Memory Representation of Alphabetic Position and ... - APA PsycNET

Journal of Experimental Psychology: Learning, Memory, and Cognition 1999, Vol. 25, No. 3, 680-701

Copyright 1999 by the American Psychological Association, Inc. 0278-7393/99/S3.00

Memory Representation of Alphabetic Position and Interval Information Jerwen Jou and James W. Aldridge

This document is copyrighted by the American Psychological Association or one of its allied publishers. This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

University of Texas—Pan American The authors conducted 3 sets of experiments. In the 1st set of experiments, participants made alphabetic position estimations. In the 2nd set, participants made interletter distance estimations. In the 3rd set, they made comparative judgments of the alphabetic order of a pair of letters. The results showed that participants had highly accurate ordinal level information about the alphabet in memory but that interval level information was systematically distorted. In addition, alphabetic serial information was found to be used in 2 distinct modes in memory, depending on whether the representation could be contained within the span of immediate memory.

The question of whether memory preserves interval scale information has been controversial for decades. Some studies seem to show clear evidence of the use of interval information (Griggs & Shea, 1977; Griggs, Townes, & Keen, 1979; Moyer & Bayer, 1976; Moyer & Landauer, 1967; Paivio, 1975; Potts, 1977). For example, when two stimuli were presented for a comparative magnitude judgment (e.g., "Which is larger?"), Moyer and his colleagues found an inverse relationship between interstimulus distance on an interval scale and reaction time (RT), with ordinal steps held constant. In other studies (Holyoak & Walker, 1976; Kerst & Howard, 1977), participants have been asked to directly estimate the interstimulus distance, with the finding that interval distance ratings correlated more highly with comparison RT than did ordinal scale measures. However, other studies of comparative judgment have found that ordinal steps, rather than interval distances, determined comparative RT (Banks, 1977; Moyer & Dumais, 1978; Potts, 1974). In fact, Banks reported that comparative judgment RT was actually a little longer in a full magnitude-range condition than in a partial range condition when the number of ordinal steps was held constant. Furthermore, Gravetter and Lockhead (1973) found

that the number of steps that people can use in making absolute judgments is not affected by the overall size of the scale, which indicates the use of ordinal but not interval information. Thus, the issue of interval preservation has typically been investigated by using a comparative judgment task in which the ordinal steps are held constant and only the interval distance is varied. However, this approach poses some problems. The comparative judgment task requires participants to determine which of two items is larger or smaller, without asking how much larger or smaller. This actually renders interval information a task-irrelevant attribute. Although memorial preservation of interval information was the primary point of concern, the use of the comparative procedure effectively created a situation in which any effect of interval information could be considered an irrelevant Stroop-like intrusion (Stroop, 1935). This is so because such a task is targeted at the constant rather than the varied aspect of the stimulus. An efficiently executed comparative judgment would, therefore, reflect only ordinal level information. Moreover, even if the comparative RTs reflect ordinal ranks of interval distances, they may not necessarily reflect the interval scale distance itself. For example, suppose RT1 > RT2 > RT3 and the stimulus Pair 1 split < Pair 2 split < Pair 3 split. In previous studies, such an ordinal correspondence between the RTs and split magnitudes was taken as evidence of preservation of interval level information in memory. In reality, this correspondence shows only that the ordinal ranking of the three interval distances is preserved, with no assurance that the specific magnitudes of the interval distances are preserved. We believe that the best way to determine the nature of memory representation of interval level information is to measure it directly with a magnitude-estimation method coupled with a comparative judgment task. Any alteration of the interval scale information in a memory representation will be revealed in the psychophysical measures, even if the ordinal ranks of the interval magnitudes are preserved.

Jerwen Jou and James W. Aldridge, Department of Psychology and Anthropology, University of Texas—Pan American. Portions of this study were presented in the 1995 Annual Meeting of the Psychonomic Society, Los Angeles. This study was supported by University of Texas—Pan American Faculty Research Grant 119140 and National Institutes of Health Minority Biomedical Research Support Grant 516335, both to Jerwen Jou. We thank one anonymous reviewer and Jane Zbrodofffor their valuable comments. We are especially grateful to William Petrusic for his many helpful suggestions and critiques. Thanks are also due to Ravi Vedantam for programming; James Nelson, Gabriel Gutierrez, and Belinda Espinoza for collecting the data of Experiments 1 and 2; Teresa Chapa and Danee Wilson for collecting the data of Experiment 3; and Gary Leka for conducting the multidimensional scaling analyses. Correspondence concerning this article should be addressed to Jerwen Jou, Department of Psychology and Anthropology, University of Texas—Pan American, Edinburg, Texas 78539-2999. Electronic mail may be sent [email protected].

The Alphabet as a Scale The scale that we chose for investigating the above question was the alphabet, for several reasons. First, alpha680


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betic memory is an important part of our permanent memory, and there is a need to understand its structure and processes. Memory for the alphabet has been extensively researched in cognitive psychology (Grenzebach & McDonald, 1992; Hamilton & Sanford, 1978; Jou, 1997; Klahr, Chase, & Lovelace, 1983; Lovelace, Powell, & Brooks, 1973; Lovelace & Snodgrass, 1971; Parkman, 1971; Scharroo, Leeuwenberg, Stalmeier, & Vos, 1994), which provides researchers with a rich information base. Second, the alphabet is a highly practiced linear order, and any alteration of the scale in memory should not be attributable to insufficient learning. Third, the length of the series exceeds the short-term-memory (STM) span of 7 ± 2 (Miller, 1956), which makes it possible to examine the processes involved in retrieving serial information that lays beyond the window of immediate consciousness (Miller, 1956; Slamecka, 1985). Fourth, unlike the scales used in previous studies that were typically subject-generated ratings, the alphabetic scale is composed of objectively delineated intervals, with each interval unit being defined as one alphabetic step. That an alphabetic interval is measured by ordinal steps makes interval information a relevant attribute in a comparative judgment because participants cannot make a comparative judgment without having the ordinal steps available in memory. Experiment 3 used this feature of the alphabet, in a letter comparison task, to obtain evidence converging with the magnitude estimation data from the first 2 sets of experiments. Aspects of Serial Order Memory The order of two or more items that are drawn from a linear series can be determined in different ways. One method for determining this order is by performing a serial search. Serial search proceeds linearly step-by-step along a memorized sequence to locate the position of an item in its relation to another item. This process is analogous to a chain association in which one item elicits the next (Jou, 1997; Slamecka, 1985; Tulving, 1985) and produces a positive correlation between the distance searched and RT (Jou, 1997; Parkman, 1971; Polich & Potts, 1977; Woocher, Glass, & Holyoak, 1978). Another method for determining the order of items is comparing the items with regard to their order-relevant features. The process of sampling the feature information from memory has been compared to a random walk between two boundaries until one boundary is reached, when the difference in order features exceeds a certain criterion (Birnbaum & Jou, 1990; Buckley & Gillman, 1974; Link, 1992; Moyer & Bayer, 1976; Pachella, 1974). At this point, an order decision is made. The serial position of a letter can almost always be correctly obtained by using external memory aids, such as fingers or pencil and paper. This approach to discovering the serial position of a letter is procedural in nature (Tulving, 1983) and was not the concern of our study. The main concern of our study was to determine how and whether people can have access to this information without resorting to such an explicit step-by-step counting. In other words, our question was the following: Is alphabetic serial information readily available in declarative memory (Anderson, 1983)?

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Position, Interval, and Comparative Judgments A single-letter serial position judgment is an absolute judgment task because the scale value of a presented item is to be determined singly, by itself (Gravetter & Lockhead, 1973; Miller, 1956; Nosofsky, 1983). On the other hand, an interval distance judgment is a type of relative judgment because the decision is contingent on the relation of the two items (Marks, 1972). If distortions in judgment are caused by cognitive processing (Holyoak & Mah, 1982), then the more processing that is involved, the more distortion will occur. In both tasks, approximately equal numbers of numerical values are to be mapped onto some alphabetic metric information in memory. However, in the serial position judgments, each numeric value is associated with only one letter, whereas in the interletter-distance judgments, any particular numeric value may be associated with multiple letter pairs. Therefore, it is possible that the alphabetic interval judgment task is cognitively more complex than the position judgment task and, therefore, more susceptible to systematic distortion. A distinction should be made between the operations that participants are asked to perform and the measurement levels that are revealed by those operations. Both tasks can reveal whether the ordinal level of the scale information is preserved in memory by showing whether the monotonic ordering of the serial positions and of the magnitudes of interletter distances is maintained or violated. However, only the interletterdistance judgment task can truly determine whether memory preserves the interval level information, for reasons to be discussed later. In the first set of experiments, we asked participants to estimate a letter's serial position (SP) in the alphabet. This task will reveal how alphabetic position is represented in memory. One important question, for example, is whether the serial position of a letter becomes available only after the serial positions of other letters are retrieved, or is available independent of other letters. Another question concerns the accuracy of the representation of alphabetic serial position information. For example, is the ordinal relationship between the letters preserved in memory monotonically at least? Are there any overall systematic distortions of the alphabetic serial positions in memory representation, or only local inexactness? In the second set of experiments, participants made interletter-distance magnitude judgments, and their judgment RT was recorded. We asked several questions in this set of experiments. First, how accurate is the memory representation of the interletter-distance information? For example, is the monotonic, ordinal relationship between alphabetic distances preserved in memory? Are there any systematic distortions of the distance information in memory, or only local inexactness? Second, is the interletter-distance information instantaneously retrievable from memory, in one single step, as frequently appears to be the case with highly overlearned information (Ericsson & Kintsch, 1995; LeFevre, Sadesky, & Bisanz, 1996; Logan, 1988)? We designed Experiment 3 to obtain an independent behavioral measure of the memory interval scale with a


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typical comparative judgment task. The validity of subjective numerical estimates in judgment studies has frequently been questioned (Huttenlocher, Hedges, & Bradburn, 1990; S. S. Stevens, 1962). The issue has been whether the numerical values assigned by the participants to their memory or sensory experience really measured the memory scale or sensation intensity, or only reflected attributes of the number mapping processes. In the context of the present study, the question becomes whether any distortion in the judgment data reflects distortion in the underlying memory scale, or simply a bias in numerical value mapping onto the underlying subjective scale (Huttenlocher et al., 1990; S. S. Stevens, 1962, 1971). Because the comparative judgment task does not involve explicit assignment of numerical values, it should be free of effects of a number-mapping process. Our intent was to determine whether the previous interval estimates measured the subjective scale that was presumably used in comparative judgments or simply reflected a bias in the number-mapping process. Memory-Quantification Processes Our study also had bearing on the question of whether memory quantification is similar to perceptual quantification in regards to a process known as subitizing (Jensen, Reese, & Reese, 1950; Kaufman, Lord, Reese, & Volkmann, 1949; Klahr, 1973; Logie & Baddeley, 1987; Mandler & Shebo, 1982). In perceptual numeration, subitizing consists of a rapid, effortless, and yet highly accurate immediate apprehension of the numerosity of a small number (typically under five) of items. This process is similar to a memory process first referred to by Ebbinghaus as the window of simultaneous consciousness (cited in Slamecka, 1985) or by contemporary cognitive psychologists as parallel processing (Townsend, 1990). One could argue that, just as in perceptual quantification, subitizing will occur in memory magnitude estimation, on the basis of the parallels between perceptual and memory processes found in numerous studies (Kosslyn, Ball, & Reiser, 1978; Moyer, 1973; Moyer & Bayer, 1976; Parkman, 1971; Polich & Potts, 1977; Shepard, 1978; Shepard & Metzler, 1981; Trabasso, Riley, & Wilson, 1975). However, this is an empirical question and will be addressed in the following experiments. In summary, the present findings will help in understanding how alphabetic information, both at the ordinal and the interval levels, is represented in memory. In addition, these experiments have implications for theories about memory processes in quantification and linear order information processing, as is explained in the General Discussion section. Experiments 1A and IB In Experiments 1A and IB, we tried to map out in as direct a manner as possible, with the least involvement of cognitive processing, a "mental map" of the alphabet as it may exist in memory. In this experiment, participants saw a single displayed letter and made a quick alphabetic positional estimate for the stimulus letter. This serial position judgment was equivalent to an absolute judgment task in which

