Treffer: Serial and Parallel Attentive Visual Searches : Evidence From Cumulative Distribution Functions of Response Times

Participants searched a visual display for a target among distractors. Each of 3 experiments tested a condition proposed to require attention and for which certain models propose a serial search. Serial versus parallel processing was tested by examining effects on response time means and cumulative distribution functions. In 2 conditions, the results suggested parallel rather than serial processing, even though the tasks produced significant set-size effects. Serial processing was produced only in a condition with a difficult discrimination and a very large set-size effect. The results support C. Bundesen's (1990) claim that an extreme set-size effect leads to serial processing. Implications for parallel models of visual selection are discussed.

Serial and Parallel Attentive Visual Searches: Evidence From Cumulative Distribution Functions of Response Times

<cn> <bold>By: Kyongje Sung</bold>
> Department of Psychological Sciences, Purdue University </cn>

<bold>Acknowledgement: </bold>I thank Richard Schweickert for his invaluable help in preparing this article. Special thanks also go to Ehtibar Dzhafarov, Zygmunt Pizlo, Robert Proctor, John Palmer, and Todd Horowitz for their critical comments on earlier versions of this article. This work was supported in part by Air Force Office of Scientific Research Grant FA9550-06-1-0380 to Richard Schweickert.

Two-stage models for visual search, such as those of Neisser (1967) and Hoffman (1979) as well as feature integration theory (Treisman & Gelade, 1980; Treisman & Sato, 1990) and guided search (Wolfe, Cave, & Franzel, 1989; Wolfe, 1994), explicitly or implicitly assume a serial attentive processing stage during visual search. In feature integration theory and guided search, visual search has two different processing stages: a parallel preattentive stage followed by a serial attentive processing stage. In the attentive stage, these models assume that only one object may be processed at a time. Failure of this assumption need not be fatal for a model. For the revised guided search model (Guided Search 2.0) in particular, Wolfe (1994) said that the assumption of seriality could be easily modified. Irrespective of whether any modification is easy, the organization of attentive processes is an aspect of search that clearly needs to be understood.

In the present study, factors intended to selectively influence the attentive processing stage of two-stage models are used to investigate searches considered for one reason or another to require attention and to be serial. These searches are (a) for a target defined by a conjunction of color and form, (b) for a target requiring a difficult form discrimination, and (c) for a target requiring an extremely difficult form discrimination. In each case, the attentional demands are manipulated to directly address the attentive (second) stage of two-stage models. The results confirm that only for an extremely difficult discrimination is there evidence of a serial search, as claimed by Bundesen (1990). Sometimes experiments shed light on a question they were not designed to resolve, and that is the case here. In two experiments in which parallel processing was confirmed, the results suggested further that the search is neither self-terminating nor exhaustive (cf. Sternberg, 1966).

These conclusions are based on response time means (Schweickert, 1978; Sternberg, 1969) and on a response time distribution analysis used in some previous studies (e.g., Fific & Townsend, 2003; Townsend & Nozawa, 1995). This analysis of interaction contrasts of response time means and distributions has been developed to discriminate serial and parallel processing systems directly. The detailed discussion of this method follows the section on the main theoretical issue of the current study, namely, the problem of discriminating serial and parallel processing.

Discrimination of Serial and Parallel Processing

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According to feature integration theory and the guided search model, parallel preattentive stages of visual processing produce a map for each feature of each stimulus in a display. The color map, for example, is produced by determining in parallel the color at each location. In some search tasks, such as finding a red target among green distractors, responses can be based solely on information from the first stage. In other tasks, a second attentive stage is required, when similarity between target and distractors requires attention for resolution, or, in the original feature integration model (Treisman & Gelade, 1980), when attention is required to combine features from different feature maps. In the attentive stage, these models assume that only one object may be processed at a time—that is, processing is serial.

Parallel preattentive processing is indicated when response times do not increase as the number of objects in the display (the set size) increases. This outcome was found, for example, by Treisman, Sykes, and Gelade (1977) when the target was pink and distractors were brown or purple. A slope of 0 for response time as a function of set size is easy to explain with a parallel model but hard to explain with a serial model (Townsend, 1971, 1972; Townsend & Ashby, 1983). A demonstration of serial processing is more demanding, because it is well-known that parallel and serial processing both are capable of producing positive slopes, on both target-present and target-absent trials (Townsend, 1971, 1972; Townsend & Ashby, 1983). A parallel model can produce positive slopes if there are capacity limitations, so the more objects a display contains, the slower each process is. Therefore, a significant set-size effect on performance is not convincing evidence for a serial search. It is also well-known that equality of slopes for target-absent trials and target-present trials is not diagnostic between parallel and serial processing (Townsend, 1971, 1972; Townsend & Ashby, 1983). A different methodology is needed to establish serial processing for cases where search is inefficient.

