Range and sequence effects in judgment - Springer Link

Perception & Psychophysics 1986. 40 (1), 53-61

Range and sequence effects in judgment G. R. LOCKHEAD Duke University, Durham, North Carolina and

J. HINSON

Washington State University, Pullman, Washington

Listeners classified three tones that differed in loudness. Two tones were always similar in intensity (2 dB separation). The third tone was either similar to or different from these two tones. Performance depended on this stimulus range: The greater the difference between two tones fixed in intensity and the third tone, the less precise was the discrimination between the two fixed tones. Performance also depended on sequence: Successive responses were positively correlated. The results show that measures of discriminability depend on stimulus range, and that measures of criterion placements change from trial to trial and depend on stimulus sequence.

ber of stimuli was held constant as stimulus range varied. The result was that the listeners' ability to differentiate between the eight tones was not measurably different between the 4OO-Hz and the 8000-Hz conditions. This means that the variability of judgments of any particular stimulus was greater when the stimuli varied over a larger range. Pollack's (1952) result is consistent with the conclusion of a channel capacity for a stimulus continuum. Such a limit on performance would occur if people attempted to locate each stimulus along a memory scale and if the ability to do this was proportional to the total stimulus range. Then response variability would be proportionally greater for larger range sets. This indicates that channel capacity is associated with stimulus range rather than (or as well as) with number of stimuli. A proportionality effect of this sort is an inescapable feature of voltmeters and many other measuring instruments. For example, for a microscope with a zoom lens, the larger the field of view (range) to be observed, the less the resolution (discriminability) in any portion of that field. Higher magnification provides greater resolution at the cost of reducing the area viewed. Univariate judgment data apparently have this same feature: resolution is proportional to range. In the spirit of Pollack's (1952) study, Gravetter and Lockhead (1973) asked subjects to identify members of various stimulus sets. Range was varied between sets by increasing the physical distance between some stimuli but not others, but the total number of stimuli was constant over conditions. The stimuli were 10 tones (greater than channel capacity) in some conditions and 3 tones (less than channel capacity) in other conditions. The tones differed in intensity. With 10 stimuli (numbered from 1 to 10 in order of intensity), Stimuli 5 and 6 were less often confused with one another when the 10 stimuli were uniformly spread

When humans classify stimuli, their performance on any particular stimulus becomes more variable when a greater number of different stimuli are added to the set. For example, a tone is more precisely identified when it is a member of a set of 6 tones, each separated by 2-dB intervals, than when it is a member of a set of 10 tones, each separated by 2-dB intervals. Such results are consistent with the concept of channel capacity, the idea that there is a performance limit in human discrimination that is analogous to the proven limit on the amount of information that can be transmitted electronically along a wire (Shannon & Weaver, 1949). Many studies show that the amount of information transmitted in judgment tasks increases linearly as the number of stimuli in the set increases, up to some limit, after which the amount of information transmitted is constant. This asymptotic level is considered the channel capacity of the system (Miller, 1956). It is known that performance on individual stimuli in these tasks depends on the range over which stimuli vary and also on the particular stimulus or response that occurred on the most recent trial. In this study we examined the ways in which these two factors, range and sequence, were important to the task of deciding which stimulus had just been presented.

Range Effects In 1952, Irwin Pollack reported a study in which listeners identified eight tones that were equally spaced on a log frequency scale. In one condition the tones ranged over 400 Hz; in another condition they ranged over 8000 Hz. Unlike many studies in which range was increased by adding more stimuli to the set, here the numThis research was supported in part by AFOSR Grant 85-032. Address correspondence to G. R. Lockhead, Department of Psychology, Duke University, Durham, NC 27706.

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Copyright 1986 Psychonomic Society, Inc.

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LOCKHEAD AND HINSON

in intensity than when extreme stimuli were spread in intensity away from the remaining 8 stimuli (e.g., 1 was made quieter, 10 was made louder, and the remaining 8 stimuli were identical in the two conditions). This is a range effect due to remote stimuli; Stimuli 5 and 6 were never confused with Stimuli 1 or 10 in either condition. In one three-stimulus condition in that report, the tones were 1000-Hz sinewaves at 70, 71, and 72 dB intensity. In other three-stimulus conditions, two of these tones were kept at their original values, and the third tone was increased or decreased in intensity. Consistent with Pollack's (1952) finding, discriminability between the unchanged tones was poorer when the stimuli varied over a large range than when they varied over a small range. That is, increasing the separation of the third tone from the other two tones decreased the ability of listeners to identify the unchanged tones. The results were well described by the equation