participants are presented with a single stimulus and asked to make a magnitude rating (Gravetter & Lockhead, 1973; Miller, 1956; Nosofsky, 1983; S. S. Stevens, 1971). Several studies that used relative judgments have shown that mental representation of distances and locations may be systematically distorted (Bimbaum & Mellers, 1978; Holyoak & Mah, 1982; Radvansky, Carlson-Radvansky, & Irwin, 1995; A. Stevens & Coupe, 1978; Thorndyke, 1981). Such distortion might be incorporated into the permanent memory for the information, or it might result from transformation of a veridical memory by response-generation procedures used in these studies (Holyoak & Mah, 1982). In the latter case, the absolute judgment task may require less processing than relative judgments and, therefore, produce less distortion of the memory information. The first question in this set of experiments was whether the memory representation preserves the alphabetic ordinal information of the letters, at least at the monotonic level. In other words, is there any violation of the ordinal monotonic relationship among the 26 letters in the memory representation? In addition, four hypotheses were tested regarding the "mental alphabet." The first hypothesis was the implicit reference-point hypothesis. According to this hypothesis, the use of a reference point will induce expanded spacing of the items closer to the reference point and lumping together of items far from it into a relatively indistinctive group (Bimbaum & Mellers, 1978; Holyoak & Mah, 1982; Hutchinson & Lockhead, 1977). In a mental map that participants produced of the locations of some U.S. cities on an east-west dimension, the distances between the locations near the reference point (either the east coast or west coast) were typically expanded, whereas those further from it were compressed. It was as if locations near the reference point were more discriminable than more distant locations (Bimbaum & Mellers, 1978; Holyoak & Mah, 1982). In the alphabetic system, a reasonable assumption of an implicit reference point would be A. Occasionally, Z might be used as a reference point as well, when letters close to it are judged. Thus, a systematically distorted positional scale generated by the participants, with wider spacing early in the alphabet and progressively denser distribution of letters later in the alphabet (a negatively accelerated estimate function), would support the implicit reference-point hypothesis. As far as the RT is concerned, the implicit reference-point theory makes no particular predictions. The second hypothesis was the sequential representation hypothesis. This hypothesis states that the serial position information of a letter can become available in memory only in relation to other letters. In memory of temporal information, researchers have found that people keep track of an event by relying on its sequential relationship to other events (Huttenlocher et al., 1990). Intuition seems to suggest that we access the serial position of a letter in the same way, except perhaps for several beginning and ending letters whose serial positions can be accessed directly. Sequential access would be reflected in linearly increasing RT, as a function of the increasing serial position. If accessing the serial position of a letter can be done from either end of the

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alphabet, an inverted V-shaped RT function, possibly asymmetrical, would be indicative of a sequential representation. The third hypothesis is the independent position-coding hypothesis, which states that in memory, there is an individual positional code associated with each letter that can be retrieved independently of other letters. An absence of systematic distortion in the estimate data, accompanied by a flat RT function, would support this hypothesis. The fourth hypothesis is the dual-mode access hypothesis, which states that the representations of the beginning and ending letters are qualitatively different from those of the middle-section letters, and therefore the access mechanisms of these two groups of letters should also be different. This hypothesis seems to.agree with intuition. There are two conceptualizations possible about the dual-mode access hypothesis, however. We termed the first one the subitizing hypothesis and the second the STM-limit hypothesis. As mentioned earlier, subitizing is a rapid, effortless, and highly accurate immediate determination of the numerosity of a small number of elements. In contrast, counting is a slow and laborious serial enumeration process for determining the quantity of a collection of elements. This process produces a steep linear RT function with the increase of the number of the items and, with 5 to 10 items, a less accurate enumeration than subitizing. When the needed time is not allowed or available for counting, or when the array size is over 20, an estimation process will be used, which yields a high error rate and a flat RT function in perceptual enumeration (Logie & Baddeley, 1987; Mandler & Shebo, 1982; Trick & Pylyshyn, 1994). Subitizing and estimation are similar in that they both amount to parallel processing (Trick & Pylyshyn, 1994). They are also different in that the former process produces highly accurate quantification, whereas the latter generates low-accuracy estimation. In the context of the alphabetic serial position judgments, the memory version of the subitizing hypothesis would say that the serial positions of the first several letters can be determined instantly and very accurately. However, serial positions of larger magnitudes could be obtained only by counting or estimating, depending on time constraints. Evidence of this change from subitizing to counting would be the appearance of a low, flat portion of the RT function for the first several letters and an abrupt rise in the slope past this point. This bending in the RT functions of perceptual quantification has been considered the earmark of subitizing (Klahr, 1973; Mandler & Shebo, 1982). The STM-limit hypothesis, on the other hand, states that participants need to conduct a serial search (Sternberg, 1969a, 1969b, 1975) in their short-term or working memory (Baddeley & Hitch, 1974) on the information being quantified. One possible mechanism would be to represent the alphabet in STM as a continuum starting from A and extending as far as the STM capacity allows. The serial search would be similar to a serial counting from A up. This count would stop when the serial representation reaches the STM limit. This process is basically the same as a stimulusresponse chain activation, with each letter serving as a stimulus to elicit the following letter, except that a counter must be maintained and incremented simultaneously. In this

process, each cycle of the stimulus-response activation presumably takes a constant time. Such a stimulus-responsechain association process may use temporal cues to determine the serial order relations of the items and is procedural in nature (Jou, 1997; Tulving, 1985). This hypothesis predicts two results. First, because the search is serial, the slope of the RT function will be linearly increasing for quantities within the search limit of STM. This can be assumed to be 7 ± 2 (Baddeley, 1994; Mandler, 1975; Miller, 1956; Shiffrin & Nosofsky, 1994). Second, once the quantity exceeds this limit, working memory can no longer conduct a serial search and will switch to an estimation process. The switch from serial search to estimation will be reflected in an attenuated correlation between RT and the number of items being quantified. Therefore, this change will appear as a discontinuity in the slope of the RT curve, just as in the case of subitizing. However, this bend will be the mirror image of the one predicted by the subitizing hypothesis. This hypothesis does not make specific predictions about systematic distortion. It does predict, as does the subitizing hypothesis, that the variability of the estimated serial positions will be smaller for those that are within the processing capacity of the STM but larger for those that result from an estimation. The larger variability would be an indication of the decrease in precision of the serial position estimation. Specifically, quantities within 7 ± 2 will be serially and more precisely processed, resulting in smaller variability in the position estimation compared with larger quantities. This means that the beginning and ending (assuming a backward search) sections of the alphabet will produce smaller variability than the middle sections. Finally, a related issue will be addressed regarding whether the serial information is represented in memory in a spatial-analogical form or in a discrete symbolic form. This issue has captured the interest of researchers for decades (Dehaene, Bossini, & Giraux, 1993; Dehaene, Dupoux, & Mehler, 1990; Huttenlocher, 1968; Moyer, 1973; Trabasso et al., 1975). We suggest that estimating the serial position of a letter by identifying and pressing a key on the keyboard to indicate its position is a mapping process between the memorial representation and an external model of that representation. The more isomorphic the external model is to the internal representation, the easier the mapping will be. We used two forms of key labelings for responding, one with numbers and the other with blank labels. We propose that participants will use numeric values as serial position indexes in the number-label (numeric) condition, but will use spatial positions in the blank condition. A faster response in the blank condition would then suggest a spatial representation in memory, whereas a faster response in the numeric condition would suggest a digital representation.

Method Participants Thirty-nine introductory psychology students at the University of Texas—Pan American (UTPA) participated in each of the number-input, numeric, and blank conditions of Experiment lAfor

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extra course credit. A separate group of 43 students participated in Experiment IB.


Materials and Design Experiment 1A. The top two rows of keys on a computer keyboard (13 keys on the first row from the "tilde [ ~ ] " sign to the "plus" sign, and another 13 keys from the "tab" key to the "right brace") were covered either with stickers labeled 1 through 26 (numeric condition), or with 26 blank stickers (blank condition) with the first and last sticker marked with a red dot. The numeric response keys were used in two conditions, the number-input and the numeric conditions. In the number-input condition, a number was displayed on the screen and participants pressed the response key labeled with the. same number. This number responding was used to estimate the response-key locating time. In the numeric condition, a letter was displayed and participants pressed a key labeled with the number that they judged represented the alphabetic serial position of the letter. In the blank condition, a letter was displayed and participants pressed a response key whose position they judged to represent the alphabetic serial position of the letter. The condition variable was a between-subjects variable. Experiment IB. The materials and design were the same as in Experiment 1A, with the following exceptions. Participants performed two rounds of number-input before the alphabetic serial position judgment task and two additional rounds after it. The 26 letters were tested over a total of six rounds. The mean RT of all four rounds of number-input was used to estimate the number-input time.

Procedure Experiment 1A. In all conditions, the instruction "Ready? Press (Enter) to start" was displayed at the beginning of the experiment. When the "Enter" key was pressed, the ready prompt disappeared, and the first stimulus item appeared. When a response key was pressed, the stimulus item disappeared and the screen turned blank for 1 s, followed by the appearance of the next item. In the number-input condition, participants were asked to press the key labeled with the number that corresponded to the number displayed on the screen. If they pressed the wrong key, an error message was displayed and the trial would be repeated later in the sequence. The set of 26 numbers was displayed for six rounds, with the order of presentation within each round randomized. In the numeric and blank conditions, 26 letters were displayed, 1 at a time, at the center of the screen in a random order for six rounds. The stimulus letter was of Courier type, point size 12, in white (a little more than medium bright) against a black background. The average screen-to-eyes distance was 41 cm. In the numeric condition, participants pressed a key labeled with a number that, according to their judgment, was the best estimate of the serial position of the letter in the alphabet. In the blank condition, the instruction was basically the same as in the numeric condition except that participants were told that they should press a blank response key of which the sequential position on the key rows, according to their judgment, best represented the alphabetic serial position of the stimulus letter. They were also told that the red dot at the beginning of the first row represented the first letter of the alphabet and the last red dot at the end of the second row represented the last letter. Participants were instructed to make their best estimates and that there were no right or wrong answers. Participants seemed to have understood the meaning of the instruction in the context of the experimental task without difficulty. It was emphasized that an instantaneous response was

required and that they should not count the letters one by one to obtain the answer. Participants were not instructed regarding the use of any letter as a reference point. A minor deception was used whereby the participants were told that if they pressed the keys at random or pressed the same keys repeatedly, the computer would detect these patterns and they would be asked to redo the experiment. Experiment IB. The procedure was the same as in Experiment 1A, with the following exceptions. Participants performed two rounds of number-input before and after the alphabetic serial position estimation trials. A numeric keypad on the right-hand side of the keyboard was used for response entry, with timing terminated when the first key was pressed. The number that was typed in appeared under the stimulus number or letter. A new trial was initiated by pressing the "Enter" key, which brought up a 1-s duration of a blank screen followed by the next item display.

Results and Discussion Experiment 1A Three dependent measures were examined: serial position estimates, variance of the estimates, and RT. When a hypothesis is contradicted by any of the three measures, it will be dropped from further consideration. Estimate data. The serial position of each of the labeled keys was converted to a number from 1 to 26, and the response mean of the serial position value for each stimulus letter was computed for each condition. Because the numberinput condition required 100% accuracy, the response measures for this condition were identical with the stimulus values. The mean estimated alphabetic serial positions for the numeric and blank conditions are plotted in Figure 1 against the number-input measures (the perfect serial position estimation function). The slope of the function of the estimated serial positions for the numeric condition was .996, which was not significantly different from 1 (f < 1), nor was that of the blank

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3i 5 1 0 1i 13 15 17 19 21 23 25 Alphabetic SP — Num-inp •— Numeric -*- Blank

Figure 1. Mean estimated alphabetic serial positions as a function of the alphabetic serial position of letters and response-key labels of Experiment 1A. SP = Serial Position; Num-inp = number input.