Separate from data on set-size effect in search, other evidence favors parallel preattentive processing in many cases of visual search. Experiments often manipulate the visual quality (contrast and brightness) of the stimuli with the intention of selectively influencing an early stage of visual processing. For Sternberg’s (1969) additive factor method, if the preattentive stage is selectively influenced by one factor (such as stimulus contrast or brightness) and the attentive stage by another factor, the combined effect on response time of manipulating two experimental factors will be the sum of their separate effects because the two stages are connected in series. Pashler and Badgio (1985) manipulated contrast to investigate the initial encoding of stimuli. The contrast of the whole display was changed (from high to low) while the set size (2, 4, or 6 items) was also manipulated. They found no interaction between contrast and set size and suggested from this that there was parallel encoding followed by a second, identification process.

Other studies using a stimulus contrast or brightness manipulation (e.g., Egeth & Dagenbach, 1991; Townsend & Nozawa, 1995) have adapted a common testing logic designed to test serial and parallel processing more directly. The basic idea was initially investigated by Schweickert (1978, 1982) as a generalization of the additive factor method of Sternberg (1969). Further developments can be found in Townsend and Ashby (1983), Schweickert and Townsend (1989), Townsend and Schweickert (1989), and Schweickert, Fisher, and Goldstein (1992). The key point of the method is to investigate the interaction between two different experimental factors that selectively influence two different mental processes. Details are discussed later, along with recent developments in this approach.

Egeth and Dagenbach (1991) used the method proposed by Schweickert (1978) to test a parallel model against a serial model. In their experiments, two stimuli were presented and their figure–background contrasts were manipulated individually. They assumed it would take more time to process a stimulus in low contrast than one in high contrast. With parallel processing, the response time in the condition when both stimuli are distractors in low contrast would be about equal to the response time in the condition when only one stimulus in a pair of distractors is in low contrast. With serial processing, the effects of changing two stimuli would be additive. Egeth and Dagenbach found evidence for a parallel model in some search tasks (finding Xs among Os and finding Ls among Ts) and evidence for a serial model in a task requiring more difficult form discrimination (finding rotated Ls among rotated Ts). The last result argues against parallel preattentive processing for difficult discriminations, if contrast is assumed to influence only preattentive processing. However, a decrease in contrast can produce a decrease in acuity, and it is possible the contrast change consequently produced a change in attention demands. The last argument provides part of the motivation for the experiments here, in which attention demands are manipulated directly.

Experiments reported by Townsend and Nozawa (1995) using a detection task shed further light on parallel preattentive processing in visual search tasks. The method they used to test various serial and parallel models was an advance over that used by Egeth and Dagenbach (1991). In essence, they examined the pattern in the interaction contrast function of response time survival functions, in addition to the pattern in response time means. The survival function is closely related to the cumulative distribution function (CDF); the survivor function at t is simply 1 minus the CDF at t. More details about the interaction contrast function and the predictions based on its pattern are given below. In the Townsend and Nozawa detection experiments, the brightness of two simple LED dots was manipulated individually, and participants were asked to detect a lighted stimulus, either bright or dim. Thus, the experimental manipulation was very similar to that of Egeth and Dagenbach’s except that the task was about stimulus detection rather than search. Townsend and Nozawa found that two lighted stimuli can be detected in parallel, which implies that the brightness manipulation has an effect on the detection processes in parallel, consistent with the predictions of two-stage models for preattentive processing in search.

To summarize, while evidence for parallel processing has been produced in experiments with a visual quality manipulation (Egeth & Dagenbach, 1991; Townsend & Nozawa, 1995), this does not rule out the possibility of a later attentive serial stage. An exception is evidence for the serial processing found by Egeth and Dagenbach (1991) when contrast was manipulated in a task requiring fairly difficult form discrimination. The question remains, though, whether inefficient search tasks necessarily implicate serial processing. In order to test whether inefficient processing is necessarily serial in visual search, one needs to test for serial processing across a range of different task difficulties for which two-stage models assume serial processing. The experiments reported here directly address this issue using experimental factors that selectively influence the second stage of two-stage models and a response time distribution analysis, as discussed in the following section.