(lId')2 = k

+ aR2,

(1)

where d' is discriminability as defined by statistical decision theory, k and a are constants, and R is the range over which criteria must vary in order for the listener to discriminate between all stimuli in the set (see Gravetter & Lockhead, 1973, pp. 213-214, for derivations). Whenever it has been examined, Equation 1 has indicated a performance decrement with increasing range. Another measure, information transmission (IT), is not always so consistent. With nonuniformly spaced stimuli, this logarithmic measure sometimes increases with increases in stimulus range, even when the subjects' precision in identifying each stimulus value decreases. This will occur whenever nearly perfect performance on the spread stimuli increases IT (compared to the normal case) to a greater degree than the range effect on the nonspread stimuli decreases IT. The present study was based on the assumptions that the ability of subjects to identify a stimulus value is associated with range and, as discussed next, that response selections on any trial are associated with the spacing between successively presented stimuli, that is, with sequence (Hartman, 1954; Lockhead, 1984; Parducci & Perrett, 1971).

Sequence Effects An early demonstration of sequence effects was reported by Garner (1953), who had listeners identify tones that differed in intensity. Although successive stimuli were selected randomly, successive responses were positively correlated. This result has been replicated often. Responses tend toward the stimulus and/or response value of the prior trial (Jesteadt, Luce, & Green, 1977; Purks, Callahan, Braida, & Durlach, 1980; Triesman & Williams, 1984), an effect called assimilation. Additionally, the more the current stimulus differs from the prior stimulus, the more the response tends toward the prior response.

This indicates that the magnitude of assimilation is correlated with the magnitude of the physical difference between successive stimuli (Holland & Lockhead, 1968).

Comparing Range and Sequence Effects One indication of channel capacity is that responses to any particular stimulus are more variable when that stimulus is a member of a larger set. Similarly, one indication of assimilation is that there are a greater number of different responses to any particular stimulus when it is preceded by a greater number of different stimuli. That is, response variability is both related to range and structured in terms of prior events. These observations allow the suggestion that whatever produces increases in response variability is related to whatever produces sequence effects. We examined this suggestion in the present study. Although there have been many studies of range and many studies of sequential effects, the relationship between the two is not commonly investigated. A reason may be that the two types of effects are usually measured differently. Sequence effects are measured within experimental conditions, because they are made visible only by trial-by-trial examinations of data. Range effects are measured between conditions and are seen by comparing the average of all responses with any particular stimulus when it is used in a small-range set and when it is used in a large-range set. Nonetheless, range and sequence effects may be related, if the following are true for identification tasks: (1) successive responses assimilate; (2) assimilation is greater when the difference between successive stimuli is greater; (3) successive stimuli are more different on average, and are more often different on any particular trial, when stimuli vary over a large range than when they vary over a small range; (4) this indicates, unless additional sequence effects further modify the data, that a stimulus should be assigned a greater number of different responses when in a large range set than when in a small range set. EXPERIMENT 1: Range and Sequence Effects Without Feedback Range and sequence effects were examined in an extension of a report showing that discriminability decreases monotonically with increases in the physical range over which judgments must be made (Gravetter & Lockhead, 1973). Sequential measures have not been reported for such data, so it has not been reported whether response variability correlates with sequence effects.

Method Stimuli. The stimuli were lOOO-Hz sine waves ofO.5-sec duration presented binaura1ly through earphones in a sound-attenuating room. There were three tones in each of three conditions: normal, low-spread, and high-spread (Figure I). Tones in the normal condition were 58, 60, and 62 dBA in intensity. In the low-spread con-

RANGE AND SEQUENCE EFFECTS

I~I 2dB

1

2

I

1

3

W I_----..jl I 1

Figure 1. Stimulus spacings for the normal (top), low-spread (center), and high-spread (bottom)conditions used in Experiments 1 and 2. dition, Stimuli 2 and 3 were identical to those in the normal condition, 60 and 62 dBA, and Stimulus I was 4 dB less intense (54 dB) than in the normal condition. In the high-spread condition, Stimuli I and 2 were identical to those in the normal condition (58 and 60 dB) and Stimulus 3 was 4 dB more intense (66 dB) than in the normal condition. Subjects. Six adults with prior experience in judgment tasks were paid for participating. Procedure. The study replicated an earlier absolute judgment study (Gravetter & Lockhead, 1973, Experiment 4). Tones in each condition (normal, low-spread, and high-spread) were presented randomly, with the restriction that each tone precede each other tone an approximately equal number of times. Tones were assigned the responses 1,2, and 3, made on a threekey keyboard. The experimental method was absolute judgment of loudness, with no feedback given after any response. Tested individually, each subject gave 250 responses in each of the three conditions, with conditions assigned in a different order to each subject.

