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Evidence for rapid extraction of numeric information Corbett, E. Jennifer 2004

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E V I D E N C E FOR RAPID E X T R A C T I O N OF N U M E R I C INFORMATION by JENNIFER E. CORBETT B. A., The Pennsylvania State University, 2000 A THESIS SUBMITTED IN P A R T I A L F U L F I L M E N T OF T H E REQUIREMENTS FOR THE D E G R E E OF M A S T E R OF ARTS in T H E F A C U L T Y OF G R A D U A T E STUDIES (Department of Psychology, Cognitive Science Programme) We accept this thesis as conforming to the required standard  T H E UNIVERSITY OF BRITISH C O L U M B I A April, 2004 © Jennifer E. Corbett, 2004  T H E UNIVERSITY OF BRITISH C O L U M B I A  F A C J L T Y OF G R A D U A T E STUDIES  Library Authorization  In presenting this thesis in partial fulfillment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission.  Jennifer E. Corbett  13/08/04  Name of Author (pl$$se pdht)  Date (dd/mm/yyyy)  Title-df Thesisf  Evidence for rapid extraction of numeric information  Degree:  Master of Arts  Department of Psychology The University of British Columbia Vancouver, BC Canada  Year:  2004  Abstract The present study investigated the rapid processing of numeric meaning. Participants compared briefly presented displays of digits, letters, or shapes. Experiment lrevealed three main findings: i . Participants were faster and more accurate when deciding which side of a display had the larger average value (when viewing displays of digits) than when determining which side of a display had the greater occurrence of a target shape (when viewing displays of letters or shapes), suggesting that numeric information was extracted faster and more accurately than information about familiarity or shape; ii. While participants compared digits faster and more accurately than they compared letters or shapes, they compared sideways digits (shapes), letters, and sideways letters (shapes) with equal speed and accuracy, showing a negative effect of sideways rotation for digits but no effect of rotation for letters, suggesting that impairment in performance produced by rotating digits may be attributed to the loss of numeric meaning and not to the loss of familiarity or shape similarities; iii. Participants compared homogeneous displays and single items faster and more accurately than they compared heterogeneous displays across all display types (digits, letters, and shapes), suggesting that the faster and more accurate comparisons of numeric information were not based on the mean value, as found for rapidly extracted geometric properties. Experiment 2 tested the effects of task instructions to compare the average value of digit displays on the rapid extraction of numeric information. It was found that even when participants were told to compare all displays based on the greater occurrence of a target shape, displays of digits were still compared faster and more accurately than displays of  familiar letters or simple shapes, suggesting that numeric meaning, not task instructions to compare digits based on average value, was driving the rapid digit comparisons. In Experiment 3, participants were allowed to view the displays of digits, letters, and shapes for as long as they wished. When participants were not under any time constraints imposed by brief stimulus presentations, they compared all display types with similar speed and accuracy, suggesting that they no longer rapidly extracted numeric information when given sufficient time to identify individual stimuli. Taken together, these results support the proposal that the visual system can rapidly represent meaningful (numeric) information when assessing briefly presented visual displays.  Table of Contents Abstract  ii  Table of Contents  iv  List of Tables  vi  List of Figures  vii  Dedication  viii  Introduction  1  Experiment 1 Method Participants Apparatus and Stimuli  8 10 10 10  Sequence of Events  11  Task Design  11 12  Results  13  Effects of Display Type on reaction time and accuracy Main effects  15 15  Paired comparisons of diplay types Paired comparisons of heterogeneous display types Effects of Rotation on reaction time and accuracy Main effects  15 15 16 16  Interactions Effects of Comparison Type on reaction time and accuracy  16 16  Main effects  16  Paired comparisons of comparison types  16  Paired comparisons of comparison types for equal set size displays  16  Effects of Stimulus Duration on reaction time and accuracy  17  Main effects  17  Difference comparisons  17  Discussion Experiment 2 Method  18 21 22  Participants  22  Task  23  Results  23  Similarity of the effects of Display Type on reaction time and accuracy between Experiments 1 and 2  23  Similarity of the effect of Comparison Type on reaction time and accuracy between Experiments 1 and 2 Discussion  23 23  V  Experiment 3  24  Method  25  Participants  25  Design  25  Results  25  Effects of Display Type on reaction time and accuracy Main effects  25 26  Paired comparisons Differences between the effects of Display type on reaction time and accuracy in Experiments 1 and 3 Discussion General Discussion Concluding Remarks Footnotes  26  References  36  Figure Captions  44  26 26 28 33 35  vi List of Tables Table 1: Experiment 1: Descriptive Statistics for the Four Display Tpyes  40  Table 2: Experiment 1: Descriptive Statistics of the Four Heterogeneous Display Types  41  Table 3: Experiment 2: Descriptive Statistics of the Four Display Types  42  Table 4: Experiment 3: Descriptive Statistics of the Four Heterogeneous Display Types  43  Vll  List of Figures Figure 1. Image averages and spectral signatures of different scene types  46  Figure 2. A n example of a trial used in Ariely (2001)  47  Figure 3. Individual stimuli for Experiments 1, 2, and 3  48  Figure 4. Examples of three display types used in Experiment 1  49  Figure 5. Effects of Display Type on reaction time and accuracy in Experiment 1  50  Figure 6. Effects of Display Type on reaction time and accuracy for heterogeneous displays in Experiment 1 51 Figure 7. Effects of Rotation on reaction time and accuracy for Experiment 1  52  Figure 8. Effect of Comparison Type on reaction time and accuracy for Experiment 1  53  Figure 9. Effects of Comparison Type on reaction time and accuracy for heterogeneous and homogeneous trials with equal set sizes in Experiment 1 Figure 10. Effect of Display Type on reaction time and accuracy in Experiment 2  54 55  Figure 11. Differences between the unlimited processing of heterogeneous displays (Experiment 3) and the processing of briefly presented heterogeneous displays (Experiment 1)  56  Dedication Many people stood behind me throughout my Masters' work. First, I am grateful to Dr. Chris Oriet for his advising on this project, and for his enthusiasm and encouragement. He has been a mentor and a great friend to me. Also, I want to thank my M A committee members, Dr. Jim Enns and Dr. Vince DiLollo, for their continued support and guidance. Thanks to my new advisors, Dr. Todd Handy and Dr. Jim Enns, for taking me on as a PhD student. While working on this research, especially towards the end, I greatly appreciated the people and resources of the Vision Lab and the Neurolmaging Lab. I also want to give a huge thanks to my R A , Rajinder Cheema for her assistance with this research. Thanks to my Mom, Dad, and sister Jill for their love and encouragement, and to all of the Corbett and Keltner family members who support and inspire Ken and I to do our best. I want to thank my best friends: Nicole Brown, Althea White, and Crystal Lambert, for their peptalks, jokes, friendship, sincerity, and advice throughout my M A study, and for taking care of me long-distance. I am very blessed to have such wonderful family and friends. I also want to thank my undergraduate supervisor, Dr. Cathleen Moore for being a great mentor and for sending me onto graduate school with research experience, enthusiasm, and creativity. Thanks to Dr. Toby Mordkoff for having me as an R A in his lab at Penn State, and thanks to Dr. Lance Hahn for getting me into the business. Thanks to great friends: Carrie Cuttler, Shabob Ghorashi, Matt Hill, Lisa Jefferies, Amanda LaMarre, Adil Leghari, Geniva Liu, Orsolya Magyar, Mark Rempel, Jelena Ristic,  ix Alexa Roggeveen, Megan Toews, Christine Tipper, Sherry Trithart, Marie Tse, and Katie Yoshida for hanging out, wasting time, taking walks, drinking coffee, eating cookies, and doing whatever else scientists do. Saiorse, Thea, and the cat, thanks for the study breaks, love, and exercise. Should I thank Paris =)? It's not like she actually DOES anything.... Foremost, I am grateful to my fiance and best friend, Kenneth R. Keltner, for his constant love and encouragement. I dedicate this thesis and all of my work to him. I am honored to have him as a partner and husband, and I hope I have made him as proud of me as I am of him.  1  Introduction Vision is the main way we acquire knowledge about our dynamic surroundings. The visual system is faced with the challenge of representing a continuously modified world. One possible way the visual system might accomplish