Methodology

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Let us assume we can represent the mental processes required to perform a task as a type of network called a critical path network. In this type of network, each pair of processes is related in one of two ways: Either one of them must follow the other, or neither must follow the other. For the task to be completed, all the processes in the network must be completed. A process starts when all its immediate predecessors are finished. The time required to complete the task on a given trial is the time to complete all the processes on the longest path through the network, called the critical path. This type of network has a long history in experimental psychology. Processes in series and processes in parallel are special cases, but networks of arbitrary complexity can be analyzed (Fisher & Goldstein, 1983; Goldstein & Fisher, 1991; Schweickert, 1978). Let us further assume that we have two experimental factors, A and B, that selectively influence two different mental processes, a and b. Suppose that each factor has two different levels, 1 (easy) and 2 (difficult), and the duration of the corresponding mental process is increased by changing the factor level from 1 to 2. Schweickert (1978) showed that the interaction between factors is different depending on how those mental processes, a and b, are organized in the network. The mean interaction contrast (mean IC) is calculated using the overall response times: <anchor name="eq1"></anchor> where E(RT11) is the mean response time when Factors A and B are both at their Level 1, and so on. When the two processes, a and b, are concurrent in the network, mean IC is less than 0 (negative interaction). When they are sequential, mean IC is 0 (additivity) or greater than 0 (positive interaction). An exception is that two sequential processes in a special form of network called a Wheatstone bridge network can produce a negative interaction (Schweickert, 1978). Because a Wheatstone bridge is not a practical possibility here, we can assume throughout the article that a Wheatstone bridge is not present.

In recent developments, a similar property diagnostic for serial and parallel processing was derived by Townsend and Nozawa (1995) using survivor functions of response time (or, equivalently, CDFs). Their results were generalized to arbitrary critical path networks by Schweickert and Giorgini (1999) and Schweickert, Giorgini, and Dzhafarov (2000). The findings here are discussed in terms of the familiar feature integration theory, guided search, and two-stage models. However, the diagnostic tests used are distribution free and, moreover, apply to arbitrary critical path networks, including networks containing processes not involved with the search itself, but with sensory, motor, or other activities. Hence the present findings are quite general.

Despite the generality of the method, there are two important assumptions that need to be satisfied in order to obtain a valid conclusion. One is called stochastic dominance, which means that if the duration of a process is prolonged by changing the level of an experimental factor selectively influencing the process (e.g., by changing the brightness of a stimulus, as in Townsend & Nozawa, 1995), then at all times t, the CDF at the easy level should be on top of or touching the CDF for the more difficult level. This is stronger than simply saying the mean response time at the easy level is smaller than that at the more difficult level (Townsend, 1990). Because of this additional assumption, the CDF interaction contrast function provides a more sensitive test. In general, if serial or parallel processing is confirmed using the interaction contrast of CDFs, it will also be confirmed using the mean IC, but not vice versa. The other important assumption is that the durations of all processes should be statistically independent or should satisfy a weaker requirement, conditional independence (Dzhafarov, 2003; Dzhafarov, Schweickert, & Sung, 2004). For more details, readers are encouraged to refer to the works cited.

Suppose as before that there are two experimental factors, each with two levels, 1 (easy) and 2 (difficult). Suppose response times are collected in each of the four combinations of levels. Let CDF11(t) denote the cumulative distribution function of the response times when both factors are at Level 1, and so on. The CDF interaction contrast function at time t is <anchor name="eq2"></anchor> Suppose the network representation and assumptions discussed above are correct, and suppose the two experimental factors selectively influence two processes. If neither process must follow the other (they are parallel, or, in network terminology, concurrent), then the CDF interaction contrast will be positive or equal to zero for all times t. That is, <anchor name="eq3"></anchor> If one process must follow the other (they are serial, or, in network terminology, sequential), then the CDF interaction contrast will be positive at the beginning (time near zero) but change its sign to negative. Further, the net area under CDF IC(t) will be 0 or negative. Figure 1 shows two simple serial/parallel networks and the predicted patterns of CDF IC(t). As just described, when two factors selectively influence the two serial processes T1 and T2, CDF IC(t) changes its sign from positive to negative, and the total area under IC(t) is zero or negative (Figure 1A). When T1 and T2 are connected in parallel, CDF IC(t) is positive or zero at all times t (Figure 1B). Note that predicted patterns of CDF IC(t) are about the behaviors of CDF IC(t) curves, not particular values. Thus, the predictions are qualitative and not quantitative.
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><anchor name="fig1"></anchor>

Other previous work has used the CDF or survival function interaction contrast to investigate memory search (Townsend & Fific, 2004), face perception (Ingvalson & Wenger, 2005; Wenger & Townsend, 2001), and time production with visual search (Schweickert, Fortin, & Sung, 2007).

