Previous studies
Previous studies have found evidence that suggests a numbers magnitude automatically activates the spatial representations associated with that magnitude and can influence our abilities to estimate and compare stimuli.
They further suggest that internal, mental spatial representations are strongly linked to external, real world representations, and there is a sort of “mapping” from our internal to external worlds. To investigate these claims, this experiment tested whether there was a higher probability to answer longer for digit strings consisting of 9’s compared to those consisting of 1’s. Participants were presented firstly with a straight reference line followed by a string of digits consisting of either 1’s or 9’s, and asked to judge whether the strings were longer or shorter than the reference. Results showed that there was a significant tendency to answer longer when presented with strings containing 9’s, which lead us to conclude that their magnitude did have an effect on length estimation.IntroductionIn general we are very good at estimating length; however, there are also many examples where we make errors.
This is due to an incorrect correspondence between the proximal and distal stimuli involved in the perception of our environments (http://arxiv.org/ftp/physics/papers/0110/0110036.pdf)The distal stimulus refers to the “actual” object or event in the outside environment, whereas the proximal stimulus refers to the input at the sense organ, in this case the pattern of light falling on the retina (www.psychology.uiowa.
edu). If these two stimuli do not correspond with each other, then our visual experience will not be veridical, i.e. genuine and truthful, not illusionary (http://dragon.uml.
edu/psych/illusion.html).This is exactly what occurs when we are presented with visual illusions. A visual illusion essentially “tricks” our visual systems into perceiving something that consistently differs from what we suppose to be correct, due to an incorrect correspondence between our proximal and distal stimuli (Wade, N.J.
; Swanston, M.T. (2001) Visual Perception: An Introduction). Visual illusions come in many forms, for example the Muller-Lyer illusion which distorts length, the Zollner illusion which distorts orientation, etc. but the result always the same; our visual systems are fooled.
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.MethodParticipants54 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.MaterialsAll 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.
DesignThe 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.ProcedureBefore 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.AnalysisData 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.