this amazing feat is though rapid processes that help the system quickly create a meaningful rough draft of the visual world. This study demonstrates rapid processing of numeric stimuli, which cannot be accounted for by familiarity or spatial similarity, but which instead may be driven by numeric meaning. Despite the dynamic nature of our environments, we perceive a stable, coherent, threedimensional world. Furthermore, a growing body of evidence suggests that the visual system does not represent all visible objects, and that our perceptions are formed using a limited amount of visual input (Irwin, 1991; Simons & Levin, 1998). How might the visual system create an illusion of a composite perceptual image, despite strong evidence that a limited amount of the dynamic environment is actually represented? Hochberg (1978), and Hock & Schmelzkopf (1980) proposed that we abstract a conceptual representation of a scene from several successive fixations. Ariely (2001), and Ariely and Burbeck (1995) further suggested that our perceptions may be generated from occasional detailed samples, together with statistical summaries of remaining areas, and an overall interpretation of the meaning or gist. The results of this study demonstrate that, when given very brief visual displays of digits, letters, and shapes, the visual system can derive numeric meaning of digits faster and more accurately than it can obtain  2  information about the familiarity of letters or spatial similarity of simple shapes, suggesting that the system may be able to rapidly represent meaningful (numeric) information. Several studies support the notion that our perceptions are formed by conceptually integrating a limited amount of visual information over successive views. Irwin (1991) asked observers to view a random dot pattern during one fixation and then to determine if a second dot pattern, presented in the successive fixation, was identical to the first pattern. He found that subjects could not reliably determine if the two patterns were identical. In addition, other experiments have shown that changing visual characteristics of words, such as letter case, does not disrupt reading or naming of the word (McConkie & Zola, 1979; Pollatsek, Rayner, & Collins, 1984). If visual processing relies on a composite representation, such changes across eye movements should have been easily detected, and should have had a disruptive effect on perception. Results from visual search support the possibility of rapid, parallel comparisons for categorically dissimilar items (i.e. a letter target among digits) (Egeth, Jonides, & Wall, 1972), whereas search for categorically similar items is a linearly increasing function of set size (Atkinson, Holmgren, & Juola, 1969). These results suggest that conceptual discrimination may be a separate and more efficient process than character identification (Posner, 1970; Brand, 1971). Further support for this proposal comes from visual search work by Jonides & Gleitman (1972). They asked subjects to detect a digit or letter target in a field of digits or letters.  3  Consistent with past results, they found that when the target and field category (digits/letters) differed, reaction times were independent of display size, whereas when the target and field were from the same conceptual category, reaction time was an increasing linear function of set size. Of particular interest is the finding that the conceptually ambiguous item "0" was processed in relation to how it was specified prior to the experiment, as "zero" or "oh." For example, an "oh" was found to "pop-out" from a field of digits, but a "zero" did not, even though both were represented by the same stimulus, "0." Because categorical meaning could be specified by task instructions, this study strongly suggested recognition at the level of conceptual category (stimulus type) rather than at the level of physical characteristics (individual stimuli), although it has not been consistently replicated (Duncan, 1983; Krueger, 1984). Barlow (1961) hypothesized that early level sensory neurons remove statistical redundancy in sensory input. It is widely agreed that such neurons appear to have adapted to extract the statistical properties of the sensory information to which they are exposed (Olshausen & Field, 1996; Simoncelli & Olshausen, 2001). Several studies have found evidence that the visual system represents structural properties of images, such as sparseness, roughness, and luminance, using statistical coding (Baddeley, 1997; Oliva & Torralba, 2001; Kersten, 1987). Figure 1 (Torralba & Oliva, 2003) illustrates how different categories of objects and environments (a) exhibit distinguishing image averages (b) and spectral signatures (c). For example, it can be seen that man-made objects tend to vary along the vertical and horizontal axis,  4  while natural images have spectral signatures that vary along many dimensions. Torralba & Oliva (2003) asked observers to predict whether an object from a given category (e.g. animal, building, vehicle) was present or absent in a rapidly presented display based only on categorically averaged second-order image statistics such as luminance and roughness (image average). Observers were well above chance at predicting the presence or absence of the given object based on its corresponding image average. Taken together, these findings suggest that the visual system may use distinguishing image statistics in representing the visual world. Recent studies provide evidence that the visual system can rapidly represent overall geometric statistical properties, such as mean size, mean color, mean orientation, and mean direction of motion when sets of similar objects are present (Ariely, 2001; Ariely & Burbeck, 1995; Teghtsoonian, 1965; Chong & Treisman, 2003; Parkes, Lund, Angelucci, & Morgan, 2001; Watamaniuk & Duchon, 1992). Furthermore, using a change detection paradigm, Hollingworth and Henderson (2000) showed that observers are faster and more accurate at detecting semantically informative changes versus changes that do not alter the scene's meaning. Several studies have shown categorically based detection and identification to be a more efficient process than character identification (Levin, Takarae, & Miner, 2001; Intraub, 1981). Thus, it is possible that our visual system is able to extract conceptual representations of images more rapidly than it can obtain detailed information based on individual items.  5  The visual world is highly redundant, containing many similar objects with fairly uniform properties (i.e. leaves on a tree, clouds in the sky, or a shelf of books). Ariely (2001) proposed that, when presented with similar items, the visual system rapidly creates a representation of the statistical properties of the set, and discards information about the individual items within the set. Ariely (2001) conducted an experiment to test this possibility using two paradigms: a member identification task and mean discrimination task. Each trial consisted of a set of circles of different sizes in the first interval, and an image of a single circle (drawn from within the size range of the first interval set) in the second interval (Figure 2). In the member identification condition, the task was to report whether the single circle (b) was a member of the first interval set (a). In the mean discrimination condition, the task was to report whether the single circle (b) was larger or smaller than the mean circle size of the first interval set (a). In the member identification condition, observers could not reliably distinguish the size of the individual circle, and could not accurately indicate if the single circle was a member of the set. In contrast, in the mean discrimination condition, observers were highly accurate in determining whether the single circle was the mean of the first set of circles. From these results, Ariely suggested that the visual system creates statistical representation of the set, not including precise information about the individual items. Chong & Treisman (2003) demonstrated that participants were equally as fast and accurate when judging which of two side-by-side displays of circles of heterogeneous sizes had the larger mean size as they were at determining which of two displays of homogeneous  6  circles had the larger mean size, or which of two single circles was larger, suggesting that the mean judgment was at least as fast and accurate as comparing individual items. In addition to mean size, other stimulus properties may be statistically represented. For example, observers are poor at judging the mean orientation of a small number of Gaussian distributed orientations, but as the number of orientations is increased, accuracy for the mean judgment is markedly improved, suggesting statistical representation of visual texture information (Dakin & Watt, 1997). Observers can also accurately estimate the mean orientation of several Gabor patches, but cannot report the orientation of individual patches, (Parkes et al., 2001). Participants can distinguish the mean direction of motion among various moving stimuli, but cannot describe the direction of motion for individual