Experiment 1

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The first experiment examines a task for which there has been debate about serial versus parallel processing. According to feature integration theory as originally formulated, if a target (e.g., a red T) requires for its definition a conjunction of features from the preattentive feature maps (e.g., color and form), attention is required and a serial search results (Treisman & Gelade, 1980, p. 99). Later, Pashler (1987) and Wolfe et al. (1989) concluded that searches for targets defined by conjunctions could be parallel. Consequently, the guided search model (Wolfe et al., 1989) allowed for parallel search for such targets, and feature integration theory was revised to allow parallel search for such targets provided the features are highly discriminable (Treisman & Sato, 1990).

Although parallel searches for conjunctive targets are now thought to be possible, earlier evidence leaves room for argument. Pashler (1987) found equal slopes for response time as a function of set size, for target-present and target-absent trials (for set sizes up to 8). But such equal slopes are not diagnostic for serial versus parallel processing (Townsend, 1971, 1972). Wolfe et al. (1989) found slopes close to 0 but actually significantly greater than 0. While a slope of 0 is evidence for parallel processing, a small positive slope can be produced by a serial model (Townsend, 1971, 1972). It is important to test the current belief of parallel processing with a more conclusive test.

In Experiment 1, the target was defined by a conjunction of color and form. The experiment was designed to overcome the criticism of experiments manipulating the contrast or brightness of the stimuli, where the manipulation influences only an early parallel stage. Instead, the manipulation aimed to change the discriminability, in terms of the form relationship, between distractors and the target. The question was whether the change from easy discriminability to moderate would allow parallel attentive search.

In the current experiment, participants searched for a red T among green Ts, red Os, and special distractors, illustrated in Figure 2. Four items were always presented. The manipulated factors are the presence or absence of the two targetlike distractors (named Type I and Type II distractors). Consider target-absent trials. In the easiest condition (no Type I or II distractors), two green Ts and two red Os were always displayed as distractors. In one of the intermediate difficulty conditions, one red O was replaced with a red upper left corner shape (Type I distractor). In the other intermediate condition, one green T was replaced with a red upper right corner shape (Type II distractor). Finally, in the hardest condition, one green T and one red O were replaced with red Type I and II distractors. Figure 2 shows a typical example of each condition when the target is absent. In the target-present condition, one green T or one red O was randomly replaced with the target, a red T.
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><anchor name="fig2"></anchor>

The subsequent experiments reported in the current study share the same logic and predictions. Thus, the details need to be discussed further at this point. In Figure 2, the only difference between Panels A and B is that a Type I distractor is substituted for one red O. Assuming processes for the unchanged stimuli remain invariant after this substitution, one can reason that the processing time for one item is changed. For that item, the processing time is changed from that for one red O to that for one Type I distractor. If we observe longer response times as a result of a substitution, we can reason that it is because it took more time to process the new distractor than the replaced one.

The special distractors are designed to pass through the early preattentive stage of current two-stage models and arrive at the second stage as likely targets. In the revision of feature integration theory proposed by Treisman and Sato (1990), distractors may be filtered from search in parallel, but only if they are sufficiently different from targets (e.g., when they activate different feature maps). If, as planned, the special distractors are moderately similar to the target, revised feature integration theory holds that the distractors will not be rejected by parallel filtering (at Stage 1). As a result, there will be more possible candidates that need to be attended to in Stage 2, as compared with when the distractors are more dissimilar to targets. In guided search, activation from the earlier, preattentive stage guides the search in the second, attentive stage (Wolfe, 1994; Wolfe et al., 1989) based on a match with the expected target’s features. However, as the special distractors were the same color as the target here, they should get the same contribution to activation from color as the target. Likewise, the special distractors should get about the same contribution to their activation as the target does from the feature of a horizontal line and from the feature of a vertical line (Duncan & Humphreys, 1989). In each case, the special distractors should be strong candidates for being selected as targets as the proposed Stage 2.