Results The first 50 trials in each condition for each subject were considered practice and are not included in the following analyses. No reported result is affected when these 50

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trials are included. No consistent differences between subjects were detected. Table I shows the frequency, combined over subjects, with which each stimulus was assigned each response in the three conditions. Stimuli I and 3 were rarely confused with one another in any condition. A spread stimulus (Stimulus I in the low-spread condition and Stimulus 3 in the high-spread condition) was identified as a nonspread stimulus on only 2.5 % of opportunities, and a nonspread stimulus was identified as a spread stimulus on only 0.4% of opportunities. Considering that subjects may occasionally strike a wrong key, it is concluded that essentially all confusions are between adjacent, nonspread stimuli. Figure 2 shows the mean response over subjects to each stimulus as a function of the just prior response in each of the three conditions. Assimilation is indicated by this analysis if the average response (the ordinate) to each stimulus (the parameter) is larger when the prior response (the abscissa) was larger, as it was for all 18 pairwise comparisons of this measure in Figure 2. This sequence effect is large. The maximum assimilation possible is 2 response units. This would occur if, for example, Stimulus 2 was called I on all trials on which it followed Response I, and was called 3 on all trials on which it followed Response 3. That extreme outcome would mean there was no discriminability. Except for the spread stimuli, on which there were essentially no errors, the average magnitude of the assimilation seen in Figure 2 is about 0.4 categories, 20% of the maximum possible. A range effect, as well as this sequence effect, is seen in Figure 2. Compared with responses in the normal condition, responses to unchanged stimuli (2 and 3 in lowspread conditions and I and 2 in high-spread conditions) converge and are more extreme in the spread conditions. This is to be expected if spreading the scale increases judgment variability, making the unchanged stimuli more often confused with one another and clearly different from a spread stimulus. Adjacent stimuli were more often confused when the third stimulus was more different from them. This is consistent with earlier reports that used many as well as few stimuli and that used a variety of ranges. Also, successive responses were positively correlated. This is consistent with prior reports of assimilation: responses tend to be greater (less) when the prior response was large (small). The purpose of Experiment I was to learn whether range effects and sequence effects might be attributable

Table 1 Frequeocy With Which Each Stimulus Was Assigned Each Response in Experiment 1 Low-Spread Condition Normal Condition High-Spread Condition Response Response Response 2 3 Stimulus I 2 3 Stimulus I 2 Stimulus 3 54 dB 14 0 58 dB 271 118 7 58 dB 229 167 382 o 71 262 63 60 dB 107 283 60 dB o 249 147 60 dB 6 66 dB I 5 408 62 dB 2 104 308 o 85 329 62 dB

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LOCKHEAO ANO HINSON

-oJ

~

3

a: t-

Z

0

W

2

(f)

~

8N=3 8N=2

~

8N=1

High Spread

Normal Spread

Low Spread

Z

0--0 0- 1 3

0-=

--0

W

en z

High Spread

Normal Spread

Low Spread

Z

3 0

2

2

0

0

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0

3

1

:::::= 1

2

3

STIMULUS ON TRIAL N-1 Figure 4. Mean response to each stimulus (the parameter), averaged over subjects, when the prior stimulus was 1, 2, or 3 in each condition in Experiment 2 (feedback).