stimuli (Watamaniuk, Sekuler, & Williams, 1989). Based on this previous research suggesting that the visual system can rapidly represent overall spatial and statistical properties of a scene, the present study examined whether this was also true of more conceptual properties, such as numeric value. Participants were presented with displays of digits, letters, or shapes. In Experiment 1, when viewing displays of digits, participants either reported which side of the display had the larger average value (in heterogeneous and homogenous multiple item display comparisons), or which side of the display had the higher digit (in single item comparisons). In the letter displays, participants reported  7  which side of the display had the greater occurrence of a target letter. In the shape displays, participants indicated which side had the greater occurrence of a target shape. The results of Experiment 1 showed that digit displays were compared faster and more accurately than letter or shape displays, which were processed with similar speed and accuracy. There was a negative effect of sideways rotation for digits but no effect of rotation for letters. These results suggested that participants extracted numeric meaning faster and more accurately than they extracted information about familiarity or shape. Participants' reaction times and accuracy for sideways digits conditions were identical to their reaction times and accuracy for letters and sideways letters, confirming that differences in spatial arrangement or symmetry were not driving the faster, more accurate comparisons of digit stimuli. Because sideways digits retained all the spatial relations found in digits, yet did not show the faster reaction times and higher accuracy of digits, spatial or symmetry differences were ruled out as a possible explanation for the reaction time and accuracy effects found for digit comparisons. Furthermore participants compared homogeneous displays and single items faster and more accurately than they compared heterogeneous displays across all stimulus types (digits, letters, and shapes), suggesting that the faster and more accurate comparisons of numeric information were not based on the mean value, as found for rapidly extracted geometric properties. Participants in Experiment 1 were instructed to compare the digit displays based on average value and to compare the other display types based on the frequency of a given target,  8  raising the question of how task instructions affected performance. Similar to Jonides and Gleitman's (1972) experiments, conceptual numeric meaning might be assigned to digit displays by the task instructions to compare the average value of the digit displays. To examine whether numeric information would still be rapidly processed even if participants were not instructed to compare digit displays based on average value, participants in Experiment 2 were instructed to compare all display types based on the frequency of a given target. The results of Experiment 2 were identical to those of Experiment 1, suggesting that numeric meaning, not task instructions to compare digits based on average value, was driving the rapid digit comparisons. Also, given the brief stimulus durations of Experiments 1 and 2, it was possible that numeric information was only rapidly extracted when observers were not given sufficient time to identify individual stimuli. If given more time, individual items may be processed fully to the level of identification and then compared. In Experiment 3, participants were allowed to view the displays of digits, letters, and shapes for as long as they wished. When participants were not under any time constraints posed by brief stimulus presentations, they compared all display types with similar speed and accuracy, suggesting that they no longer rapidly extracted numeric information when given sufficient time to identify individual stimuli. Experiment 1 Building upon previous research demonstrating that the visual system can rapidly represent overall spatial and statistical properties of a scene, Experiment 1 investigated whether  9  this was also true of more conceptual properties, such as numeric value. Participants were asked to make comparisons between sets of meaningful familiar digits, familiar letters, or simple shapes. If numeric meaning is extracted faster and more accurately than information about familiarity or shape, then participants should show faster reaction times and higher accuracy for digits than for letters or shapes. If participants' reaction times and accuracy for sideways digits conditions were identical to their reaction times and accuracy for letters and sideways letters, but different from their reaction times and accuracy for digits, this would confirm that differences in spatial arrangement or symmetry were not the basis of any faster, more accurate comparisons of digit stimuli. Because sideways digits retained all the spatial relations found in digits, if they did not show similar reaction times and accuracy as digits, then spatial or symmetry differences could be ruled out as a possible alternative explanation for the observed results. Furthermore, digits and letters were rotated sideways to produce the sideways digits and sideways letters conditions, respectively. If numeric meaning is the basis for faster reaction times and higher accuracy for digit comparisons, then rotating digits sideways should cause the numeric meaning and familiarity of the digits to be lost, and rotating letters sideways should eliminate the familiarity of the letters. Therefore, the data should demonstrate a negative effect of sideways rotation for digits, but no such effect of rotation for letters if numeric meaning is driving faster and more accurate comparisons of digits versus all other display types. Also, as previous research (Chong & Treisman, 2003) indicates that the visual system statistically represents  10  geometric properties such as average size, participants in Experiment 1 made three types of comparisons (heterogeneous, homogeneous, and single item comparisons) within each display type. If mean value was the basis of rapid digit processing, then within each type of display participants should exhibit similar reaction times and accuracy for heterogeneous, homogeneous, and single digit comparisons. To investigate possible differences in processing over time, stimuli were presented at three durations: 80 ms, 200 ms, and 650 ms. Method Participants Nine University of British Columbia undergraduates participated in Experiment 1. Participants received two extra credits in a department psychology course or $10 in exchange for their voluntary participation. A l l had normal or corrected-to-normal vision.  Apparatus and Stimuli In all experiments, stimuli were presented on e M A C computers, which also performed all timing functions and recorded participants' responses. Participants viewed the screen with both eyes from approximately 60 cm. The 8 individual stimuli were block character digits, letters, and shapes (Figure 3). Each of the digit and letter stimuli subtended approximately 0.75° * 0.25° visual angle, and each shape stimulus subtended approximately 0.25° * 0.75° visual angle. Shapes were made by rotating the digits and letters 90° to the left, creating sideways digits and  11  sideways letters. Each display was divided vertically into two halves, each half containing either a radial array of 6 items, or a single item. Radial arrays subtended approximately 4° visual angle, with individual stimuli separated by an average of 1°. Radial arrays or single items were vertically centered on the screen, and separated from central fixation by an average horizontal distance of 2.25°. Both halves of the screen contained the same stimulus type (digit, sideways digits, letters, or sideways letters), and also contained one of three comparison types: heterogeneous, homogeneous, or single item comparisons. Sequence of events Each trial began with a 100 ms fixation cross in the center of the screen, signaling that the stimulus display was about to appear. After the offset of the fixation cross, the stimulus display, consisting of items arranged in two side-by-side radial arrays or two single items, was shown for 80 ms, 200 ms, or 650 ms, followed by a blank screen until the participant responded. After the participant responded, she was given feedback in the center of the screen, a "+" for a correct response, and a " -" for an incorrect response. Task When viewing displays of digits, the participant had to indicate which side of the display had the larger average value. When presented with displays of letters, the participant's task was to indicate which side of the display had the larger number of q's, and when viewing displays of shapes, observers were required to indicate which side had the larger amount of a target shape  12  (in, or LT ). Participants were instructed to compare the displays as quickly and accurately as -  possible. Design The experimental design allowed for several manipulations within subjects: Display Type (digits, sideways digits, letters, or sideways letters), Rotation (upright digits and letters versus