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condition, .974, significantly different from 1 (t < 1). There was also no significant difference between the two slopes (t < 1). The lack of a significant deviation of the serial position estimation functions from 1 can be taken to mean that there was no systematic distortion (expansion or compression) in the memory representation of the alphabet. On the basis of this evidence, the implicit reference-point hypothesis can be rejected. As can be seen, there was not a single violation in the mean estimated serial positions of the monotonic ordinal relation among the letters. Accuracy was measured by the absolute error (i.e., deviation of the estimated values from the perfect function). Under- and overestimation were not differentiated. These absolute error scores were compared between three response modes, including the numeric and blank conditions of Experiment 1A and the numeric keypad condition of Experiment IB, which was reported following Experiment 1 A. There was no significant difference in error between the response modalities. The mean absolute errors were as follows: the numeric condition, 1.02; the blank condition, 1.27; and the numeric keypad condition, 1.25 (F < 1). Thus, the use of different response-key labels and different response-key layouts did not seem to make a difference in the accuracy of the estimates. This result indicated that extra numerical information that was provided in the response keys did not improve the accuracy of estimation. Thus, we suggest that the letters were not coded in memory with numerical values but that numerical values can be retrieved or activated when needed. The estimate data alone were not inconsistent with the independent positioncoding hypothesis, which says that there exists an independently accessible serial position code for each letter. However, this conclusion may be premature without examining the RT data. The estimate data did show that participants have veridical knowledge of the serial positions of letters. Estimation variance data. The second response measure to be examined was the variance of the estimates, which reflects positional uncertainty of the estimates (Nairne, 1991, 1992). The mean standard deviations as a function of the serial position and the condition are shown in Figure 2. Visual inspection of the curves indicated that the variance of the middle portion of the serial position estimates was larger than that of the two terminal sections, consistent with the dual-mode access hypothesis. A mixed-factor analysis of variance (ANOVA), with condition as a between-subjects variable and serial position as a within-subjects variable, was performed on the standard deviations to determine if one condition produced more precise estimates. The main effect of condition was not significant, F(l, 75) < 1.00, with the mean standard deviation of the estimated serial position being 1.08 for the numeric condition and 1.11 for the blank condition. The main effect of serial position was significant, F(25, 1875) = 26.10, p < .001, MSE = 1.01. The Condition X Serial Position interaction was not significant (F < 1.00). Thus, the results from the variance analysis were consistent with those of the position estimation in that both indicated that numerical information provided in response keys did not add precision to the estimation. A trend analysis was conducted for the standard devia-

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13 Alphabetic SP | — Numeric •— Blank

Figure 2. Mean standard deviations of the estimated serial positions (SPs) as a function of the alphabetic serial position of letters and response-key labels of Experiment 1 A.

tions of the estimated serial positions over the 26 letters for the numeric and the blank conditions combined. The analysis showed that the linear trend was significant, F(l, 1976) = 40.53, p < .001, MSE = 1.31, as was the quadratic trend, F(l, 1976) = 407.18, p < .001, MSE = 1.31. Thus, the variance pattern supported the dual-mode access hypothesis in that the serial positions of the terminal (i.e., beginning and ending) letters were accessed with less uncertainty than the middle letters, suggesting different access mechanisms for these two classes of letters. Nevertheless, one could argue that the variability pattern of the serial position estimation is not inconsistent with the independent position-coding hypothesis, assuming that the precision of an independent estimation is lower in the middle than at or near the ends of the alphabet. However, it is still premature to draw this conclusion before examining the RT data pattern. Thus, the conclusion from the position estimate data and their variance was that, overall, people have very accurate immediate intuition for the location of a letter in the alphabet, with no systematic distortion, although the acuity of this intuition is lower in the middle portions of the alphabet. However, the variance data themselves could not further differentiate the two versions of the dual-mode accounts. The RT data will be diagnostic on this issue as well as on the issue of sequential representation and an independent position code. RT data. The mean RT as a function of serial position and condition are presented in Figure 3. The functions showed two clear features. One was an overall bowedness, and the other was a central dip in both the numeric and blank condition curves. Each of these features are addressed in detail later. The purpose in measuring the time of the number-input condition is to determine if the serial position estimation time could simply be accounted for by responsekey pressing time. To answer this question, two mixed-


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9 11 13 15 17 16 2 Alphabetic SP — Num-inp -- Numeric — Blank Figure 3. Mean reaction time (RT) of alphabetic serial position (SP) estimation as a function of the alphabetic serial position of letters, response-key labels, and experiment condition of Experiment 1 A. Num-inp = number input.

factor ANOVAs were performed, each comparing a keylabel condition with the number-input condition. A significant interaction of condition with the serial position would indicate that the slope of the RT function of the serial position judgment is different from that of the number-input function and therefore cannot be accounted for by the latter. The mixed-factor ANOVA, with condition as the betweensubjects variable and serial position as the within-subjects variable, compared the numeric with the number-input condition. The results showed that the condition effect was significant, F(l, 76) = 43.55, p < .001, MSE = 3,014,996, as was the serial position effect, F{25, 1900) = 49.65, p < .001, MSE = 98,477. The critical interaction was significant, F(25, 1900) = 11.83,/? < .001, MSE = 98,477. The same ANOVA comparing the blank condition with the numberinput condition showed that all the above three effects were again significant: condition, F(l, 76) = 19.89, p < .001, MSE = 2,442,155; serial position, F(25,1900) = 49.54,/? < .001, MSE = 74,988; and Condition X Serial Position interaction, F(25, 1900) = 8.87, p < .001, MSE = 74,988. Thus, each of the two RT judgment functions was different from the number-input function and, so, should have measured more than simply the time for locating the response key and entering the response. However, it is possible that the significant Condition X Serial Position interaction occurred because of the two dips of Serial Positions 13 and 14. To test this possibility, the ANOVAs were repeated, with the data of Serial Position 13 and 14 removed. The same results were obtained. For the numeric versus number-input condition, condition, F(l, 76) = 46.23, p < .001, MSE = 2,834,344; serial position, F(23, 1748) = 56.74, p < .001, MSE = 92,032; and Condition X Serial Position interaction, F(23, 1748) = 12.57, p < .001, MSE = 92,032. For the Blank versus the number-input condition, condition, F(l, 76 ) =21.69, p
.05, SE = 4.71, and 4 ms (without Serial Positions 13 and 14), t < 1, neither of which was significant. The slope of the ending section was -202 ms, which was significant, f(154) = -7.12,/? < .001, SE = 28.20. Thus, the segmental regression tests strongly confirmed the dual-access-mode hypothesis. As noted, participants seemed to use a serial algorithm for estimating the positions of the extreme letters but a parallel or direct estimate process for the letters in the middle portions of the alphabet. The pattern of the serial positionestimate variance as a function of the alphabetic serial position was consistent with this hypothesis in that the estimate precision declined (i.e., the variance increased)

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when the serial access process was changed into a direct access mechanism. It is interesting, however, that the accuracy of the estimation (as measured by the mean estimated serial position) was unaffected by the change of the access mode. A question remains about the process underlying the linearly decreasing portion of the RT function toward the end of the alphabet. One simple possibility is that participants conducted either a backward search from the end of the alphabet to the letter or a forward search from the letter to the end of the alphabet. Subtracting the "distance" obtained by either method from 26 would then yield the desired serial position. This would be an example of the use of complimentary-sets information, a strategy found to be used in a number of contexts by both humans and animals (Cook, Brown, & Riley, 1985; Jou et al., 1996). A second question concerns the nature of the central dips at Positions 13 and 14 (see Figure 3). Were the dips caused by locational distinctiveness of Response Keys 13 and 14 (Key 13 was located at the end of the first row and Key 14 at the beginning of the second row) or by a special memory status of the letters M and N? The answer seemed to be the latter, because the number-input condition did not show this position advantage for Serial Positions 13 and 14. In addition, the variances of these two points (shown in Figure 2) were relatively lower, which agrees with the special memory-status hypothesis. Another issue related to the central dips is whether the whole curve should be viewed as the combination of two separate linear order systems or a single linear order with a local depression. We argue for the latter viewpoint. If M (Serial Position 13) is considered the endpoint of a separate series, then this point should be as accessible as either of the two terminal points of the alphabet. Inspection of Figure 3 indicates that this is not the case. To confirm this observation, an ANOVA was conducted on the RTs of four serial positions—1, 13, 14, and 26—for the numeric and blank conditions. Neither condition nor the Condition X Serial Position interaction effect was significant. However, the serial position effect (Serial Position 1 = 1,000 ms, Serial Position 13 = 1,677 ms, Serial Position 14 = 1,697 ms, and Serial Position 26 = 1,147 ms) was highly significant, F(3, 228) = 98.52, p < .001, MSE = 102,197. A Newman-Keuls post hoc comparison showed that the mean RTs of Serial Positions 13 and 14 were significantly larger than those of Serial Positions 1 and 26, with the mean RT of Serial Position 26 still significantly larger than that of Serial Position 1. The difference between Serial Positions 13 and 14 was not significant. Furthermore, the drops in RT from the plateau to M, as well as the rise from N back to the plateau, were abrupt. The changes lacked the graded slopes of a serial position RT curve from a linear order system. For example, if M were the endpoint of an initial series, not only should RT be very low for M, but RT should also drop gradually as M is approached. Therefore, it seems more parsimonious to treat the central dips as a minor aberration in a single, linear order system than the boundaries of two separate subsystems of linear orderings.


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The RT functions also failed to suggest a hierarchical memory structure for the alphabet. Klahr et al. (1983) proposed that the letters are stored in memory in a hierarchical structure composed of chunks, with each chunk having an access entrance point and each letter within a chunk retrieved through a serial search process. The RT functions we observed were not consistent with such a hierarchical model of alphabet retrieval. If the serial position of a letter is accessed by first accessing the subgroup entrance point and then linearly searching through the chunk to the letter, then the curve should show a stepwise ripple pattern, with each wave having a shallower rise on the left-hand side but a steep drop on the right-hand side. Our RT curves did not show such a wavy pattern. Other differences between our results and those of Klahr et al. (1983) may be seen by comparing our Figure 3 and 4 with their Figures 3 and 4. Several differences are evident. First, our serial position-estimation RT curves showed a high plateau in the middle region, which Klahr et al.'s results did not. Second, our serial position RT curves showed two steep side slopes on both ends of the plateau, which Klahr et al.'s did not. Third, the curves of Klahr et al. showed clear, regular spikes, which ours did not. Fourth, the dips in Klahr et al.'s curves all touched a minimum value for the curve, which neither the central dips nor other dips on the plateau of our curves did. The differences between the RT patterns do not, however, necessarily imply that the findings of Klahr et al. (1983) were wrong. We think that a different type of alphabetic knowledge or memory was measured in our study than in their study, and, therefore, the different results do not necessarily constitute a contradicton. In Klahr et al.'s study, participants were presented a letter and asked to name either the preceding or the following letter. We suggest that this task measured chain stimulus-response association memory

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15 17 Alphabetic SP — Num-inp

— SP Estimate |

Figure 4. Mean reaction time (RT) of alphabetic serial position (SP) estimation as a function of the alphabetic serial position of letters and experiment condition of Experiment IB. Num-inp = number input.

of the alphabet that is procedural in nature (Jou, 1997; Tulving, 1985). The serial position estimation task in this experiment, on the other hand, measured the declarative knowledge (Anderson, 1983) of the alphabetic serial position code. The former type of memory serves a different function than the latter, and the ability to perform the former does not always imply the ability to perform the latter. For instance, being able to name the letter P when given O does not necessarily mean that one can also tell the correct serial position of the letter P or O. The Condition X Serial Position interaction demonstrated that the judgment function and the number-input function have different slopes. Still, one concern about the dual-mode access conclusion is whether the linear layout of the response keys had at least contributed to the slope of the serial position judgment functions. It was possible that an ends-inward search for a target key might have in part contributed to the linear rise and fall sections of judgment functions. A separate trend test for the number-input function showed a significant linear, F(l, 950) = 283.56, p < .001, MSE =36,822, as well as a quadratic, F(l, 950) = 533.23, p < .001, MSE = 36,822, trend. To test this ends-inward key-row search hypothesis, we conducted Experiment IB by using the square layout of the numeric keypad on the right-hand side of the keyboard as the response keys. Any change in the shape of the judgment function that was due to a change in the response-key layout should indicate to what extent the judgment RT curves were a function of the response-key layouts.

Experiment IB The same trend analyses and ANOVAs as for Experiment 1A were conducted except that both the condition and serial position variables in the ANOVAs were within-subjects variables. Results were the same as for Experiment 1, with two exceptions. First, the number-input RT function was flat, with no indication of a linear or quadratic trend. The function was completely consistent with that of Logie and Baddeley (1987), who also used a numeric keypad. Second, the three regions in the estimate RT function became even more distinct in this experiment, with best fitting lines produced by joining points at / and X (SSdev = 571,164, second best SSdev = 571,246 for H and X). Clearly, no part of the estimate RT function of Experiment 1A derived from either the linear arrangement of the response keys or from an ends-inward search strategy applied to the arrangement. The mean RTs of the serial position judgment and the numberinput are shown in Figure 4.