RANGE AND SEQUENCE EFFECTS

59

Table 2 Frequency With Which Each Stimulus Was Assigned Each Response in Experiment 2

Low-Spread Condition Response Stimulus 1 2 3 351 45 0 54 dB 60 dB 6 266 124 62 dB 5 107 302

Normal Condition Response Stimulus 1 2 3 58 dB 264 126 6 60 dB 43 242 III 62 dB 5 79 330

Usually, performance is less variable and more accurate when feedback is given in judgment tasks than when feedback is withheld. The data in Tables 1 and 2 do not reflect this, at least not strongly. Either feedback was not important to performance here or the subjects in Experiment 1 were generally more reliable than those in Experiment 2. The SDT analysis reported for Experiment 1 was repeated for Experiment 2, except that the reported sequential measures were in terms of prior stimuli rather than of prior responses. The results are reported in Figure 5, where HRs and FARs are reported separately for trials in which the prior stimulus was 1, 2, and 3. For all comparisons available in Figure 5, discrirninability was numerically poorer (the HR, FAR data point is nearer the major diagonal) in the spread conditions than in the normal condition. This replicates the finding in Experiment 1. Also as in Experiment 1, HR and FAR both depend on the prior stimulus. This again indicates that the criterion is not invariant within an experimental condition. Rather, the position of the criterion depends on sequence.

W

~

a: ~

GENERAL DISCUSSION Discrirninability between two stimuli was poorer in these experiments when all stimuli in the set varied over a large range than when they varied over a small range. This is consistent with many prior studies of range effects and of channel capacity. When stimuli vary over a large range, precision in identifying any particular stimulus decreases. Additionally, successive responses were positively correlated in all conditions of both experiments. This is consistent with earlier studies showing assimilation in judgment tasks. Sequence Effects Successive responses are overly similar here (Figures 2 and 4) and in all other examined judgment data (see Lockhead, 1984). In terms of SDT, this trial-to-trial contingency would occur if criteria shifted along the decision axis away from each response (also see Warren, 1985). Such shifts would be seen as hit rates (HRs) and false alarm rates (FARs) that depended on sequence. The anal-

98

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95

95

90

90

Normal

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spread}~

Normal

70

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1

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80

High-Spread Condition Response Stimulus I 2 3 58 dB 263 132 I 60 dB 112 280 4 66 dB 0 6 408

Low Spread

2

2 3

50

3

40 30 2

5

10

20 30 40 50 60 70 80

2

5

10

20 30 40 50 60 70 80

FALSE ALARM RATE Figure 5. HRs and FARs for the low-spread Oeft panel) and high-spread (right panel) conditions in Experiment 2, along with the comparable rates for the normal condition, when the prior stimulus was 1, 2, or 3, averaged over subjects.

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LOCKHEAD AND HINSON

yses reported here (Figures 3 and 5) demonstrate that these rates do depend on sequence. An example describes this dependency. Consider the low-spread, no-feedback condition (Figure 3, left panel). A hit was recorded when Stimulus 3 was called 3; a false alarm was recorded when stimulus 2 was called 3. If the current response was 3, assimilation would mean a tendency for the next response to be large. This means that the criterion for discriminating 3 from 2 moves toward 2, increasing HRs and FARs. Consider a sequence in this condition in which Stimulus 3 was followed by Stimulus 2 and the response to 2 was correct. Because of assimilation, the above-considered criterion now tends away from 2, back toward 3. Relative to the previous trial, this increases the probability that the next stimulus will be called 2, decreasing HRs and FARs compared with those obtained when the prior response had been 3. Suppose, instead, that the response to Stimulus 2 had been 1. Then the criterion moves even closer (or more reliably) toward 3 than when the response had been 2. This is because assimilation is greater when successive events are more different, and 1 is more different from 3 than is 2. This results in even more greatly reduced HRs and FARs. That such results occurred regularly in the low-spread condition is seen in the left panel of Figure 3. The same analysis shows that sequence determines HR and FAR in high-spread data as well (right panel of Figure 3). This analysis also describes relations between sequence, HR, and FAR in the feedback data (Figure 5), although these results are not as regular as those in the no-feedback data. The reason for this reduced contingency between successive trials is that feedback gives the subject information that can be used to correct or otherwise adjust the relation between the response scale and the stimulus scale (Ward & Lockhead, 1971). Nonetheless, criterion shifts associated with prior stimulus values are still quite visible in Figure 5.