sideways digits and letter, respectively), Comparison Type (heterogeneous, homogeneous, or single), and Stimulus Duration (80 ms, 200 ms, or 650 ms). Each subject participated in 12 experimental conditions. Each of the display types was presented at one of three durations. In each condition, only one type of display was presented: digits, sideways digits, letters, or sideways letters. The order of conditions was counterbalanced across participants. Within each condition, there were 16 heterogeneous, 16 homogeneous, and 16 single item trials. The order of these trials was randomized, with each trial having an equal probability of being presented over the course of the condition. For heterogeneous trials, both stimuli of a given display type were randomized within the radial arrays as much as possible (in individual item position and proportion), to create 16 trials where the left array had more of the target stimulus. For homogeneous trials, the 16 initially identical arrangements, with 6 of one stimulus on the left and 6 of the other stimulus on the right, were varied with respect to the frequency and position of stimuli in both arrays to produce four trials of 6 items in each array, and three trials of 5,4,3,and 2 items in each array for a total of 16 trials of homogeneous items. Similarly, for single item  13  trials, each stimulus was presented randomly within imaginary side-by-side radial arrays, with an average separation of 4.5° between the stimuli about the center of the screen. The resulting 48 trials, in which the left array contained the larger average value or the greater occurrence of the target, were switched about the vertical axis to create 48 more trials in which the right side of the display now contained the larger average value or the greater occurrence of the target. Each condition contained 4 blocks of 48 trials. Before beginning each condition, participants were given as many practice trials as needed to be able to indicate that they understood the task. Figure 4 shows the sequence of a heterogeneous digits trial (a), a homogeneous letters trial (b), and a single sideways digits (shape) trial (c). Results Two dependent variables were measured in all experiments: reaction time and accuracy. In all experiments, only correct responses were considered in reaction time analyses. To determine the effect of numeric meaning, the results of Experiment 1 were first analyzed using a repeated-measures A N O V A that examined within-participant factors of Display Type (digits, sideways digits, letters, or sideways letters), Comparison Type (heterogeneous, homogeneous, or single), and Stimulus Duration (80 ms, 200 ms, or 650 ms). To analyze unique effects for digit displays, for each participant the mean reaction time for digit displays was compared to the average of the mean reaction times for the remaining three  14  display types (sideways digits, letters, and sideways letters). This comparison was also made for response accuracy. To further determine the contribution of numeric meaning, the effect of rotation for digits and letters was analyzed using a second repeated measures A N O V A that examined within subjects factors of Display Type (digits, letters) and Rotation (upright, sideways). To assess whether numeric meaning was represented using the mean value of displays, for each participant the mean reaction time for heterogeneous digit displays was compared to the average of the mean reaction times for homogeneous and single digits. Again, the corresponding comparison was made for response accuracy. As single and homogeneous comparisons ranged in set size from 1 to 6 items per array, but all heterogeneous comparisons were made between arrays of 6 items, a further comparison was made for reaction times and accuracy between heterogeneous displays of 6 digits and homogeneous displays of 6 digits. To determine whether digits were processed differently over time than stimuli in the other three display types, for each participant the average reaction time and accuracy for a given heterogeneous display type (digits, sideways digits, letters, and sideways letters) at the 80 ms stimulus duration was subtracted from the average reaction time and accuracy at the 650 ms stimulus duration. The resulting mean reaction time and accuracy differences for heterogeneous digit displays were then compared to the average mean reaction time and accuracy differences of the remaining three types of heterogeneous displays.  15  Effects of Display Type on reaction time and accuracy i. Main effects There was a significant main effect of Display Type on reaction time, F(3,24)=8.805, p<.001, and accuracy, F(3,24)=10.790, p<.001 (Figure 5 a & b). ii. Paired comparisons Digits were processed faster, t(8)=-7.47, p<.001, and more accurately, t(8)=6.25, p<.001,than the average of the mean reaction times and accuracy for the other three display types (sideways digits, letters, and sideways letters) (Figure 5a & b). On average, participants required 485 ms to respond correctly to digit displays and were 87% accurate. Table 1 shows the complete descriptive statistics of the four display types for Experiment 1. iii. Paired comparisons of heterogeneous display types Comparing only heterogeneous displays across the four display types yielded similar results, with significantly faster mean reaction times and greater accuracy for heterogeneous digits than for the average mean reaction times and accuracy of the remaining three heterogeneous display types, t(8)=-4.905, p<.001 (reaction time), t(8)= 4.564, p<.05 (accuracy) (Figure 6a& b). Accuracy for each heterogeneous display type was significantly different from chance (50%), all t(8)'s >4.400, all g's<.05. On average, when responding to heterogeneous displays of digits, participants required 700 ms to respond correctly and were  16  67% accurate. Table 2 shows the complete descriptive statistics for the four heterogeneous display types for Experiment 1. Effects of Rotation on reaction time and accuracy i.  Main effects A second analysis of the within subjects factors of Display Type (digits, letters)  and Rotation (upright, sideways) revealed main effects of Display Type, F(l,8)=5.386, p_<.05, and Rotation, F(l,8)=8.652, p_<.05 on reaction time (Figure 7a) and a main effect of Rotation, F(l,8)=15.501, p_ <.05 on accuracy (Figure 7b). ii.  Interactions There was a significant interaction effect of Display Type and Rotation,  F(l,8)=20.609, p<.05, on reaction time. Effects of Comparison Type on reaction time and accuracy i.  Main effects Contrary to the results of Chong and Treisman (2003), there was a highly  significant main effect of Comparison Type on reaction time, F(2,16)=19.950, g<.001, and accuracy, F(2.16)=431.326, p<.001. ii. Paired comparisons of comparison types Mean reaction times, averaged over the homogeneous and single digit displays, were significantly faster than mean reaction times for heterogeneous digit displays  17  t(8)=5.940, g<.001. The same comparison was made for mean response accuracy and yielded similar results, t(8)=-16.184, p<.001. The same pattern of comparison type effects was found for the remaining three display types, all t(8)'s>5.000, all g's<.001 (reaction time), all t(8)'s<-15.800, all p's<.001 (accuracy) (Figure 8a & b). iii. Paired comparisons of comparison types for equal set size displays Furthermore, homogeneous digit displays of set size 6 were compared faster, t(8)=6.110, g<.001, and more accurately, t(8)=-16.267, p<.001, than heterogeneous digit displays. The same pattern of comparison type effects was found for the remaining three display types, all t(8)'s>5.100, all p_'s<.001 (reaction time), all t(8)'s<-15.500, all p's<.001 (accuracy) (Figure 9c & d). Effects of Stimulus Duration on response time and accuracy i. Main effects There was not a significant main effect of Stimulus Duration on reaction time or accuracy. ii.  