered accordingly. This was found in this experiment – the numbers in the digit strings shouldn’t have any bearing on our abilities of estimation, as they technically have nothing to do with the task we are being asked to perform. However, they do appear to influence us, biasing us and distorting our abilities to compare and estimate length, which does support the findings of previous research by Fischer.
Future studies could repeat the experiment, controlling for methodological errors that were not addressed in this study. All 54 participants were presented with the stimuli (i.e. the reference lines followed by the probes) at the same time, which lead to viewing differences across the participants. This may have affected the ability to estimate length, or to see the screen as clearly. The population also could have been more randomly allocated. The vast majority of this population were female and aged around 20, and all were 3rd year psychology students. If the experiment was repeated, a more varied range of people could be included which would control for any differences in age, social background, or gender. There was also a small sample size for this experiment. Testing a larger group would increase the reliability of the results.
Despite these shortcomings in methodological design, the results of this experiment strongly support the findings of previous researchers that not only do visual illusions affect our ability to estimate size, length or orientation; number magnitude can have a similar effect.
References
Fischer, M.H. (2001) Number Processing Induces Spatial Performance Biases, Neurology 57 (5): 822-826
Fischer MH, Castel AD, Dodd MD, and Pratt J. (2003) Perceiving Numbers Causes Spatial Shifts of Attention, Nature Neuroscience 6 (6): 555-556
Wade, N.J. & Swanston, M.T. (2001) Visual Perception: An Introduction (2nd Ed.) Psychology Press Ltd
Websites:
http://arxiv.org/ftp/physics/papers/0110/0110036.pdf
http://dragon.uml.edu/psych/illusion.html
http://www.psychology.uiowa.edu/Classes/31001/SENSATION98.doc