Summary Several findings were robust and consistent across Experiments 1A and IB. First, neither of the slopes of the functions of estimated alphabetic position in Experiments 1A and IB was different from 1. This result indicated that people have a highly accurate intuitive sense of the location of a letter in the alphabet, with no overall systematic distortion of the memory scale, although the acuity of the knowledge of the

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location of a letter was not as high in the middle portion of the alphabet as in the beginning and end of it. Second, the steep linear slopes of the beginning and ending sections of the RT functions suggested a serial search mechanism, whereas the middle plateau section was consistent with the concept of direct access, or estimation. This finding was counterintuitive because introspection seems to suggest the opposite. As evident in the data, the sizes of the serial search sections were very close to the STM span of 7 ± 2. Therefore, the entire picture best fits the STM-limit account of the dual-mode access hypothesis. Third, the RT data from Experiment 1A suggested that the memory representation of the alphabetic scale is likely in a spatial or analog form rather than in a digital form. Fourth, it should be noted that the memory-quantification process, unlike its perceptual counterpart, gave no indication of subitizing. Finally, Klahr et al.'s (1983) task of naming the preceding and following letters measured the alphabetic stimulus-response chain association, whereas our serial position-estimation task measured the declarative knowledge of serial positions of letters.

Experiment 2A Experiment 1A and IB showed that people have highly accurate memory representations of alphabetic, serial position information. The alphabetic ordinal relationship is preserved, with no systematic distortion of the metric scale. Experiments 2A further examined the memory representation of alphabetic-distance information. This second set of experiments consisted of interletter-distance judgment tasks. The task was equivalent to a psychophysical judgment of alphabetic distance. A question of interest is whether this judgment is subject to the distortions and biases typical of psychophysical judgments (Radvansky et al., 1995; S. S. Stevens, 1962, 1971; S. S. Stevens & Greenbaum, 1966), even though the alphabet is highly overlearned. Again, the two central issues are as follows: first, whether the monotonicity of the ordinal relationship of the distances is preserved and, second, whether there are systematic distortions in the memory representation of the alphabetic interval level information. If more cognitive processing leads to a higher probability of systematic errors (Banks, Fujii, & KayraStuart, 1976; Holyoak & Man, 1982; Radvansky et al., 1995) and if it is assumed that the interval distance judgment is more complex than the serial position judgment, then systematic distortion is more likely to occur in judging alphabetic distances than serial positions. Estimate data provide answers to the these questions. The RT data can be used to test several hypotheses. The direct retrieval hypothesis says that the alphabetic interval information can be retrieved in one step without engaging in a serial computing operation. This hypothesis is based on the findings that highly overlearned information, including numeric or quantitative information, is retrievable from memory in a single step (Ericsson & Kintsch, 1995; LeFevre et al., 1996; Logan, 1988; Logan & Klapp, 1991;). A flat RT-ID function would support this hypothesis. The algorithmic computing hypothesis, on the other hand, says that the

distance information is not directly available in memory and has to be computed in working memory by some algorithm. This would result in an approximately linear RT increase as a function of interletter distance. The dual-mode memory access hypothesis states that the values of small distances are determined in a differenct way than those of large ones. The subitizing versus STM-limit conceptualizations of this hypothesis can be tested one more time with distance judgments.

Method Participants Thirty-eight introductory psychology students at UTPA participated in the experiment for extra course credit. Two participants seemed to be pressing the keys at random, and their data were excluded from analysis.

Materials and Design Only the middle 20 letters of the alphabet (D through WO were used to construct the stimulus letter pairs. The first 3 and last 3 letters of the alphabet were not included because these 6 letters may have a special memory status. Without these 6 letters, the distancejudgment results can be interpreted with fewer complications. We constructed 190 distinct pairs of letters from these 20 letters by using the upper half of the 20 X 20 matrix that was generated by pairing each of the 20 letters with each of the others. First, the pairs were ordered alphabetically. Then, the letter pairs in alphabetical order were numbered from 1 to 190. The 2 letters in the odd-numbered pairs remained in their original order, but the order of the even-numbered pairs was reversed. The letter orders that were generated this way were coded as Order 1. Order 2 was the reverse of Order 1. These two orders were counterbalanced across the participants. Twenty keys of the bottom two rows of the keyboard (10 on each row: A to ";" on the upper row and Z to "/" on the lower row) were labeled with 1 through 20, and the middle 5 keys of the top alphabetic row of keys (R to 7) on the keyboard were labeled with numbers from 21 through 25? With the middle 20 letters of the alphabet used, the maximum interletter distance possible was 19. The response keys labeled with the numbers 20 to 25 were set up as distractors and provided responses if participants had a tendency to overestimate certain distances.

Procedure The procedures were basically the same as those of the first set of experiments except that the response numbers ranged from 1 to 25. The 25 numbers were presented for two rounds. The first round was viewed as practice. The second round's RTs were used as an estimate of the RT for pressing number keys. After the numberinput phase, the alphabetic-distance-judgment task began. Letter pairs were presented one at a time on a computer screen. The two letters were separated by two spaces in the display. Participants were told to make the quickest and best estimate of the interletter 2 The reason why the keys for the largest 5 numbers were placed on top of the two labeled rows was that adding these 5 distractor response keys was an afterthought that occurred to us subsequent to having set up the keyboard. Placing them in the middle of the top row avoided a complete rearrangement of the response keys.

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distance rather than counting the letters one by one to obtain the answers. They were given three examples in the instructions on how to make an estimate (e.g., "the alphabetic distance between K and P was 5"). Only one key needed to be pressed for the input of both a one- and a two-digit number. Again, the same minor deception was used as in previous experiments to discourage participants from pressing the keys randomly or a same key repeatedly. There was a short break in the middle of the distancejudgment task. The whole experiment took about an hour to complete.


Results and Discussion Estimated interletter distance and RT served as the dependent measures for this set of experiments. If a hypothesis was contradicted by any of the two dependent measures, it was dropped from further consideration.

f 9 '11 13 15 Interletter Distance —Wm-inp-^Dist Est|

Estimate Data The mean estimated distances are plotted in Figure 5 against the objective distances and the hypothetically perfect performance function. As can be seen, the estimated distances showed noticeable regression toward the mean. At short distances, there was a tendency toward overestimation, whereas at large distances, the opposite trend occurred. The regression of the estimated distance on the objective distance yielded a slope of .77, which was significant, r(682) = 64.87, p < .001, SE = .012. This slope was significantly different from 1, f(34) = -4.48, p < .01, SE = 1.70. Therefore, the graphic indication of the regression toward the mean was corroborated. The regression effect was consistent with reports from other domains of psychophysical judgment (Radvansky et al., 1995; S. S. Stevens, 1962, 1971; S. S. Stevens & Greenbaum, 1966). However, as shown in Figure 5, the monotonic, ordinal magnitude relationship among the distances was preserved in memory. This is a much more striking finding than that for the serial

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Interletter Distance --- Num-inp -o- Estimate | Figure 5. Mean estimated interletter distances as a function of the actual interletter distances of Experiment 2A. Num-inp = number input

Figure 6. Mean reaction time (RT) of interletter-distance estimation as a function of the actual interletter distances, and experiment condition of Experiment 2A. Num-inp = number input; Dist. Est. = distance estimation.

position memory because each distance can be associated with intervals between many different letters.

RTData The mean interletter-distance-judgment RTs along with the number-input RT as a function of the interletter distance were plotted in Figure 6. An ANOVA comparing the distance estimation and number-input data showed that the condition effect was significant, F(l, 35) = 228.30, p < .001, MSE = 32,927,414, as was the effect of interletter distance, F(18, 666) = 19.03, p < .001, MSE = 1,203,960. The Condition X Interletter Distance interaction was significant, F(18, 666) = 12.41, p < .001, MSE = 1,203,960. Thus, the interletter-distance-judgment function differed in slope from the number-input function. The early portion of the interletterdistance-judgment function showed a steep linear increase as a function of the increasing interletter distance being judged, which contradicted the direct retrieval hypothesis. The curve then leveled off, suggesting a change in the distance estimation process. A least squares analysis that . was similar to those performed for previous experiments was conducted, under the assumption that the function consisted of two linear segments. The best fitting lines were obtained with a joining point at Distance 4 (SSdev = 102,080; second best SSdev = 211,019 for Distance 3). The observed general increase of RT with the increased judged distance was consistent with the findings from perceptual judgments of line lengths in which the time of estimating line length was positively correlated with the line length (Hartley, 1977). Two aspects of the data need further discussion. First, the initial linear section of the curve extended over only four items instead of seven, which does not quite agree with the STM-limit view. However, this does not necessarily contra-

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diet the STM-limit account because researchers followingMiller (1956) have found the STM span to be more variable than 7 ± 2 (Baddeley, 1994; Broadbent 1971; Mandler, 1975). Baddeley proposed a span of 3 to 15 and Broadbent argued for a span of 3, whereas Mandler (1975) showed the STM span for retrieving-category instances from long-term memory to be under 5, with an average of 3.65. The complexity of the judgment task might have lowered the processing capacity of STM. Second, the section of the curve after the bend was not flat enough to indicate a direct retrieval or access. The algorithmic computing hypothesis could therefore not be clearly rejected for this section. However, the fairly sizable slope of the curve after Value 4 might have derived from a mixture of instances of direct estimation and letter-by-letter mental counting. This suggestion appears plausible given that the overall RT was quite high. Experiment 2B tested this construing of the slope of the latter portion of the curve. Segmental regressions were performed on the interletterdistance-judgment RT function, with interletter distance = 4 as the joining point. The slope of the beginning section (Interletter Distances 1 to 4) was 614 ms, which was significant, f(142) = 539,p < .001, SE = 113.92, as was the slope of the later section (Interletter Distances 4 through 19) of 134 ms, r(574) = 5.59, p < .001, SE = 24.04. Although both slopes were significant, that of the beginning section was more than four times the slope of the later section. A comparison of the two slopes showed that the slope of the beginning section was significantly larger than that of the later section, t(716) = 16.15,/? < .001, SE = 29.70. Thus, to argue for a single, homogeneous serial process to have underlain the retrieving of the two classes of distance values would appear strained. However, if the slope of the latter section indeed derived from interspersed serial counting, then increasing the speed demand should minimize the slope. Other evidence has showed that participants often do not use the most efficient mechanism to retrieve interletter-distance information from memory without being pressured (Aldridge, Jou, Leka, & Espinoza, 1998). The direct retrieval mechanism of the dual-mode retrieval hypothesis needs stronger evidence to support it than that shown in Experiment 2A. Moreover, the RT curves shown in Figure 6 were missing the terminal, downward section shown in the serial position estimates. We hypothesize that the RT functions of the interletter distance should parallel those of the serial positions, and we predict that when all 26 letters are used, the missing terminal linear portion of the interletter-distance function will appear. This further confirmation is important for the dual-mode access theory, which says that the extreme values of the series are represented in, and retrieved from, memory by a qualitatively different mechanism than the large middle section. Experiment 2B In Experiment 2B, we gave greater emphasis in the instructions to speed and to avoiding letter-by-letter counting. We expected this to further flatten the middle portion of

the RT curve. In addition, all 26 letters were used in constructing the letter pairs for testing the hypothesis that the RT function for interletter distance should parallel that of the serial position in shape.

Method Participants Forty UTPA introductory psychology students participated in the experiment for extra course credit.

Materials and Design All 26 letters were used in the letter-pair construction, resulting in a total of 325 distinct stimulus letter pairs. The algorithm for generating letter pairs, letter orders within a pair, and counterbalancing was the same as in Experiment 2A.

Procedure The procedures were the same as in Experiment 2A, with the following exceptions. There was a greater emphasis in the instructions on speed and avoiding counting the letters up and down, one by one. The response keys were set on the two top rows of the keyboard (not counting the function keys), so that the keys for the last 5 values (21 to 25) continued from Response Key 20 on the same row.