Difference comparisons Furthermore, the average reaction time and accuracy for a given heterogeneous  display type (digits, sideways digits, letters, and sideways letters) at the 80 ms stimulus duration was subtracted from the average reaction time and accuracy at the 650 ms stimulus duration. The resulting mean reaction time and accuracy differences for  18  heterogeneous digit displays were not significantly different from the average mean reaction time and accuracy differences of the remaining three types of heterogeneous displays. However, the average reaction time difference for heterogeneous digits was significantly different from 0, t (8)=3.172, p<.05, echoing the nonsignificant trend for digit displays to be processed faster at shorter stimulus durations. Discussion The goals of Experiment 1 were to determine whether numeric information could be processed faster and more accurately than information about familiar letters or simple shapes, to determine whether the mean value was the basis of rapid numeric judgments, and to determine whether there were any differences between how digits and the other displays types were processed over time. The main effect of Display Type and the paired comparisons for digits versus the other three display types showed that digits were compared faster and more accurately than items in the other three display types. Participants' reaction times and accuracy for sideways digits conditions were identical to their reaction times and accuracy for letters and sideways letters, but different from their reaction times and accuracy for digits, confirming that differences in spatial arrangement or symmetry were not the basis of the faster, more accurate comparisons of digit stimuli. It is important to note that display types vary in three aspects: numeric meaning, familiarity, and shape. Digits have numeric meaning, familiarity, and shape similarities as possible basis for rapid processing, letters have familiarity and shape similarities,  19  and sideways digits and sideways letters have shape similarities that may be the basis for comparisons. Therefore, the advantage (in terms of reaction time or accuracy) for digits versus the other three display types can be attributed to numeric meaning, and any effect of rotation for digits that is not present for letters can be attributed to a loss of numeric meaning from rotation. Comparing the effect of Rotation for digits and letters allowed for a second confirmation that numeric meaning was driving the rapid reaction times and higher accuracy for digit comparisons. Digits were significantly impaired by rotation as seen by the main effects of Display Type and Rotation and the interaction effect of Display Type and Rotation on reaction time, and supported by the main effect of Rotation on accuracy. No such impairments from rotation were found for letters. On the contrary, letters, sideways letters, and sideways digits were compared with similar speed and accuracy, suggesting that numeric meaning not present in these display types was driving the rapid digit comparisons. The digit displays showed both a reaction time and accuracy advantage that could not be explained by familiarity or shape, was eliminated by rotation, and thus could be attributed to the additional aspect of numeric meaning. Therefore, the first conclusion of Experiment 1 was that numeric information could be processed faster and more accurately than information about familiarity or shape. However, it was unclear whether numeric meaning of digits or task instructions to compare digit displays based on average numeric value was the basis of rapid digit comparisons.  20  While these results clearly show an advantage for processing numeric meaning, they do not support the idea that such comparisons are accomplished by numeric statistical descriptors such as those found by Chong and Treisman (2003). These researchers found that the thresholds for comparing the mean size of heterogeneous arrays of circles were comparable to those for the size of circles in homogeneous arrays, or for single circles. They concluded that instead of representing the size of each individual circle in the display, the visual system created a perceptual representation of the set using mean size as a statistical descriptor. On the contrary, the results of Experiment 1 showed a significant main effect of Comparison Type on both reaction time and accuracy. Analysis of digit displays showed that the average mean reaction times and accuracy of homogeneous and single comparisons were significantly faster than the mean reaction times for heterogeneous comparisons, indicating that the mean judgment was not the basis the rapid digit comparisons. To determine further whether average numeric value of displays was statistically represented, reaction time and accuracy for heterogeneous and homogeneous displays of set size 6 were compared. Again, comparisons between homogeneous digit displays of set size 6 were made faster and more accurately than between heterogeneous digit displays. If these results were do to a reduced numeric difference between heterogeneous displays of digits versus the larger numeric difference between homogeneous or single displays of digits, then there should only be an effect of Comparison Type for digit displays. However, the pattern of impaired performance for heterogeneous versus homogeneous and single  21  comparisons was constant across all display types. A l l results of Experiment 1 indicated that the mean value was not likely to be the basis for the rapid extraction of numeric information. A final question was whether the process responsible for representing numeric information behaved differently over time than the processes responsible for representing familiar letters or simple shapes. Although the results of Experiment 1 showed a counterintuitive trend for all displays to be compared faster at shorter stimulus durations, this trend was only significant for comparisons between heterogeneous displays of digits. Taken together with the result that accuracy was unaffected by stimulus duration in any comparison, it is possible that participants used whatever extra time they were given at longer stimulus durations in an attempt to verify their answers, although this did not improve performance. Similar results showing slower reaction times with longer stimulus durations have been found for comparisons of simple displays (Klein, 1982), suggesting that generalizations cannot be made between reaction times for brief and long stimulus exposures. Experiment 2 From the results of Experiment 1, it was unclear whether numeric meaning or task instructions to compare digit displays based on average numeric value were the basis for faster and more accurate digit comparisons. The controversial finding of Jonides and Gleitman (1972), that an ambiguous stimulus could be processed faster if it were defined as conceptually different from a field of distractors than if it were defined as conceptually similar to a field of distractors  22  suggested that conceptual meaning could be specified by task instructions. The faster and more accurate processing of digit displays found in Experiment 1 may also have been due to the task instructions to compare digits based on average value and to compare letters and shapes based on amount. The alternative explanation was that when comparing which display had more of a given stimulus, numeric meaning of digits was causing participants to compare the digit displays faster and more accurately than the other display types. To determine whether the rapid digit processing found in Experiment 1 was due primarily to the unique task instructions to compare the average value of digit displays or due to the numeric meaning of digits, participants in Experiment 2 were told to compare all display types based on the larger amount of a target shape. If the task instructions to compare the average value of digit displays were responsible for the faster reaction times and higher accuracy for digit comparisons found in Experiment 1, then changing the task instructions should eliminate these effects for digit displays in Experiment 2. Method Participants Twelve University of British Columbia undergraduates participated in Experiment 2 in exchange for two extra credits in a department psychology course or monetary compensation ($10). A l l had normal or corrected-to-normal vision.  23  Task Experiment 2 was identical to Experiment 1 in all respects except task instructions concerning digit displays. This time, instead of deciding which digit display had the larger average value or which letter or shape display had more of a target character, participants were instructed to indicate which display contained the greater occurrence of a character (now 5 for digit displays). Results To determine whether numeric meaning was given by the nature of the experimental task or specified by task instructions, the results of Experiment 2 were compared to those of Experiment 1. Analysis of the combined data from Experiments 1 and 2 showed no significant main effects of Task Instructions on reaction time or accuracy. Discussion As illustrated by comparing Figure 11 to Figure 5 and Table 3 to Table 1, the results of Experiment 2 mirrored those of Experiment 1. The experiments differed only in task instructions for digit displays, yet produced identical results, indicating that changing the instructions did not affect how participants compared digit displays. Contrary to the results of Jonides and Gleitman (1972), which suggested that conceptual meaning could be assigned to stimuli by task instructions, participants compared digits faster and more accurately than the other display types regardless of whether numeric meaning was specified by task instructions. Therefore, it can be  24  concluded that numeric meaning of the digit stimuli, and not task instructions to compare digits based on average value, was basis for the rapid digit comparisons. Experiment 3 In Experiment 3, participants were allowed to view the displays of digits, letters, and shapes for as long as they wished. Given the brief stimulus durations of Experiments 1 and 2, it was possible that numeric information was only rapidly extracted when observers were not given sufficient time to identify individual stimuli. If given more time, individual items may be processed to the level of identification and then compared. If, contrary to the results of Experiment 1 for brief stimulus durations, the results of Experiment 3 showed equal speed and accuracy for all four display types, and reaction times in Experiment 3 were longer those of Experiment 1 but accuracy in Experiment 3 was higher than in Experiment 1 across all display types, then this would suggest that numeric information was no longer rapidly extracted when viewing time was unlimited. Rather, it would indicate that participants now processed each stimulus to the level of identification, allowing for slower yet more accurate comparisons. However, if numeric information was rapidly extracted even when participants were not under time constraints that would make meaningful numeric information more practical to extract than in formation about the identity of individual stimuli, then similar reaction times and accuracy patterns should be found for both experiments.  