It is conceivable that participants need not process red Os or green Ts in the later, attentive stage. This leads to a different conception of the process organization, in which the presence of a Type I or Type II distractor adds a new process in the attentive stage, rather than prolonging the duration of an existing process. Nevertheless, if the Type I and Type II distractors are processed serially, one would expect an increased time for the Type I distractor in one intermediate condition; an increased time for the Type II distractor in the other intermediate condition; and in the hardest condition, an increased time for the Type I distractor plus increased time for the Type II distractor (see Figure 2). Despite the two different possible situations depending on whether red Os or green Ts are processed in the second stage or not, the attentive stage of the task can still be represented technically as a network with four processes in series, with some processes having a duration of 0 in the easier conditions. Similar reasoning applies in later experiments.

Figure 3 shows two possible network models, serial versus parallel, under consideration based on the discussion so far. Each model in Figure 3 represents a possible model for the second stage of two-stage models. If one assumes as before that there are four processes corresponding to four stimuli and the process durations of unchanged stimuli (T0s and T3s in Figure 3) remain invariant by the substitution of other stimuli for other processes (T1s and T2s), these network models and experimental manipulations satisfy the conditions required for the mean IC and CDF IC(t) test (Dzhafarov et al., 2004; Schweickert et al., 2000). The conditions are that (a) the network representation is a directed acyclic serial/parallel network in which all the gates are AND gates; (b) there are two experimental factors that selectively influence two different processes embedded in the network in such a way that when the level of a factor is changed, the corresponding CDFs for the duration of the influenced process exhibit stochastic dominance; and (c) the process durations are mutually independent random variables (Schweickert et al., 2000) or conditionally independent random variables (Dzhafarov et al., 2004) at all levels of the two factors.
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><anchor name="fig3"></anchor>

Note that serial models and two-stage models with a serial processing stage make different predictions from parallel models concerning the patterns of mean IC and CDF IC(t) only for target-absent conditions. Although data from all the conditions are analyzed, the focus here is on the target-absent condition because it requires that participants process all four stimuli to make sure there is no target. If a target is present and the search is self-terminating, the participant might not process all four stimuli, preventing strong conclusions from being made.

Ideally, enough data would be obtained from each participant for an individual analysis, as was done in the experiments of Townsend and Fific (2004) and Ingvalson and Wenger (2005), where participants took part in over 30 sessions. This was not feasible in the current study. A useful aspect of the methodology is that the predictions are qualitative, so it is meaningful to average over participants. For example, if some quantity is predicted to be nonnegative for every participant, then the average over participants is predicted to be nonnegative. It is possible that the true model for individual participants is neither serial nor parallel, or is serial for some and parallel for others, but their average CDF IC(t) shows the pattern for serial or parallel processing. This possibility cannot be rejected, but it is unlikely that the average statistic would show a clear signature of a serial or parallel system under these circumstances.

In many visual search experiments, the display is brief. If parallel processing is found, one could argue that it occurs because participants are forced to use parallel processing as best they can. In the present case, to allow ample time for serial processing to develop (if it is available), the display remained until the participant responded or 10 s elapsed.

<h31 id="xhp-34-6-1372-d270e579">Method</h31>

<bold>Participants</bold>

Fifteen undergraduate students (4 female and 11 male) from Purdue University participated in this experiment for course credit. All reported normal or corrected-to-normal visual acuity and normal color vision.

<bold>Apparatus</bold>

Stimulus presentation and response collection were done on IBM PS2 computers running Micro Experimental Laboratory software (Schneider, 1988). Response times were recorded to the nearest millisecond. Stimuli were presented on a 15-in. color monitor in 640 × 480 graphics mode at a 60-Hz vertical refresh rate. The same apparatus was used in all experiments reported in this article.

<bold>Stimuli</bold>

All stimuli were 8 pixels wide and 9 pixels high. They were displayed in an imaginary 2 × 2 array (18 pixels wide, 20 pixels high, approximately 1 cm × 1 cm; 2-pixel gap between stimuli) centered on a monitor. Distance between the monitor and the participant’s head was approximately 50 cm, so the visual angle was approximately 1.15°.

<bold>Procedure</bold>

The experiment had two sessions, each with eight blocks of trials including one practice block. There were 56 trials in each block. All possible combinations of the factors (target presence, Type I distractor presence, and Type II distractor presence) were randomly presented an equal number of times within a block. Each session took about 50 min.

Each trial started with a fixation cross (“+”) in the middle of the monitor for 1 s, followed by the display. The display remained until the participant responded or 10 s elapsed. Participants were asked to press the z key as soon as they found the target and the slash key if they did not. Feedback (a correct or wrong message) was given for all responses, along with a beep for erroneous responses.