Results and Discussion Estimate Data The mean estimated distances are plotted in Figure 7 against the objective distance and the hypothetically perfect performance function. A visual inspection showed that the estimated interval values preserved the ordinal relationship among the distances. The slope of the mean estimated values

11 13 15 17 19 21 23 2S Interletter Distance i—Num-inp -^Dist. Est. | Figure 7. Mean estimated interletter distances as a function of the actual interletter distances of Experiment 2B. Num-inp = number input; Dist. Est. = distance estimation.


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was .83, which was significant, t{991) = 95.71, p < .001, SE = .0087. Although there was a regression toward the mean, the slope of this function was larger than that obtained from Experiment 2A (.77). However, this slope of .83 was significantly smaller than 1, f(38) = -3.8, p < .001, SE = 1.99, replicating the conclusion from Experiment 2A. The increased slope may have resulted from the greater estimation accuracy for the last several distance values. If the function is truncated at Distance Value 19, the function appears almost identical to that of Figure 5. Figure 7 shows, however, that when the full range of the alphabet was used, there is some indication of a bounding effect (Huttenlocher et al., 1990). Specifically, the participants seemed to be aware of the lower and upper bounds of the distance and used that information to aid their judgments. Again, the two main results were replicated (i.e., the alphabetic-distance ordinal level information was preserved, but the memory scale of the interval information was systematically distorted in the form of a regression towards the means).

RTData The mean judgment RTs along with the mean numberinput RT as a function of the interletter distance are plotted in Figure 8. An ANOVA comparing the distance judgment and the number-input RT data was conducted. The condition effect was significant, F(l, 39) = 101.16, p < .001, MSE = 36,801,973, as was the effect of interletter distance, F(24, 936) = 18.18,/? < .001, MSE = 561,824. The Condition X Interletter-Distance interaction was also significant, F(24, 936) = 6.13, p < .001., MSE = 561,824. Greater emphasis on avoiding counting seemed to have substantially reduced the overall RT and the slope of the high-distance region of the curve (cf. Figure 6 and Figure 8). The use of the full

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^Num-inp — Dist. Est. I Figure 8. Mean reaction time (RT) of interletter-distance estimation as a function of the actual interletter distances, and experiment condition of Experiment 2B. Num-inp = number input; Dist. Est. = distance estimation.

alphabet also produced a downward trend at the terminal section of the curve. A visual inspection of Figure 8 indicated that the distance-judgment RT function showed three distinct sections, with the first few distance values having a steep slope, the middle section having a much smaller slope, and the last several distance values having a steep slope, which paralleled the serial position estimate RT functions. The best-fitting three linear segments were produced with joining points at Distances 3 and 18 (SSdev = 424,003, second best = 453,151 for Distances 5 and 18). It seemed that the use of the entire alphabet gave the participants a scope of the range of interletter-distance values and, as a result, invoked a linear backward-search mechanism or a complementary-sets strategy for the last several distance values. Segmental regressions that were based on the best estimated joining points showed the slope of the beginning section (Interletter Distances 1 to 3) to be 566 ms, which was significant, r(118) = 4.60, p < .001, SE = 123.12; that of the middle section (Interletter Distances 3 to 18) to be 67 ms (a 50% reduction from Experiment 2A), which was significant, ?(638) = 4.01,/? < .001, SE = 16.71; and that of the ending section (Interletter Distances 18 to 25) to be -187 ms, which was significant, r(317) = -3.56, p < .001, SE = 52.56. The difference between the slope of the beginning section and that of the middle section was significant, f(756) = 19.37, p < .001, SE = 25.78. These results further strengthened the STM-limit account of the dual-mode access hypothesis. It is possible that the change in the shape of the distance-judgment function from Experiment 2A to 2B was caused by the instruction that stressed speed more, by the introducing of the beginning and ending three letters, or by both. Although the design of the experiments had these two variables confounded, we examined the data of a subset of letter pairs of this experiment that matched the entire letter set of Experiment 2A by excluding the data that contained any of the letters A, B, C, X, Y, or Z. We conducted an ANOVA on these two combined data sets. The mean RTs of distance judgments as a function of experiment and interletter distance are shown on Figure 9. The two judgment RT functions showed that, overall, the responses in Experiment 2B were faster than in Experiment 2A for the identical set of stimulus letter pairs. In addition, the curve of Experiment 2B showed a moderate downward trend in the high interletterdistance region. The overall mean RT of Experiment 2A was 5-,832 ms and that of Experiment 2B was 4,132 ms. The difference was significant, F(l, 74) = 15.56, p < .001, MSE = 66,870,534. The interletter-distance effect and the Experiment X Interletter-Distance interaction were both significant, F(18, 1332) = 24.23, p < .001, MSE = 1,671,138, and F(18, 1332) = 4.73, p < .001, MSE = 1,671,138, respectively. It is fair to conclude that the emphasis on speed in Experiment 2B produced an effect of lowering the overall RT, and the introduction of the terminal letters gave participants a sense of the entire range of the distance and, consequently, caused them to adopt a backwardsearching mechanism or a complementary-sets strategy in computing the values of very large interletter distances. A visual inspection of the number-input function in Figure

ALPHABETIC MEMORY


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9 11 13 15 17 19

Interletter Distance

i—' Exp2A^-Exp2B] Figure 9. Mean reaction time (RT) of interletter-distance estimation of the middle 20 letters of Experiments 2A and 2B. Letters A, B, C, X, Y, and Z were dropped from Experiment 2B. Exp = experiment; Est. = estimation. 8 suggested a linear and quadratic trend in the function. A trend analysis confirmed this expectation, with the linear F(l, 936) = 184.48, p < .001, MSE = 114,366, and the quadratic F(l, 936) = 148.54, p < .001, MSE = 114,366. Because the possibility still existed that response input from the linearly arranged keys might have contributed to the steep linear sections of the judgment function, we used the numeric keypad in Experiment 2C to rule out this possibility.

Experiment 2C Experiment 2C replicated the results of Experiment 2B with 35 participants, with the exceptions that the numberinput RT function was flat and the slope of the middle section of the interletter-distance-RT function flattened to a nonsignificant 15 ms. The interletter-distance judgment and number-input mean RTs as a function of interletter distance are presented in Figure 10. The three best fitting segments were produced with joining points at 4 and 22 (SSdev = 446,609, second best SSdev = 459,272 for Distances 4 and 20, respectively). Thus, in Experiment 2C, the data pattern supported the dual-mode access hypothesis even more unequivocally, because the insignificant slope of the middle section completely ruled out any possibility of an algorithmic computing mechanism, and the persistent steep slopes of the terminal sections allayed the concern about a response contribution to them. Summary of Experiments 2A-2C The major finding of the second set of experiments was that systematic distortion occurred in estimation of interletter distance despite the fact that the alphabet has been greatly overlearned. This suggests that the memory limitation in interval level information representation is a fundamental one. However, in spite of the distortion in the interval level

693

information, the memory representation did preserve the ordinal ranks of the distance magnitudes. In line with the findings in the alphabetic serial position judgments, the results further showed that small distance values seemed to be retrieved in a serial manner (algorithmic computing), whereas larger ones seemed to be retrieved in a parallel or single-step process, which was consistent with the STMlimit concept. A related important finding across the three distance-judgment experiments was that in memory quantification, there was no indication of subitizing for small magnitudes. In direct contrast to the perceptual process, small quantities in memory had to be serially enumerated, and larger ones were directly estimated. The data further indicated that the serial mechanism used to access the extreme values generally produced only a moderate improvement in accuracy (see Figures 5 and 7). The distance-judgment RT function in Figure 6 showed a moderate slope, even beyond the first few values. If the slope resulted from the fact that some portion of the trials involved mental counting, was the nature of the counting the same as that of the serial algorithm that presumably produced the steep slopes of the first and last several values? Probably not. First, the slope was much shallower. Second, it seemed to be strategy- or instruction-dependent, because it largely disappeared in Figures 8 and 10. In contrast, the steep slopes of the first and last several distance values were not affected by the instructions and, therefore, must have been more fundamental in nature. One interpretation of the observed distortion in distance estimation in Experiments 2A, 2B, and 2C is that the estimates were derived from a distorted alphabet representation. However, the serial position-estimate data suggest that this is not the case. To further examine this possibility, we computed all possible pairwise interletter distances from the estimated alphabetic serial position scales in the numeric

W 1 5 17 19 2^23^5 Interletter Distance ~--- Dist. Est. | Figure 10. Mean reaction time (RT) of interletter-distance estimation as a function of the actual interletter distances, and experiment condition of Experiment 2C. Num-inp = number input; Dist. Est. = distance estimation.


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JOU AND ALDRIDGE

and blank conditions and their mean distances were computed. Then, we computed the slopes of these distance functions to determine to what extent they deviated from 1. The slope that was computed from the numeric condition was .996, which is not different from 1, t < 1; the slope from the blank condition was .974, which was not different from 1 either, f(37) = 1.55, p > .10, SE = 0.74. These results supported the idea that the regression toward the mean that was observed in the alphabetic-distance estimation in the second set of experiments did not originate from an inaccurate alphabet memory representation. If participants had a veridical alphabet scale, the systematic distortion must have then occurred in the process of performing the mental subtraction, or distance estimation. An interesting observation was the consistent overestimation of the interletter distance of 1 between two adjacent letters (see Figures 5 and 7), even though 1-unit interletter distance (allowing for some small random errors) between two adjacent letters would be derivable by subtraction from the serial position estimates. The highly accurate interletter distances derived this way from their serial position estimates were not, however, participants' actual interletter-distance estimations, which were systematically distorted. We performed a multidimensional scaling (Kruskal & Wish, 1978) on the participants' interletter-distance estimates to produce an alphabetic interpositional map. A one-dimensional scaling yielded a stress value of .0267, and a two-dimensional scaling yielded a stress value of .0217. Neither alphabetic map corresponded with the participants' directly produced position-estimate functions in Figures 1 and 4. However, as expected, the two-dimensional representation of the alphabetic positional layout revealed the same important features of the interletter-distance structure that the interletter-distance-judgment functions did in Figures 5 and 7. Figure 11 presents the one-dimensional and twodimensional alphabet maps of the middle 20 letters generated by a nonmetric multidimensional scaling from the estimated interletter distances of Experiment 2A.3 As can be seen, the one-dimensional map shows an unevenly spaced string of letters that is different from the function that was directly obtained from participants serial position estimates. Also, unlike the straight line of the serial position-estimate function, the arch of the alphabetic mental map in the two-dimensional representation essentially shows the same distortion as did the interletter-distance-judgment function in Figure 5, namely, the underestimation of large and overestimation of small distances. This observation reinforced the proposition that absolute and relative judgments are different (Banks, 1977; Gravetter & Lockhead, 1973; Nosofsky, 1983) and that data produced by the two processes are not mutually derivable from each other. One last concern is about the source of the distortion in the distance estimation. The question is whether the distortion lies in the distance scale itself or in the number-mapping process. The distortion could be the product of faulty distance computation. However, it is also possible that participants might have an accurate memory scale of the distance, but a faulty or biased number-mapping process

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Dimension 1 Figure 11. One- and two-dimensional mental alphabet maps produced by a nonmetric multidimensional scaling from the estimated interletter distances of the 190 pairs of letters in Experiment 2A.

(Huttenlocher et al., 1990; S. S. Stevens, 1962, 1971). In other words, we may ask whether the apparent distance distortion originated from an inaccurate memory interval scale or from an erroneous number-assigning process. Experiment 3 was conducted to answer this question. Experiment 3 The central question for Experiment 3 was whether the distortion lies in the memory scale itself or arises from the number-mapping process that is implicit in reporting. In this experiment, we presented pairs of letters one at a time, and participants made an ordinal (comparative) judgment of which letter came earlier or later in the alphabet. Numerous studies have shown distance effects in comparative judgments for linear-order stimuli (Banks, 1977; Banks et al., 1976; Birnbaum & Jou, 1990; Jou, 1997; Lovelace & Snodgrass, 1971; Moyer, 1973; Moyer & Bayer, 1976; 3

The alphabet maps generated by the multidimensional scaling from the interletter-distance estimate data of Experiments 2B and 2C, and the RT data of Experiment 3 basically replicated the alphabet map pattern in Figure 11. This suggests that these measures are all tapping the same memory representation of the alphabetic distances.