25  Method Participants Nine University of British Columbia undergraduates participated in Experiment 3 and received an extra credit in a department psychology course or monetary compensation ($5) in exchange for their voluntary participation. A l l had normal or corrected-to-normal vision. Design In all but two respects, the design of Experiment 3 was identical to that of Experiment 1. Participants compared digit displays based on the larger average value and compared letter and shape displays based on the greater occurrence of a target. This time, rather than manipulating stimulus duration, the stimulus display remained on the screen until the participant responded. Subjects were instructed to respond as quickly and accurately as possible. Also, because Experiments 1 and 2 provided no support for the idea that the mean judgment was the basis for the rapid digit comparisons, participants in Experiment 3 compared only heterogeneous displays of digits, letters, and shapes. Participants again completed 4 blocks of 48 trials. Results Effects of Display Type on reaction time and accuracy i. Main effects There was a significant main effect of Display Type on reaction time, F(3,24)=4.761, p<.05, but not on accuracy.  26  ii. Paired comparisons The mean reaction times for digit displays were compared to the average mean reaction times for letter and sideways letter displays . No significant 1  difference was found. Similarly, there was not a significant difference between the mean accuracy for digit displays and the average mean accuracy for the remaining three display types (Figure 11) (Table 4). Differences between the effects of Display type on reaction time and accuracy in Experiments 1 and 3 Because Experiments 1 and 2 ruled out the possibility of the mean numeric value as the basis for the rapid extraction of numeric meaning, Experiment 3 contained only heterogeneous trials. Therefore, the results of Experiment 3 were only compared to results for heterogeneous trials in Experiment 1. The mean reaction times and accuracy for heterogeneous digit displays in Experiment 3 were significantly faster and more accurate than the mean reaction times and accuracy for heterogeneous digit displays in Experiment 1, t(8)=4.968, p<.05 (reaction time), and t(8)=3.953, p_<.05 (accuracy) (Figure 11) (Figure 4 versus Figure 1). Discussion The results of Experiment 3 revealed that comparisons between digit displays were made with similar speed and accuracy as comparisons between displays of letters or shapes, suggesting that numeric information was no longer rapidly utilized when participants were not under time  27  constraints that might make numeric meaning more practical to extract than information about the identity of individual items. Because no significant reaction time or accuracy differences were found between digits, letters, or sideways letters, the main effect of Display Type on reaction time can be attributed to the unique contribution of sideways digits. The faster reaction times for heterogeneous digit displays in Experiment 1 (in which viewing time was manipulated) versus reaction times for digits in Experiment 3 (in which viewing time was unlimited) suggested that when there were no limits on the amount of time spent viewing each display, participants no longer rapidly compared digit displays based on numeric meaning. Instead, as indicated by the significantly longer reaction times found across all display types in Experiment 3 versus Experiment 1 and the equal reaction times across display types in Experiment 3, digits were now processed in a similar manner as letters and shapes. The accuracy for digit comparisons was also significantly greater in Experiment 3 than in heterogeneous trials of Experiment 1 and equal across display types in Experiment 3, suggesting that participants may now have processed the digit stimuli to the level of identification in a similar manner as letters and shapes. Contrary to the results of Experiment 1 for brief stimulus durations, the results of Experiment 3 suggested that numeric information was no longer rapidly extracted when viewing time was unlimited. Rather, participants processed each stimulus to the level of identification, allowing for slower yet more accurate comparisons. A n interesting finding of Experiment 3 was that  28  sideways digit displays were processed more slowly than all other display types, but with comparable accuracy. This result was also seen in the form of a nonsignificant trend in Experiment 1. This result suggests that participants' responses were somehow inhibited when processing these displays. A possible post-hoc explanation of these results could be that participants had enough time to identify the items as sideways digits and thus attempted to process them as such. Further support for this proposal comes from direct observation. When viewing sideways displays, most participants in Experiment 3 tilted their heads to the side. When questioned, these participants reported that they were attempting to obtain a better view of the sideways displays. Participants were then told to maintain upright head position for the duration of the experiment. It is highly possible that participants recognized the sideways digits and sideways letters and compared them as such (instead of comparing them as shapes, as instructed). If so, then the process responsible for the rapid extraction of numeric information may have interacted with the process responsible for identifying the digits in a way that caused the significantly longer reaction times observed for sideways digits in Experiment 3 and influenced the same nonsignificant trend in Experiment 1, or the additional response time may have been the extra time it took for participants to tip their heads. General Discussion Overall, this study provided evidence that numeric meaning was rapidly extracted from digit displays whereas items in letter and shape displays were processed to the level of identification.  29  In Experiment 1, it was found that digits were processed faster and more accurately than familiar letters or simple shapes. Participants' reaction times and accuracy for sideways digits conditions were identical to their reaction times and accuracy for letters and sideways letters, but different from their reaction times and accuracy for digits, confirming that differences in spatial arrangement or symmetry were not the basis of the faster, more accurate comparisons of digit s t i m u l i . Comparing the effect of Rotation for digits and letters allowed for a second confirmation that numeric meaning was driving the rapid reaction times and higher accuracy for digit comparisons. Because letters, sideways letters, and sideways digits were compared with similar speed and accuracy, the results of Experiment 1 further suggested that numeric meaning not present in these display types was driving the rapid digit comparisons.  The digit displays  showed both a reaction time and accuracy advantage that could not be explained by familiarity or shape and was eliminated by rotation, and thus could be attributed to the additional aspect of numeric meaning. Therefore, the first conclusion of Experiment 1 was that numeric information could be processed faster and more accurately than information about familiarity or shape. The second implication of Experiment 1 was that the statistical mean was not likely to be the basis for the rapid extraction of numeric value. While the results of Experiment 1 showed an advantage for processing numeric meaning, they did not support the idea that such comparisons are accomplished by numeric statistical descriptors such as those found by Chong and Treisman (2003). The results of Experiment 1 not only showed a significant main effect of Comparison  30  Type on both reaction time and accuracy, but also revealed that comparisons between homogeneous digit displays of set size 6 were made faster and more accurately than between heterogeneous digit displays. If statistical descriptors were used to represent the mean value in digit displays, then the heterogeneous displays should have been rapidly averaged, yielding similar reaction times and accuracy as those found for homogeneous comparisons of equal set size. However, the heterogeneous disadvantage may be explained by