Range Effects

There was reason to expect that all range effects would be due to successive stimulus differences. If this were so, then channel capacity findings would be explained by sequence effects. This line of reasoning, which is based on a summary of observed sequence effects, suggests that the following may be true of identification tasks: (1) Each stimulus is compared with the memory of the prior stimulus. (2) Successive comparisons are more difficult or less precise when successive stimulus differences are large. Thus, performance in this case is relatively poor. (3) It is statistically true that successive stimulus differences are larger on average and larger more often in large range sets than in small range sets. (4) Therefore, average performance might be expected to be poorer on large range sets than on small range sets. This analysis may correctly describe some of the processing involved, but it cannot be all of the story con-

ceming range. If it were, HRs and FARs would be the same in narrow-range conditions as in wide-range conditions on trials following a nonspread stimulus, because stimuli and successive stimulus differences would then be identical in the two conditions. In fact, however, performance is not the same in these two conditions. The ratio HR/F AR is consistently larger in the normal set than in the spread sets (Figures 3 and 5). This is true even when the prior stimulus and the current stimulus were physically identical in the two conditions. This indicates that discriminability as measured here was better for the small range sets than for the large range sets. Hence, there is an unidentified effect of range on discriminability, in addition to the one-trial-back sequence effect measured here. CONCLUSIONS When subjects are asked to identify the value of some attribute of a stimulus, discriminability, response variability, and mean response all depend on stimulus sequence and on the range over which judgments are made. Although univariate judgment tasks are simple to describe, these complex data demonstrate that they are not simple for subjects to perform. To identify an attribute's value in absolute judgment tasks using stimuli that vary along a single physical dimension, people (and birds; see Hinson & Lockhead, 1986) apparently remember the recent past (the prior stimuli and responses and feedback) and classify the stimulus in terms of its relations to those memories. Memories are often unreliable, calculating relations between memories and the current perception can be complex, and judgments are often biased. Consequently, responses are often in error. These errors are not random. They depend lawfully on context and on sequence: Discriminability for fixed stimuli decreases monotonically with increasing range of the other stimuli in the set, successive responses are positively correlated, and criteria for judgment shift away from the value of the prior trial. Clearly, attributes' values are not identified simply or directly. Judging the value of a stimulus attribute is a dynamic process and a complex task, and the data produced by such tasks reveal some aspects of how memory functions.

REFERENCES W. R. (1953). An informational analysis of absolute judgments of loudness. Journal ofExperimental Psychology, 46, 373-380. GRAVETIER, F., & LocKHEAD, G. R. (1973). Criterial range as a frame of reference for stimulus judgment. Psychological Review, 80, 203-216. GREEN, D. M. (1964). Consistency of auditory detection judgments. Psychological Review, 71, 392-407. HARTMAN, E. B. (1954). The influence of practice and pitch-distance between tones on the absolute identification of pitch. American Journal of Psychology, 67, 1-14. HINSON, J., & LOCKHEAD, G. R. (1986). Range effects in successive discrimination procedures. Journal of Experimental Psychology: Animal Behovior Processes, 12, 270-276. GARNER,

RANGE AND SEQUENCE EFFECTS HOLLAND, M. K., & LOCKHEAD, G. R. (1968). Sequential effects in absolute judgments of loudness. Perception & Psychophysics, 3, 409-414. JESTEADT, W., LUCE, R. D., & GREEN, D. M. (1977). Sequential effects in judgments of loudness. Journal ofExperimental Psychology: Human Perception & Performance, 3, 92-104. LocKHEAD, G. R. (1984). Sequential predictors of choice. In S. Kornblum & J. Reguin (Eds.), Preparatory states and processes (pp. 2747). Hillsdale, NJ: Erlbaum. MILLER, G. A. (1956). The magical number seven, plus or minus two. Psychological Review, 63, 81-97. PARDUCCI, A., & PERRETT, L. F. (1971). Category rating scales: Effects of relative spacing and frequency of stimulus values. Journal of Experimental Psychology, 89, 427-452. POLLACK, I. (1952). The information of elementary auditory displays: II. Journal of the Acoustical Society of America, 24, 745-749.

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PURKS, S. R., CALLAHAN, D. J., BRAIDA, L. D., & DURLACH, N. I. (1980). Intensity perception: X. Effect of preceding stimulus on identification performance. Journal ofthe Acoustical Society ofAmerica, 67, 634-637. SHANNON, C. E., & WEAVER, W. (1949). The mathematical theory of communication. Urbana: University of Illinois Press. TRIESMAN, M., & WILLIAMS, T. C. (1984). A theory of criterion setting with an application to sequential dependencies. Psychological Review, 91, 68-111. WARD, L. M., & LOCKHEAD, G. R. (1971). Response system processes in absolute judgment. Perception & Psychophysics, 9, 73-78. WARREN, R. M. (1985). Criterion shift rule and perceptual homeostasis. Psychological Review, 92, 574-584. (Manuscript received October 28, 1985; revision accepted for publication May 27, 1986.)