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Moyer & Landauer, 1967; Parkman, 1971; Trabasso et al., 1975; Woocher et al., 1978). Distance effects refer to the decreasing RT as a function of increasing distance. The distance effect is interpreted in this study as a behavioral measure of the participant's memory scale of the interletter distance (Birnbaum & Jou, 1990). As noted earlier, the interval distance in this experiment was a task-relevant property because it was measured in units of ordinal steps, which is the controlling property in a comparative judgment task. Although both distance estimation and the RT of the comparative judgments are response measures of the memory distance scale, the RT measure may more directly reflect the scale than the distance estimation. The responding with a number to a pair of letters to indicate the interletter distance requires more cognitive steps than computing the distance in memory. The former task involves computing the distance, digitizing the possibly analogical distance, and reporting the product of this internal mental process. There has been evidence that people are often inaccurate in reporting the contents of their mental states or processes (Ericsson & Simon, 1980; Nisbett & Wilson, 1977) and biased in assigning numerical values to metric information in memory (Huttenlocher et al., 1990). Therefore, in theory, the distortion could have resulted from assigning systematically biased numbers to an accurate memory scale. Two hypotheses will be tested: scale distortion and recoding distortion. The former hypothesis says that the memorial data themselves are distorted and that the numerical estimates only reflect this distortion. The latter hypothesis says that the memorial scales are veridical, and the distortion arises from the process of recoding the original distance scale into a numerical code. If the RT of the comparative judgment task, which is an independent behavioral measure of the alphabetic distance in memory, correlates more with the estimated distance than with the actual distance, then the scale-distortion hypothesis will be supported. If the RT of the comparative judgment correlates more with the actual distance, then the recoding-distortion hypothesis will be supported.

Experiment 2A. The 190 pairs of letters were presented once in the "choose the earlier letter" instruction and once in the "choose the later letter" instruction, which yielded a total of 380 trials. The number-input part of the experiment 2A was not used in this experiment because the response choice involved only two keys.

Procedure The letter pairs were presented in the same manner as in Experiment 2A. Participants were asked in the first block of trials to choose, from a pair of letters, the letter that was earlier and in the second block, the one that was later in the alphabet. The order in which these two choices were presented was counterbalanced across the participants. If the answer was the letter on the left-hand side, they pressed the z key; if it was on the right-hand side, they pressed the "/" key. They were told to poise their two index fingers on the two response keys and respond as fast and as accurately as they could. When an error was made, a beep and a warning, "You made an error! Be careful next time," were given. At the end of the experiment, the computer displayed the accuracy score to the participants. If the score was lower than .90, the participant was asked to redo the experiment. Three participants repeated the experiment to complete it. At the completion of each 95 of the total 380 trials, the participants could take a short break. The whole experiment took about 45 min.

Results and Discussion The overall accuracy score was .95. Inaccurate responses were not included in the analysis. The mean RT as a function of choice and the interletter distance is presented in Figure 12. An ANOVA was performed, using choice, interletter distance, and letter order in the stimulus pair as factors. The mean RT was 1,234 ms for choosing the earlier letter and 1,286 ms for choosing the later letter. The difference was significant, F(l, 68) = 5.21, p < .05, MSE = 337,300. The effect of interletter distance was significant, F(18, 1189) =

g 2200

Method Participants Thirty-five introductory psychology students at UTPA participated in the experiment for extra course credit.

Materials and Design Exactly the same set of letter pairs that were used in Experiment 2A (ID judgment) were used. The first 3 and last 3 letters were excluded because there is evidence that stimulus pairs in comparative judgments that include end or near-end items of a linear ordering are responded to differently than the rest of the items (e.g., the extreme items in the stimulus pair can provide sufficient information for making a choice without considering the other member; Banks, 1977; Birnbaum & Jou, 1990; Lovelace & Snodgrass, 1971; Potts, 1974; Scholz & Potts, .1974). The letter order within a pair was counterbalanced in the same way as in

Interletter Distance --Earlier-^Later ] Figure 12. Mean reaction time (RT) of the alphabetic-order judgment as a function of choice and the actual interletter distance of Experiment 3.


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117.68,/? < .001, MSE = 140,926. The Choice X Interletter Distance interaction was marginally significant, F(18, 1182) = 1.60, p = .052, MSE = 57,471. No other effects were significant. A trend analysis showed that the decreasing linear trend of the mean RT with increasing interletter distance was significant, F(l, 612) = 1,339.93, p < .001, MSE = 51,204, indicating a significant decrease in RT as the distance between the two letters increased. The quadratic trend was also significant, F(l, 612) = 144.88, p < .001, MSE = 51,204, indicating a leveling off of the slope as distance reached a high level, which replicates Jou's (1997) recent results and those of others using numerical, alphabetic, and perceptual stimuli (see Banks, 1977). The major question in this experiment is which of the two measures—the actual distance, or the estimated distance—is a better predictor of the RT of the comparative judgment. To answer this question, a multiple regression was conducted, using the comparative judgment RT as the criterion and the actual distance and the estimated distance obtained from Experiment 2A as two predictors. The input data points for the dependent measure were the mean RTs (averaged over the two choices and over participants) of the 380 pairs of letters. The data points for the predictors were the actual interletter distances and the mean estimated interletter distances of the same 380 letter pairs produced by participants in Experiment 2A. The simple correlations among these three measures were .83 between interletter distance and the estimated distance, .81 between the comparative judgment RT and interletter distance, and .84 between the comparative judgment RT and the estimated distance. The multiple-regression results showed that the partial regression coefficient for the estimated distance was -135, which was highly significant, f(377) = -5.50, p < .001, SE = 24.56, in contrast to the counterpart of 35 for the actual distance, which was not significant, f(377) = 1.81,/? > .05, SE = 20.03. The critical partial correlation results obtained here replicated those from an earlier pilot experiment in which only "choose the earlier letter" instruction was used. Thus, when the estimated distance was partialed out, the actual distance showed no significant predictive power. On the contrary, when the actual distance was partialed out, the estimated distance was still a highly significant predictor. Hence, the multipleregression results supported the idea that both the estimated distance and the comparative judgment RT measured the same psychological entity (i.e., the subjective alphabetic distance). Accordingly, the hypothesis of scale distortion was supported, suggesting that the distortion probably originated from a distorted memory-distance scale rather than from a distorted recoding of the memorial scale into a numeric form. This conclusion is consistent with the fact that the serial position judgments were highly accurate. If the participants had not been able to correctly map the 25 or 26 numbers to their corresponding memorial data, the position estimations would not have been as accurate as they were.

General Discussion

Memory Representation of Ordinal Level and Interval Level Alphabetic Information The issue of whether interval level properties of magnitudes are represented in memory along with ordinal properties has been controversial (Banks, 1977; Banks, Mermelstein, & Yu, 1982; Gravetter & Lockhead, 1973; Moyer & Bayer, 1976; Potts, 1974). Some studies showed that memory retains only the ordinal properties of magnitude (Banks, 1977; Gravetter & Lockhead, 1973; Moyer & Dumais, 1978; Potts, 1974), whereas others found that both the ordinal and the interval properties are represented (Griggs & Shea, 1977; Griggs, Townes, & Keen, 1979; Holyoak & Walker, 1976; Kerst & Howard, 1977; Moyer & Bayer, 1976; Moyer & Landauer, 1967; Paivio, 1975; Potts, 1977). In these studies, either accuracy or RT of comparative judgments was used as the dependent measure. As noted earlier, however, interval level information is actually a task-irrelevant attribute when a comparative judgment is used in which the ordinal steps are held constant and only interval distances are varied. It is possible that in these circumstances, the interval level information exerts an effect only before participants fully develop an effective strategy. Moreover, in previous studies, the effect that was interpreted as the interval effect actually measured only the ordinal rank of the magnitudes of the intervals. The psychophysical method we used in the current study circumvented these problems. Both the serial position and interval distance judgments showed that the ordinal scale of the alphabet was perfectly preserved in memory representation. However, our psychophysical judgment method also revealed that interval level information was transformed by expanding small intervals and shrinking large ones. This distortion resulted in a reduction of the difference between the large and the small intervals, without affecting the ordinal ranking of the intervals. If only comparative judgment RT had been used, this distortion could not have been observed. The limitation in preserving undistorted, interval scale properties may be a fundamental constraint on our retention of quantity information. It may explain, for example, why letter grades are adopted so much more widely than percentage grades in the academic system.

Absolute and Relative Judgments Serial position estimation in Experiments 1A and IB was a type of absolute judgment (Gravetter & Lockhead, 1973; Miller, 1956; Nosofsky, 1983; S. S. Stevens, 1971), whereas interletter-distance judgments in Experiment 2A, 2B, and 2C were relative judgments (Holyoak & Mah, 1982). Although the responses in both forms of judgment were similar, the slopes of the position-estimation functions were 1, whereas the slopes of the distance-estimation functions showed clear regression toward the mean. In addition, the time required for making the positional judgments was much lower than the time required by the distance judgments. Why was the judgment highly accurate in one case but systematically distorted in the other? One possibility is that the distance


ALPHABETIC MEMORY

judgments involved more cognitive processing, which led to greater susceptibility to errors (Holyoak & Man, 1982). When the cognitive system is overloaded, information loss occurs in the transmission from input to output (Miller, 1956). Regression toward the mean, as observed in the distance judgment, is basically a form of interval level information loss. As noted earlier, if this deficiency in the system occurs in information that is as highly overlearned as the alphabet, it seems likely to occur with any information. Again, we found that absolute judgment and relative judgment involve two different mental processes, consistent with the view of some other authors (Banks, 1977; Gravatter & Lockhead, 1973; Hutchinson & Lockhead, 1977). In a relative judgment, one item is judged with respect to another. In an absolute judgment, according to Gravatter and Lockhead, a judgment is made in relation to the participant's memory of the whole series. In our study, the interletter distances that were mathematically derived from the alphabetic serial position representation were highly accurate and could not, therefore, account for the systematic distortions in the actual estimates. Similarly, an attempt at application of multidimensional scaling (Kruskal & Wish, 1978) to the estimated interletter distances returned only a second dimension that tautologically restated the fact that short distances were overestimated and long distances were underestimated. The mind apparently does not directly derive one representation from the other. The distorted mental maps constructed from relative judgment data in some studies (Birnbaum & Mellers, 1978; Holyoak & Mah, 1982) may have been the products of the relative judgment tasks used. Hence, our conclusion regarding these two types of judgments agrees with Banks (1977), Gravetter and Lockhead (1973), and Hutchinson and Lockhead (1977) that different memory representations are used for absolute and relative judgments. Finally, it is worth noting that the highly accurate, alphabetic positional judgments were not consistent with Miller's (1956) historical conclusion that the maximum number of identifications that people could make in an absolute judgment was 7 ± 2. Experiment 1A and IB showed that people could correctly make 26 positional identifications for the alphabet.