repetition effects, which could have caused the homogeneous and single displays to become familiar to subjects over the course of the experiment. In heterogeneous displays, individual stimuli could be combined to produce many different displays, but in homogeneous and single displays, the stimuli were always the same, allowing for only two possible displays. While an attempt was made to make the homogeneous and single displays as novel as possible by varying set size and item position, heterogeneous displays may nevertheless have been more novel. Future research comparing several different displays of heterogeneous, homogeneous, and single stimuli is needed to determine whether the mean judgment is, in fact, not advantageous for displays of similar digits. Therefore, it cannot be concluded that digits are rapidly averaged in the same manner as geometric properties such as mean size. The difference between the processing of numeric information and the advantage shown for statistically represented geometric properties (Chong & Treisman, 2003) may be mechanical in nature. As previously mentioned, it has been widely accepted that early sensory neurons  31  function to remove redundancy in visual input (Barlow, 1961). Recent work suggests that simple receptors similar to receptors for color and orientation may subserve statistical descriptors (Olshausen & Field, 1996; Simoncelli & Olshausen, 2001). A biological predisposition for a summated representation of geometric properties such as average size would account for the differences in judgments of average size and average value. While average size could be a summated value from a small pool of basic size receptors, average value is a more cognitive process, requiring some further processing of meaning. The digit advantage found in the present experiments could thus not be explained by such simple mechanisms as those that may be responsible for statistical descriptors The final conclusion of Experiment 1 was that the process responsible for representing numeric information behaved in similar manner over time as the processes responsible for representing familiar letters or simple shapes. Although the results of Experiment 1 showed a counterintuitive trend for all displays to be compared faster at shorter stimulus durations, this trend was only significant for comparisons between heterogeneous displays of digits. Taken together with the result that accuracy was unaffected by stimulus duration in any comparison, it is possible that participants used whatever extra time they were given at longer stimulus durations in an attempt to verify their answer, although this did not improve performance.  32  The results of Experiment 2 showed no effect of task instructions on digit processing. When told to search for a larger occurrence of a target in digit displays, observers again responded faster and more accurately when comparing digit displays than other display types. As in the category effect found by Jonides and Gleitman (1972), if task instructions were the cause of faster comparisons between displays of digits, then equating the task instructions across conditions should cause the advantage to disappear. From the identical results of Experiments 1 and 2, it can be concluded that the numeric meaning of digit stimuli, not the task instructions to compare digits based on average numeric value, lead to the rapid extraction of numeric information. However, future research is needed to determine whether conceptual meaning can be specified by task instructions. For example, the conceptually ambiguous stimulus might be processed differently if it were to be specified as a letter "s" instead of a digit "5" in future experiments. Also, changing the quantitative comparison task to a more qualitative task may influence how such ambiguous stimuli are processed. In Experiment 3, it was determined that numeric information was not rapidly extracted when sufficient time was given to identify individual stimuli. In Experiment 3, participants were allowed to make comparisons without the time constraints of the brief presentations used in the previous experiments. Although participants were given unlimited time to compare displays, task instructions stressed accuracy and speed equally. The results of Experiment 3 revealed similar reaction times and accuracy for all stimulus types, with the exception of increased  33  reaction times for sideways digits. These results suggested that the process responsible for the rapid extraction of numeric information acts to provide a quick summary of the visual display, but is abandoned in favor of more accurate information when stimuli can be processed to the level of identification. Overall, it was demonstrated that meaningful information about familiar digits was processed faster than information about familiar letters or simple shapes, regardless of whether participants were instructed to compare digit displays based on average value or on the greater occurrence of a target shape. However, this study did not find evidence for statistical descriptors of numeric information: responses to heterogeneous digits were slower and less accurate than to homogeneous digits or to single digits. When sufficient time was given for individual items to be identified, numeric meaning was no longer rapidly extracted. Concluding Remarks Overall, the results of this study demonstrated that, when given very brief visual displays of digits, letters, and shapes, the visual system can derive numeric meaning of digits faster and more accurately than it can obtain information about the familiarity of letters or spatial similarity of simple shapes, suggesting that the system may be able to rapidly represent meaningful (numeric) information. As our ever-changing environments must be represented, the visual system may rely on such rapid processes to create a meaningful representation of the visual world. This study  34  demonstrated rapid processing of numeric stimuli, which cannot be accounted for by familiarity or spatial similarity, but which instead may be driven by numeric meaning. The visual system may use these rapid processes to form "quick and dirty" "just in time representations" of our dynamic surroundings that act as an outline and hold together the illusion of visual perception.  35  Footnotes 1. In Experiment 3, it was noted that mean reaction times were significantly greater for sideways digit comparisons than for the average of the mean reaction times of the other three display types, t(8)=-2.976, p_<.05. For this reason, digit displays were compared only to the average of letter and sideways letter displays.  36  References Ariely, D. (2001). Seeing sets: Representations by statistical properties. Psychological Science. 12. 157-162. Ariely, D., & Burbeck, C. A. (1995). Statistical encoding of multiple stimuli: A theory of distributed representation. Investigative Ophthalmology and Visual Science. 36 (Supplemental). 8472 (Abstract). Atkinson, R. C , Holmgren, J. E., & Juola, J. F. (1969). 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American Journal of Psychology. 78. 392-402. Torralba, A., & Oliva, A. (2003). Statistics of natural image categories. Network: Computation in Neural Systems. 14. 391-412. Watamaniuk, S. N . J., & Duchon, A. (1992). The human visual system averages speed information. Vision Research. 32. 931-941. Watamaniuk, S. N . J., Sekuler, R., & Williams, D. W. (1989). Direction perception in complex dynamic displays: The integration of direction information. Vision Research. 29.4759.  40  Table 1 Experiment 1: Descriptive Statistics of the Four Display Types for Reaction Time (ms) and Accuracy (in parenthesis').  Display Type  N  Min  Max  Mean  Std. Dev.  Digits  9  386.25  519.32  483.73  40.12  (.80)  (.91)  (.87)  (.03)  508.10  783.55  629.83  78.41  (.72)  (.89)  (.80)  (.05)  471.73  882.37  621.35  115.03  (.78)  (.88)  (.84)  (.02)  501.61  762.03  619.81  90.17  (.79)  (.88)  (.84)  (.03)  Sideways Digits  Letters  Sideways Letters  9  9  9  41  Table 2 Experiment 1: Descriptive Statistics of the Four Heterogeneous Display Types for Reaction Time (ms) and Accuracy ("in parenthesis).  Display Type  N  Min  Max  Mean  Std. Dev.  Digits  9  425.40  698.27  596.68  79.57  (.57)  (.74)  (.67)  (.05)  538.17  909.09  687.46  117.31  (.52)  (.70)  (.58)  (.06)  498.98  1065.43  741.89  157.40  (.53)  (.69)  (.61)  (.05)  544.32  967.93  696.73  137.12  (.54)  (.69)  (.63)  (.05)  Sideways Digits  Letters  Sideways Letters  9  9  9  42  Table 3 Experiment 2: Descriptive Statistics of the Four Display Types for Reaction Time (ms) and Accuracy (in parenthesis').  Display Type  N  Min  Max  Mean  Std. Dev.  Digits  12  393.24  584.40  507.82  54.72  (.85)  (.90)  (.87)  (.01)  496.76  889.27  652.02  106.59  (.65)  (.88)  (.83)  (.07)  437.06  779.70  611.63  109.48  (.75)  (.88)  (.83)  (.03)  447.16  805.34  615.23  91.66  (.73)  (.88)  (.81)  (.05)  Sideways Digits  Letters  Sideways Letters  12  12  12  43  Table 4 Experiment 3: Descriptive Statistics of the Four Heterogeneous Display Types for Reaction Time (ms) and Accuracy ("in parenthesis').  Display Type  N  Min  Max  Mean  Std. Dev.  