Numerical cognition is the idea that a living being has a number sense similar to a

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1 Sample Lab Report Jane Doe Intro to Cognitive Psych Lab Report #9 1/1/2007 Introduction Numerical cognition is the idea that a living being has a number sense similar to a sense of smell or touch. Much evidence points to the actual existence of this sense from a crude number sense demonstrated in animals and young children. While this sense is quite coarse in both sets of evidence and is subject to systematic errors, the overall data indicates that the idea of number has some salience even within the brain of a child. In children, there is a difference in the way that small and large numbers are perceived. When small numbers are presented, the exact quantity is known and it is limited to a set size of 3. In contrast, large set sizes are known only approximately such that it would be easy to tell that a set size of 30 is larger than a set size of 15 but quite difficult when comparing set sizes of 20 and 16. There is a theory that the same is true of adult humans. One set of evidence that lends itself to this theory is that in many different forms of writing, number 1, 2, and 3 (also sometimes 4) are represented by special characters that are very similar to each other but not to representations of other numbers. The ability of humans to enumerate items in everyday life may have been important evolutionarily especially when assessing threat levels. While it may no longer be as salient, a theory exists that says that humans have the ability to subitize small set sizes rapidly and accurately (up to a set size of 3). This experiment was designed to test this theory. When reaction times are measured for the enumeration of various set sizes, subtization would lead to a two-part curve where the first part, for small set sizes, would

2 be relatively flat and the second part, for larger set sizes, would be linear. If subitization does not exist, the curve will be fully linear corresponding with increased reaction time for each increase in set size. Methods Subjects were seated in front of a computer screen. Instructions were presented on the screen indicating that the subject should determine the number of items presented on the screen. In this case, the items were small squares. Subjects were instructed that they should respond by pressing the key on the keyboard corresponding with the number of items. Subjects finally were instructed to respond as quickly as possible but without sacrificing accuracy. The experiment itself consisted of 90 total trials where the number of items presented varied between one and nine items. Each of the nine set sizes was presented 10 times and the order in which the set sizes were presented was random. Response time was measured and was averaged based on the set sizes such that for each subject, the data output of the experiment was nine response times each averaged from 10 trials. This data was then averaged across the group and across the class and plotted versus set size. Results Figure 1 is a graph of my individual average response times for each set size (N=1). Figure 2 is a graph of the group average response times for each set size (N=4). Figure 3 is a graph of the class average response times for each set size (N=16). All three sets of data demonstrate that reaction time is positively correlated with set size. Figures 2 and 3 show for the group and class data that reaction time always increases with increased set size except for the largest set size. The reaction time

3 increases at a slower rate with the smaller set sizes as is evident by the smaller slope in the left part of the graphs and begins to dramatically increase when the set size changes from three to four for Figure 2 and from four to five for Figure 3. Figure 1 indicates that my individual response times are generally faster than the group or class averages and also that the sharp increase in my response time occurs when the set size changes from four to five. It also evident from examining the slopes at various points that in Figure 1, the rate of change in reaction time is less for almost all points when compared to the slopes in Figures 2 and 3. This is likely just due to the fact that Figures 2 and 3 show averages of reaction times across groups of people whereas Figure 1 presents a single subject s data. Examining other individual data (not shown) that factored into Figures 2 and 3 indicates that those slopes also differ from Figures 2 and 3 with some having greater slopes and some having smaller slopes. Discussion The data presented here in Figures 1, 2 and 3 clearly demonstrates that subitization does take place. The effect may clearly vary between individual data as Figure 1 demonstrates subitization of up to four and possibly five items while Figures 2 and 3 demonstrate that average data shows subitization of up to three and possibly four items. Examination of the individual subject data that contributed to Figures 2 and 3 demonstrates a wide range in reaction times for almost all set sizes indicating that possibly some individuals subitize more than four items while others subitize less and that it is only upon averaging that a set size of four becomes the set size where a shift from subitization to simply counting occurs.

4 It is quite interesting to note that when in Figures 2 and 3 the graphs switch to linear functions that the increase in reaction time per increase in set size is ms. This is related to the word length effect wherein it takes an English speaking person approximately 321 ms to articulate a number. What this possibly indicates is that once a set size threshold is reached, the subject resorts to counting and so the increase in reaction time per increase in set size is as a result of the subject internally verbalizing each number as he/she counts the items on the screen. Another interesting thing to note in all three figures is the flattening of the curve between set sizes of eight and nine. It is possible that this is simply an artifact of the experiment as subjects were told that no set size would be higher than nine and so upon seeing a large number of squares on the screen the subject did not necessarily have to count all of them to determine how many were there and thus producing a shorter reaction time. An interesting way of testing this in the future would involve not informing the subjects of the maximum set size used or in simply throwing in set sizes that are larger than the ones that are actually being tested to see if it is truly an artifact and that subjects still need to internally count each item. There exist various theories for how subitization exists from associating certain set sizes to certain geometrical shapes (Mandler & Shebo, 1982) to those that believe that the small set size just lends itself to less error simply because they are small (Gallistel & Gellman, 2000). As mentioned in the introduction, I believe that it may have played a very key role evolutionarily especially in the realm of detecting predators. The ability to determine two versus three predators may determine whether or not an animal or human sought to defend their territory or cede it because of a fear of losing to the predators. It is

5 clearly not advantageous to subitize for large numbers in this case because a group of five predators is equally as dangerous as a group of six predators to a lone individual. Because subitization has subsisted throughout evolution it indicates that it is a hardwired function and not something that is learned. Benefits of it in the current world are not immediately clear however it may be useful for video game players who need to interact with their visual world often more quickly than the average person needs to. Reference Gallistel CR, Gelman II (2000). Non-verbal numerical cognition: From reals to integers. Trends in Cognitive Sciences, 4, Mandler G, Shebo BJ (1982). Subitizing: An analysis of its component processes. Figures Individual Data RT (ms) Set Size Figure 1. Reaction time was measured for determining the number of items presented on a computer screen. Set sizes varied between one and nine with each set size being presented 10 times. Reaction times shown are average across those 10 trials (N=1).

6 Group Data RT (ms) Set Size Figure 2. Reaction time was measured for determining the number of items presented on a computer screen. Set sizes varied between one and nine with each set size being presented 10 times. Reaction times shown are average across those 10 trials and then averaged across the group (N=4). Class Data RT (ms) Set Size Figure 3. Reaction time was measured for determining the number of items presented on a computer screen. Set sizes varied between one and nine with each set size being presented 10 times. Reaction times shown are average across those 10 trials and then averaged across the class (N=16).