Memory Representation of the Alphabet The lack of systematic expansion and compression in the alphabetic position estimates reinforced the position that in Experiments 1A and IB, participants did not compute a letter's position using A as an implicit reference point. Thus, the alphabetic position judgment data were not consistent with the reference-point theory in which an implicit reference point is used to determine the relative locations of objects (Birnbaum & Mellers, 1978; Holyoak & Mah, 1982). It may be that people do resort to this process for constructing a mental representation for less familiar things but not for very familiar materials such as the alphabet. In additon, the data did not suggest that participants used multiple reference points either. The marked pattern of cyclic zig-zags observed by Klahr et al. (1983) is missing from the present data. We suggest that the hierarchical

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pattern of the letters in Klahr et al. study was the product of the stimulus-response association task used in that study. Also, the evidence for using the middle point as a reference point is weak at best. If participants used the middle point as a reference point, this reference point must have been qualitatively different from, for example, A. An inspection of the RT curves in Figures 3and 4 indicated that the central points (M and N) were definitely not accessed as readily as were A and Z, if they were to be considered reference points. The central dip, relative to the overall configuration or to the two terminal points of the entire curve, seemed to be more of a local minimum on the high-middle plateau than a global anchoring point. One consistent general pattern in the RT functions across Experiments 1A, IB, 2A, 2B, and 2C was that the slopes of the beginning and ending portions of the functions were linear and steep, whereas that of the middle portions, aside from some local fluctuations, showed a plateau. This pattern suggested a two-mechanism quantification process, with a serial mechanism determining the values of small magnitudes and a direct retrieval process being used for large quantities. The largest alphabetic positions and distances may have been determined either by a backward serial searching or by a complementary-sets strategy. The STM span appeared to determine which mode would be used. The robust pattern of RT data across the position and distance judgments led us to propose a dual-memory-mode representation of the alphabetic serial information in particular and of quantitative information in general. When the magnitude of the information is within the STM span, it is represented and processed in STM in a serial manner. However, when it exceeds the STM span, it is retrieved directly from longterm memory in a parallel fashion, independently of an anchor. One additional point is worth noting. Although the direct retrieval mode applied to the middle section of the values took, overall, a longer time than the serial retrieval process used for the terminal sections, the direct retrieval mode had a faster processing rate and, therefore, was still more efficient than the serial mode. For example, if the processing rates of Serial Position 5 and Serial Position 20 in Figure 4 are compared, the rate for Serial Position 5 is 160 ms per serial position compared with 67 ms per serial position for 20. The blank condition in Experiment 1A showed significantly lower RT relative to the numeric condition without loss.of accuracy. Therefore, we propose that the internal representation of the alphabet takes the form of an analog continuum, in agreement with other findings about the representation of serial information (Dehaene et al., 1993; Huttenlocher, 1968; Moyer, 1973; Moyer & Bayer, 1976; Moyer & Landauer, 1967; Paivio, 1978; Scholz & Potts, 1974; Trabasso et al., 1975). In such a representation, each letter is associated with a spatial positional code, although the spatial code can be transformed into a digital one when necessary. It might be the digitization or the numerical recoding of the spatial position that took additional time. Why should the alphabetic information be represented in an analog form rather than in a digital form? The answer may be that a digital representation would be more costly in

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memory and attentional resources. After all, people can normally hold only 7 ± 2 discrete pieces of information simultaneously in STM (Miller, 1956).


Memory Quantification Processes: Subitizing Not Found An interesting question is why subitizing is not present in memory quantification. We suggest that actually seeing stimuli is different from activating and scanning them in memory. The latter is more difficult than the former because in perceptual processing, the stimuli are external, whereas in memory processing, the stimuli must be represented internally. According to this view, memory cannot perform subitizing because it is burdened by generating and retaining the information in addition to processing it. If processing a stimulus perceptually can be likened to performing one task, processing the stimulus in memory is similar to performing multiple, simultaneous tasks. Unlike perceptual enumeration, quantification in memory revealed an inverse relation between the processing mode (serial vs. parallel) and numerosity. In perception, an immediate, effortless, and accurate apprehension of less than four or five elements can be attained by the process of subitizing that is manifested in a flat RT function and almost perfect accuracy over this range of quantity (Jensen et al., 1950; Kaufman et al., 1949; Klahr, 1973; Logie & Baddeley, 1987; Mandler, 1975; Mandler & Shebo, 1982; Trick & Pylyshyn, 1994). The quantity of the additional elements beyond this range can be determined only by a serial counting process, generating an RT function with a steep linear slope and a higher error rate. Experiments 1 A, IB, 2A, 2B, and 2C showed a relationship in memory between quantity and RT that was opposite of that found in perception. Small magnitudes, not large ones, were quantified by a serial process, and large magnitudes were quantified by a parallel process. As noted, the internal generation and representation of the stimuli in memory may take cognitive or attentional resources, which precludes the parallel processing of the stimuli of small numerosities. The external presentation of the stimuli in the perceptual mode, on the other hand, frees up the attentional resources and makes them available for the fast parallel processing, or subitizing. Another difference between perceptual and memorial modalities is yet to be explained. Our data showed that in the memory mode, when the quantity became larger than could be handled by STM, the processing switched to a paralleldirect-estimation mode. At this point, RT became independent of the size of the memory arrays. Again, this finding appeared to contradict findings in perceptual quantification that a serial counting mechanism is used for magnitudes of this range. But did it? Logie and Baddeley (1987) and Klahr (1973) reported that, as the stimulus set size increased over 20 in perceptual quantification, participants switched from a serial counting mode to an estimation mode. At this point, RT became either constant or only weakly related to the set size. Hence, at a deeper level, there is a coherence between these two seemingly discrepant findings across the two cognitive domains. The only difference is that the informa-

tion-magnitude threshold for the switch from a serial processing mode to a parallel mode is higher in perception than in memory. In spite of superficial dissimilarities, we suggest that limitations in memory and attentional capacities underlie both perceptual and memorial quantification. In both domains, a direct estimation is used when information exceeds the processing capacity. In both domains, serial processing occurs when information quantity is within the perceptual capacity, in one case, and STM span in the other. The absence of subitizing in memory is not inconsistent with this attention-memory-span limitation explanation. According to this concept, subitizing is the product of an abundance of processing resources for very small amounts of information, typically a set of three or four elements. Subitizing and direct estimation are both parallel processing in the sense that the RT functions remain flat over a certain range of stimulus array sizes (Townsend, 1990). Yet, they are used under very different conditions. The critical difference between these two time-constant processing modes is in the accuracy of the output information. Subitizing produces highly accurate output information, whereas direct estimation generates low-accuracy responses. Hence, there are two types of parallel processing in quantification—one used in an information underload condition, namely, subitizing, and one in information overload condition, namely, direct estimation. When the information load is at the intermediate level, the cognitive system tends to adopt a serial mode of processing.

Two Processes in Relative Judgments and Their Implications As shown by the second set of experiments and Experiment 3, a relative judgment can yield either a distance effect (the inverse correlation between distance and RT) or a reverse distance effect (a positive correlation between the two variables), at least over a certain range of values. Two different cognitive processes were used by the participants in these experiments. We termed one process comparison (Birnbaum & Jou, 1990; Holy oak & Patterson, 1981) and the other serial search (Jou, 1997; Holy oak & Patterson, 1981; Moyer & Bayer, 1976). Comparison and serial search are qualitatively different processes. Comparison was likened by some theorists to a random walk between two boundaries until one boundary was reached (Birnbaum & Jou, 1990; Buckley & Gillman, 1974; Link, 1992; Luce, 1986; Pachella, 1974). The random walk is a process of sampling information from memory iteratively for each of the two items being compared, until the cumulated information difference between the items exceeds a preset criterion for a positive or negative decision. The duration of this process depends on the distance or difference between the two items. When the distance between the two items is small, the information distributions of the two items overlap more, and a greater number of iterative samplings is required to cumulate sufficient information to exceed the decision criterion. The opposite is true when the distance is large. Therefore, RT is inversely related to the distance between

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the two items and the distance-effect results (Birnbaum & Jou, 1990; Hamilton & Sanford, 1978; Moyer & Bayer, 1976; Moyer & Landauer, 1967). As far as letter comparison is concerned, each letter may be stored in memory in terms of such semantic features as, among others, "alphabetic earliness" or "lateness." The further apart the two letters are in the ordering, the more different the features are. Consequently, each sampling of the features in a comparison is more likely to yield above-criterion evidence, leading to a faster response (Birnbaum & Jou, 1990; Buckley & Gillman, 1974; Holyoak & Patterson, 1981). Serial search, on the other hand, operates by covering the distance between two items unit-by-unit, typically at a constant rate, yielding a reverse distance effect (Moyer, 1973; Moyer & Bayer, 1976; Parkman, 1971; Polich & Potts, 1977; Woocher et al., 1978). This memory search as an information-retrieving process is procedural in nature (Jou, 1997; Tulving, 1985). A stimulus-response chain is learned when the series is first acquired. When participants make an interletter-distance judgment, they can reactivate this stimulus-response chain association by running through the sequence. When such a sequential item-activation process is invoked, items are retrieved from memory in a temporal sequence (Jou, 1997). In terms of time required, a long interitem distance is favorable to a comparison process, whereas a short distance is favorable to a serial search mechanism. People were found to adopt one or the other process in processing linear-order stimuli, producing apparently inconsistent patterns of relationship between distance and RT (Jou, 1997). The concept of the cognitive system adopting one of these two different mechanisms or a mixture of the two can provide a coherent explanation for such inconsistencies as those reported in numerous studies of binary judgments on linear-order stimuli (Grenezebach & McDonald, 1992; Hamilton & Sanford, 1978; Jou, 1997; Lovelace & Snodgrass, 1971). The concept of a chain association has long been discarded in favor of a remote association or hierarchical structure as a mechanism of organizing or processing serial information (Capaldi, 1985; Estes, 1985; Mandler, 1985; Potts, 1972, 1974; Slamecka, 1985). The fast response in comparative judgment to a pair of items that are far apart in an ordering and the slow response to a pair of close items have been interpreted by cognitive psychologists as evidence against the principle of association by proximity (Potts, 1972, 1974; Slamecka, 1985). The distance and ordinal judgments in the present study showed that the associationists and the cognitive psychologists were talking about two different processes. The associationists were talking about serial search, whereas the cognitive psychologists were talking about comparison. These two processes have different functions to serve. The "association" between two distant items that the cognitive psychologists have been arguing for is based on comparing two items at one point in time, whereas the association that the associationists favor is based on a serial activation of items over a period of time. Hence, the principle of association by proximity and that of remote association may both be valid. The controversy arose from a failure to understand that two different kinds of

mental processes with different functions were being compared.

Conclusions Memory appears to be very good at preserving ordinal scale information, including the ordinal ranks of the interval magnitudes. However, memory appears liable to distortion when representing the interval scale information itself. The null, interval scale effects found in some studies (Banks, 1977) might be due to participants' successful suppression of the task-irrelevant attributes of the stimuli in comparative judgments. Also, quantification of even well-learned serial information in memory did not seem to manifest the parallel process of subitizing small quantities that is found in perceptual enumeration. Rather, small quantities were computed by a serial process, and large ones were computed by a direct estimate process. Finally, two types of relative judgments can be performed on a pair of linear-order stimuli. Comparison yields a distance effect, whereas serial search yields a reverse distance effect, with each type tapping into the opposite aspect of the same memory scale. References Aldridge, J. W. (1981). Levels of processing in speech production. Journal of Experimental Psychology: Human Perception and Performance, 7, 388^107. Aldridge, J. W., Jou, J., Leka, G., & Espinoza, B. (1998, April). Analysis of articulatory suppression enhancement of alphabetic judgments. Paper presented at the Annual Meeting of the Southwestern Psychological Association, New Orleans, LA. Anderson, J. R. (1983). The architecture of cognition. Cambridge, MA: Harvard University Press. Baddeley, A. D. (1994). The magic number seven: Still magic after all these years. Psychological Review, 101, 353-356. Baddeley, A. D., & Hitch, G. (1974). Working memory. In G. A. Bower (Ed.), The psychology of learning and motivation (Vol. 8, pp. 47-89). San Diego, CA: Academic Press. Banks, W. P. (1977). Encoding and processing of symbolic information in comparative judgments. In G. H. Bower (Ed.), The psychology of learning and motivation (Vol. 11, pp. 101-159). New York: Academic Press. Banks, W. P., Fujii, M., & Kayra-Stuart, F. (1976). Semantic congruity effects in comparative judgments of magnitudes of digits. Journal of Experimental Psychology: Human Perception and Performance, 2, 435—447. Banks, W. P., Mermelstein, R., & Yu, H. K. (1982). Discriminations among perceptual and symbolic stimuli. Memory & Cognition, 10, 265-278. Birnbaum, M. H., & Jou, J. W. (1990). A theory of comparative response time and "difference" judgments. Cognitive Psychology, 22, 184-210. Bimbaum, M. H., & Mellers, B. A. (1978). Measurement and the mental map. Perception & Psychophysics, 23, 403^1-08. Broadbent, D. E. (1971). The magic number seven after fifteen years. In A. Kennedy & A. Wilkes (Eds.), Studies in long-term memory (pp. 2-18). New York: Wiley. Buckley, P. B., & Gillman, C. B. (1974). Comparisons of digits and dot patterns. Journal of Experimental Psychology, 103, 11311136. Capaldi, E. J. (1985). Anticipation and remote association: A