Digits  9  719.54  3501.95  1921.69  833.30  (.60)  (1.00)  (.86)  (.13)  1228.20  4718.40  3427.97  1251.61  (.68)  (.99)  (.86)  (.09)  720.98  4071.05  2482.34  1125.06  (.59)  (.97)  (.84)  (.13)  912.65  4571.86  2366.44  1146.82  (.64)  (.96)  (.83)  (.12)  Sideways Digits  Letters  Sideways Letters  9  9  9  44  Figure Captions Figure 1. (Torralba & Oliva, 2003). Different categories of objects and environments (a) exhibit distinguishing image averages (b) and spectral signatures (c). Figure 2. . A n example of a trial used in Ariely (2001). Each trial consisted of a set of circles of different sizes in the first interval (a), and an image of a single circle (b) in the second interval. In the member identification condition, the task was to report whether the single circle (b) was a member of the first interval set (a). In the mean discrimination condition, the task was to report whether the single circle (b) was larger or smaller than the mean circle size of the first interval set (a). Figure 3. Individual stimuli for Experiments 1, 2, and 3. Items are meaningful familiar shapes (digits), familiar shapes (letters), or unfamiliar shapes (sideways digits and sideways letters). Figure 4. Examples of three display types used in Experiment 1: (a) Heterogeneous digits (on this trial, observers would indicate "left"), (b) homogeneous letters (observers would indicate "right"), and (c) single shapes (observers would indicate "left"). Figure 5. Effects of Display Type on reaction time and accuracy in Experiment 1 (n=9). Digit displays were processed fastest (a) and most accurately (b) over all stimulus durations. Figure 6. Effects of Display Type on reaction time and accuracy for heterogeneous displays in Experiment 1 (n=9). Heterogeneous digit displays were processed faster (a) and more accurately (b) than the other three types of heterogeneous displays.  45  Figure 7. Effects of Rotation on reaction time and accuracy for Experiment 1 (n=9). Rotating digits increased reaction time (a) and decreased accuracy (b), but rotating letters had no effect. Figure 8. Effect of Comparison Type on reaction time and accuracy for Experiment 1 (n=9). Homogeneous and single comparisons were made faster (a) and more accurately (b) than heterogeneous comparisons for all display types. Figure 9. Effects of Comparison Type on reaction time and accuracy for heterogeneous and homogeneous trials with equal set sizes in Experiment 1 (n=9). Homogeneous displays of 6 items were compared faster (c) and more accurately (d) than heterogeneous displays. Figure 10. Effect of Display Type on reaction time and accuracy in Experiment 2 (n=12). Digit displays in Experiment 2 were processed faster (a) and more accurately (b) than letters or shapes, similar to the reaction times (Figure 5a) and accuracy (Figure 5b) found for digits displays in Experiment 1. Figure 11. Differences between the unlimited processing of heterogeneous displays (Experiment 3) and the processing of briefly presented heterogeneous displays (Experiment 1) (both n's=9). Digit displays in Experiment 3 were not processed faster (a) or more accurately (b) compared to heterogeneous displays of letters or shapes when stimulus duration was unlimited. Also, briefly presented heterogeneous displays in Experiment 1 were processed faster (a) but with lower accuracy (b) than heterogeneous displays in Experiment 3.  46  Scene scale I-5 m  5-50 m  SO-5QOID  >500m  1-5 m  5-50m  5»5UOui  >SBO«  Figure 1. (Torralba & Oliva, 2003). Different categories of objects and environments (a) exhibit distinguishing image averages (b) and spectral signatures(c) as a function of the mean distance between observer and principal scene elements (scene scale). Each image average and spectral signature was calculated with 300-400 images.  47  Figure 2.. A n example of a trial used in Ariely (2001). Each trial consisted of a set of circles of different sizes in the first interval (a), and an image of a single circle (b) in the second interval. In the member identification condition, the task was to report whether the single circle (b) was a member of the first interval set (a). In the mean discrimination condition, the task was to report whether the single circle (b) was larger or smaller than the mean circle size of the first interval set (a).  48  Digits  Sideways Digits  Letters  Sideways Letters  2  ru i_n  p c|  •_ cr  CJ  Figure 3. Individual stimuli for Experiments 1, 2, and 3. Items are meaningful familiar shapes (digits), familiar shapes (letters), or unfamiliar shapes (sideways digits and sideways letters).  49  Figure 4. Examples of three display types used in Experiment 1: (a) Heterogeneous digits (on this trial, observers would indicate "left"), (b) homogeneous letters (observers would indicate "right"), and (c) single shapes (observers would indicate "left").  50  (a) Effect of Display Type - Experiment 1  800  0.7 ' 0  200  400  600  800  Stimulus Duration (ms)  Figure 5. Effects of Display Type on reaction time and accuracy in Experiment 1 (n=9). Digit displays were processed fastest (a) and most accurately (b) over all stimulus durations.  51  (a) Effect of Display Type for Heterogeneous Comparisons - Experiment 1 800  700 E  cc 600 CD CD  500  400 Digits  Sideways Digits  Letters  Sideways Letters  Display Type  (b) Effect of Display Type for Heterogeneous Comparisons - Experiment 1 0.8 0.75 CP 0.7 _ % 0.65  C CD D  -  <" 4  M  0.6 0.55 0.5  *  ^  1-/ 1  Digits  Sideways Digits  Letters  Sdieways Letters  Display Type  Figure 6. Effects of Display Type on reaction time and accuracy for heterogeneous displays in Experiment 1 (n=9). Heterogeneous digit displays were processed faster (a) and more accurately (b) than the other three types of heterogeneous displays.  52  (a) Effect of Rotation - E x p e r i m e n t 1 800  700  c  •  600  CU  Upright  m Sideways  ro 03 500  400 Digits  Letters Display T y p e  (b) Effect of Rotation - Experiment 1  0.9 0.88 0.86 g>0.84 g 0.82 o c 0.8  • Upright a Sideways  ro <u  2  0.78 0.76 0.74 0.72  Letters  Digits Display Type  Figure 7. Effects of Rotation on reaction time and accuracy for Experiment 1 (n=9). Rotating digits increased reaction time (a) and decreased accuracy (b), but rotating letters had no effect.  (a) Effect of C o m p a r i s o n T y p e - Experiment 1 800 i  Digits  Sideways Digits  Letters  Sideways Letters  Display T y p e  (b) Effect of Comparison Type - Experiment 1 1  i  Digits  Sideways Digits  Letters  Sideways Letters  Display Type  Figure 8. Effect of Comparison Type on reaction time and accuracy for Experiment 1 (n Homogeneous and single comparisons were made faster (a) and more accurately (b) than heterogeneous comparisons for all display types.  54  (a) Effect of C o m p a r i s o n T y p e (equal set sizes) - Experiment 1 800  700  a:  H • Heterogeneous (set size=6)  600  • H o m o g e n e o u s (set size=6)  500  400 Digits  Sideways Digits  Letters  Sideways Letters  Display T y p e  (b) Effect of Comparison Type - Experiment 1 1 I  Digits  Sideways Digits  Letters  Sideways Letters  Display Type  Figure 9. Effects of Comparison Type on reaction time and accuracy for heterogeneous and homogeneous trials with equal set sizes in Experiment 1 (n=9). Homogeneous displays of 6 items were compared faster (c) and more accurately (d) than heterogeneous displays.  55  (a)  Effect of Display Type - Experiment 2  800 |  700  -•—Digits •  oc 600  -•— Letters  c  ro cu  Sideways Digits  -A—Sideways Letters  500 400 200  400  600  800  Stimulus Duration (ms)  (b) Effect of Display Type - Experiment 2  1  g. 0.95 | 0.9 | 0.85 CD 0.8  -•—Digits - • — S i d e w a y s Digits -•— Letters -A—Sideways Letters  CD  ^  0.75 0.7  200  400  600  800  Stimulus Duration (ms)  Figure 10. Effect of Display Type on reaction time and accuracy in Experiment 2 (n=12). Digit displays in Experiment 2 were processed faster (a) and more accurately (b) than letters or shapes, similar to the reaction times (Figure 5a) and accuracy (Figure 5b) found for digits displays in Experiment 1 (n=9).  56  (a) Effect of Display T y p e - E x p e r i m e n t 3 vs. E x p e r i m e n t 1 4000 3SOO 3000 j§_ 2 S O O cE  2000  S  1 500  cr  HH |S|8  1000  li ft:  ffl fli  a Experiment 3 • Experiment 1  500 O  Digits  Sideways Digits Heterogeneous  Letters Display  Sideways Letters  Type  (b) Effect of Display T y p e - E x p e r i m e n t 3 vs. E x p e r i m e n t 1  1 0.95 0.9  Jf I S  Bp  • Experiment 3  0.75 0.7 0.65  a Experiment 1  f-n--  If!  0.6 0.55 0.5 Digits  Sideways Digits Heterogeneous  Letters Display  Sideways Letters  Type  Figure 11. Differences between the unlimited processing of heterogeneous displays (Experiment 3) and the processing of briefly presented heterogeneous displays (Experiment 1) (both n's=9). Digit displays in Experiment 3 were not processed faster (a) or more accurately (b) compared to heterogeneous displays of letters or shapes when stimulus duration was unlimited. Also, briefly presented heterogeneous displays in Experiment 1 were processed faster (a) but with lower accuracy (b) than heterogeneous displays in Experiment 3.  

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