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JOU AND ALDRIDGE

configural approach. Journal of Experimental Psychology: Learning, Memory, and Cognition, 11, 450-454. Cook, R. G., Brown, M. R, & Riley, D. A. (1985). Flexible memory processing by rats: Use of prospective and retrospective information in the radial maze. Journal of Experimental Psychology: Animal Behavior Processes, 11, 453-469. Dehaene, S., Bossini, S., & Giraux, P. (1993). The mental representation of parity and number magnitude. Journal of Experimental Psychology: General, 122, 371-396. Dehaene, S., Dupoux, E., & Mehler, J. (1990). Is numerical comparison digital? Analogical and symbolic effects in two-digit number comparison. Journal of Experimental Psychology: Human Perception and Performance, 16, 626-641. Ericsson, K. A., & Kintsch, W. (1995). Long-term working memory. Psychological Review, 102, 211-245. Ericsson, K. A., & Simon, H. A. (1980). Verbal reports as data. Psychological Review, 87, 215-259. Estes, W. K. (1985). Levels of association theory. Journal of Experimental Psychology: Learning, Memory, and Cognition, U, 444-449. Gravetter, E, & Lockhead, G. R. (1973). Criterial range as a frame of reference for stimulus judgment. Psychological Review, 3, 203-216. Grenzebach, A. P., & McDonald, J. E. (1992). Alphabetic sequence decisions for letter pairs with separations of one to three letters. Journal of Experimental Psychology: Learing, Memory, and Cognition, 18, 865-872. Griggs, R. A., & Shea, S. L. (1977). Integrating verbal quantitative information in linear orderings. Memory & Cognition, 5, 287291. Griggs, R. A., Townes, K. J., & Keen, D. M. (1979). Processing numerical quantitative information in artificial linear orderings. Journal of Experimental Psychology: Human Learning and Memory, 5, 282-291. Hamilton, J. M. E., & Sanford, A. J. (1978). The symbolic distance effect for alphabetic order judgments: A subjective report and reaction time analysis. Quarterly Journal of Experimental Psychology, 30, 33-43. Hartley, A. A. (1977). Mental measurement in the magnitude estimation of length. Journal of Experimental Psychology: Human Perception and Performance, 3, 622-628. Holyoak, K. J., & Mah, W. A. (1982). Cognitive reference points in judgements of symbolic magnitude. Cognitive Psychology, 14, 328-352. Holyoak, K. J., & Patterson, K. K. (1981). Apositional discriminability model of linear order judgments. Journal of Experimental Psychology: Human Perception and Performance, 7, 1283— 1302. Holyoak, K. J., & Walker, J. H. (1976). Subjective magnitude information in semantic orderings. Journal of Verbal Learning and Verbal Behavior, 15, 287-299. Hudson, D. J. (1966). Fitting segmented curves whose join points have to be estimated. Journal of the American Statistical Association, 61, 1097-1125. Hutchinson, J. W., & Lockhead, G. R. (1977). Similarity as distance: A structural principle for semantic memory. Journal of Experimental Psychology: Human Learning and Memory, 3, 660-678. Huttenlocher, J. (1968). Constructing spatial images: A strategy in reasoning. Psychological Review, 75, 550-560. Huttenlocher, J., Hedges, L. V., & Bradburn, N. M. (1990). Reports of elapsed time: Bounding and rounding processes in estimation. Journal of Experimental Psychology: Learning, Memory, and Cognition, 16, 196-213. Jensen, E. M., Reese, E. P., & Reese, T. W. (1950). The subitizing

and counting of visually presented fields of dots. Journal of Psychology, 30, 363-392. Jou, J. (1997). Why is the alphabetically middle letter in a multiletter array so hard to determine? Memory processes in linear-order information processing. Journal of Experimental Psychology: Human Perception and Performance, 23, 17431763. Jou, J., Aldridge, J. W., Nelson, J. A., Barragan, Z. P., Duran, J. B., & Luna, C. (1996, July). Memory search of complementary sets of information. Paper presented at the American Psychological Society's annual meeting, San Francisco. Kaufman, E. L., Lord, M. W, Reese, T. W., & Volkmann, J. (1949). The discrimination of visual number. American Journal of Psychology, 62, 498-525. Kerst, S. M., & Howard, J. H. (1977). Mental comparison for ordered information on abstract and concrete dimensions. Memory & Cognition, 5, 227-234. Klahr, D. (1973). Quantification processes. In W. G. Chase (Ed.), Visual information processing (pp. 3-34). New York: Academic Press. Klahr, D., Chase, W. G., & Lovelace, E. A. (1983). Structure and process in alphabetic retrieval. Journal of Experimental Psychology: Learning, Memory, and Cognition, 9, 462—477. Kosslyn, S. M., Ball, T. M., & Reiser, B. J. (1978). Visual images preserve metric spatial information: Evidence from studies of image scanning. Journal of Experimental Psychology: Human Perception and Performance, 4, 47-60. Kruskal, J. B., & Wish, M. (1978). Multidimensional scaling. Beverly Hills, CA: Sage. LeFevre, J., Sadesky, G. S., & Bisanz, J. (1996). Selection of procedures in mental addition: Reassessing the problem size effect in adults. Journal of Experimental Psychology: Learning, Memory, and Cognition, 22, 216-230. Link, S. W. (1992). The wave theory of difference and similarity. Hillsdale, NJ: Erlbaum. Logan, G. D. (1988). Towards an instance theory of automatization. Psychological Review, 95, 492-527. Logan, G. D., & Klapp, S. T. (1991). Automatizing alphabet arithmetic: I. Is extended practice necessary to produce automaticity? Journal of Experimental Psychology: Learning, Memory, and Cognition, 17, 179-195. Logie, R. H., & Baddeley, A. D. (1987). Cognitive processes in counting. Journal of Experimental Psychology: Learning, Memory, and Cognition, 13, 310-326. Lovelace, E. A., Powell, C. M., & Brooks, R. J. (1973). Alphabetic position effects in covert and overt alphabetic recitation times. Journal of Experimental Psychology, 99, 405^08. Lovelace, E. A., & Snodgrass, R. D. (1971). Decision time for alphabetic order of letter pairs. Journal ofExperimental Psychology, 88, 258-268. Luce, R. D. (1986). Response times. New York: Oxford University Press. Mandler, G. (1975). Memory storage and retrieval: Some limits on the reach of attention and consciousness. In P. M. A. Rabbitt & S. Domic (Eds.), Attention and performance, Vol. V(pp. 499-516). New York: Acedemic Press. Mandler, G. (1985). From association to structure. Journal of Experimental Psychology: Learning, Memory, and Cognition, U, 464-^68. Mandler, G., & Shebo, B. J. (1982). Subitizing: An analysis of its component processes. Journal of Experimental Psychology: General, 111, 1-22. Marks, D. F. (1972). Relative judgment: A phenomenon and a theory. Perception & Psychophysics, 11, 156-160. Miller, G. A. (1956). The magical number seven, plus or minus

701


ALPHABETIC MEMORY

two: Some limits on our capacity for processing information. Psychological Review, 63, 81-97. Moyer, R. S. (1973). Comparing objects in memory: Evidence suggesting an internal psychophysics. Perception & Psychophysics, 13, 180-184. Moyer, R. S., & Bayer, R. H. (1976). Mental comparison and the symbolic distance effect. Cognitive Psychology, 8, 228-246. Moyer, R. S., & Dumais, S. T. (1978). Mental comparison. In G. H. Bower (Ed.), The psychology of learning and motivation (Vol. 12, pp. 117-155). New York: Academic Press. Moyer, R. S., & Landauer, T. K. (1967). The time required for judgments of numerical inequality. Nature, 215, 1519-1520. Nairne, J. S. (1991). Positional uncertainty in long-term memory. Memory & Cognition, 19, 332-340. Nairne, J. S. (1992). The loss of positional certainty in long-term memory. Psychological Science, 3, 199-202. Nisbett, R. E., & Wilson, T. D. (1977). Telling more than we can know: Verbal reports on mental processes. Psychological Review, 84, 231-259. Nosofsky, R. M. (1983). Information integration and the identification of stimulus noise and criterial noise in absolute judgment. Journal of Experimental Psychology: Human Perception and Performance, 9, 299-309. Pachella, R. G. (1974). The interpretation of reaction time in information-processing research. In B. Kantowitz (Ed.), Human information processing: Tutorials in performance and cognition (pp. 41-81). Hillsdale, NJ: Erlbaum. Paivio, A. (1975). Perceptual comparison through the mind's eye. Memory & Cognition, 3, 635-647. Paivio, A. (1978). Mental comparisons involving abstract attributes. Memory & Cognition, 6, 199-208. Parkman, J. M. (1971). Temporal aspects of digits and letter inequality judgments. Journal of Experimental Psychology, 91, 191-205. Polich, J. M., & Potts, G. R. (1977). Retrieval strategies for linearly ordered information. Journal of Experimental Psychology: Human Learning and Memory, 3, 10—17. Potts, G. R. (1972). Processing strategies used in the encoding of linear ordering. Journal of Verbal Learning and Verbal Behavior, 11, 727-740. Potts, G. R. (1974). Incorporating quantitative information into a linear ordering. Memory & Cognition, 2, 533-538. Potts, G. R. (1977). Integrating new and old information. Journal of Verbal Learning and Verbal Behavior, 16, 305-320. Radvansky, G. A., Carlson-Radvansky, L. A., & Irwin, D. E. (1995). Uncertainty in estimating distances from memory. Memory & Cognition, 23, 596-606. Scharroo, J., Leeuwenberg, E., Stalmeier, P. F. M., & Vos, P. G. (1994). Alphabetic search: Comment on Klahr, Chase, and Lovelace (1983). Journal of Experimental Psychology: Learning, Memory, and Cognition, 20, 236-244. Scholz, K. W., & Potts, G. R. (1974). Cognitive processing of linear orderings. Journal of Experimental Psychology, 102, 323-326. Shepard, R. N. (1978). The mental image. American Psychologist, 33, 125-137.

Shepard, R. N., & Metzler, J. (1981). Mental rotation of threedimensional objects. Science, 171, 701-703. Shiffrin, R. M., & Nosofsky, R. M. (1994). Seven plus or minus two: A commentary on capacity limitations. Psychological

Review, 101,357-361. Slamecka, N. J. (1985). Ebbinghaus: Some associations. Journal of Experimental Psychology: Learning, Memory, and Cognition, 11, 414-435. Stemberg, S. (1969a). The discovery of processing stages: Extensions of Donders' method. Acta Psychologica, 30, 276-315. Stemberg, S. (1969b). Memory-scanning: Mental processes revealed by reaction-time experiments. American Scientist, 57, 421-457. Stemberg, S. (1975). Memory scanning: New findings and current controversies. Quarterly Journal of Experimental Psychology, 27, 1-32. Stevens, A., & Coupe, P. (1978). Distortion in judged spatial relations. Cognitive Psychology, 10, 422-437. Stevens, S. S. (1962). The surprising simplicity of sensory metrics. American Psychologist, 17, 29-39. Stevens, S. S. (1971). Issues in psychophysical measurement. Psychological Review, 78, 426-450. Stevens, S. S., & Greenbaum, H. B. (1966). Regression effect in psychophysical judgment. Perception & Psychophysics, 1, 439446. Stroop, J. R. (1935). Studies of interference in serial verbal reaction. Journal of Experimental Psychology, 18, 643-661. Thomdyke, P. W. (1981). Distance estimation from cognitive maps. Cognitive Psychology, 13, 526-550. Townsend, J. T. (1990). Serial vs. parallel processing: Sometimes they look like tweedledum and rweedledee but they can (and should) be distinguished. Psychological Science, 1, 46-54. Trabasso, T., Riley, C. A., & Wilson, E. G. (1975). The representation of linear order and spatial strategies in reasoning: A developmental study. In R. Falmagne (Ed.), Psychological studies of logic and development (pp. 201—229). Hillsdale, NJ: Erlbaum. Trick, L. M., & Pylyshyn, Z. W. (1994). Why are small and large numbers enumerated differently? A limited-capacity preattentive stage in vision. Psychological Review, 101, 80-102. Tulving, E. (1983). Elements of episodic memory. Oxford, England: Oxford University Press. Tulving, E. (1985). Ebbinghaus's memory. What did he leam and remember? Journal of Experimental Psychology: Learning, Memory, and Cognition, 11, 485-490. Woocher, F. D., Glass, A. L., & Holyoak, K. J. (1978). Positional discriminability in linear orderings. Memory & Cognition, 6, 165-173.

Received June 17,1998 Revision received October 14,1998 Accepted October 20, 1998

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