<h31 id="xhp-34-6-1372-d270e608">Results</h31>

<bold>ANOVA of mean response times and error rates</bold>

Erroneous responses were removed (the largest error rate among 15 participants was 5.4%, and the mean error rate was 2.5%). For each possible combination of the factors, response times less than 250 ms or greater than three standard deviations above the mean were defined as outliers. There were 1.51% of such outliers removed from the correct responses. A repeated measures analysis of variance (ANOVA) was conducted, using the mean response time of each participant in each condition as the dependent variable.

The main effect of target presence was significant, F(1, 14) = 35.06, MSE = 2,386.03, p &lt; .0001, partial eta squared (ηp<sups>2</sups>) = .715. The main effect of Type I distractor presence was significant, F(1, 14) = 97.06, MSE = 587.15, p &lt; .0001, ηp<sups>2</sups> = .874. Also, the main effect of Type II distractor presence was significant, F(1, 14) = 39.14, MSE = 1,046.93, p &lt; .0001, ηp<sups>2</sups> = .737. All two-way interactions were significant: target presence and Type I distractor presence, F(1, 14) = 45.58, MSE = 379.81, p &lt; .0001, ηp<sups>2</sups> = .765; target presence and Type II distractor presence, F(1, 14) = 48.64, MSE = 377.36, p &lt; .0001, ηp<sups>2</sups> = .777; and Type I and II distractor presence, F(1, 14) = 17.06, MSE = 203.49, p &lt; .005, ηp<sups>2</sups> = .549. But the three-way interaction was not significant, F(1, 14) = 0.05, MSE = 154.58.

Table 1 shows the mean response times and error rates. As the ANOVA showed, response times tended to be faster when the target was present than when it was absent. Also, presence of Type I and/or Type II distractors increased response times. However, their effects were obvious only in the target-absent condition.
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><anchor name="tbl1"></anchor>

Further analysis showed that when the target was absent, the main effects of Type I and II distractor presence were both significant, F(1, 14) = 103.04, MSE = 665.34, p &lt; .001,ηp<sups>2</sups> = .880, and F(1, 14) = 57.10, MSE = 999.82, p &lt; .001, ηp<sups>2</sups> = .803, respectively. The interaction between Type I and II distractors was also significant, F(1, 14) = 7.21, MSE = 218.00, p &lt; .05, ηp<sups>2</sups> = .340, which implies that the mean IC from the target-absent condition was significantly less than 0. When the target was present, the two main effects and the interaction between presence of Type I and II distractors were all significant: Type I presence, F(1, 14) = 19.03, MSE = 301.62, p &lt; .005, ηp<sups>2</sups> = .576; Type II presence, F(1, 14) = 5.28, MSE = 424.47, p &lt; .05,ηp<sups>2</sups> = .274; and interaction of Type I and II distractor presence, F(1, 14) = 13.66, MSE = 139.07, p &lt; .005, ηp<sups>2</sups> = .494.

Analysis of error rates showed that participants made more errors when the target was present than when it was absent, F(1, 14) = 20.11, MSE = 3.42, p &lt; .001, ηp<sups>2</sups> = .590, which is a common finding in visual search experiments (Zenger & Fahle, 1997). The presence of Type I and Type II distractors did not increase the error rates, F(1, 14) = 0.72, MSE = 2.49, and F(1, 14) = 0.00, MSE = 6.83, respectively. Two two-way interactions were significant: target presence by Type I distractor presence, F(1, 14) = 5.61, MSE = 4.43, p &lt; .05, ηp<sups>2</sups> = .286, and target presence by Type II distractor presence, F(1, 14) = 6.93, MSE = 3.08, p &lt; .05, ηp<sups>2</sups> = .331. This analysis indicates that the effects of Type I and II distractors on error rates were larger when the target was present than when it was absent. However, the Type I distractor presence by Type II distractor presence interaction was not significant, F(1, 14) = 1.60, MSE = 2.65. Also, the three-way interaction was not significant, F(1, 14) = 1.66, MSE = 3.12.

When the target was present, the error rates remained constant regardless of presence of Type I and II distractors. Further ANOVA on error rates showed that when the target was present, no effects were significant. When the target was absent, error rates increased when Type I and II distractors were present, F(1, 14) = 6.77, MSE = 2.95, p &lt; .05, ηp<sups>2</sups> = .326, and F(1, 14) = 4.87, MSE = 2.20, p &lt; .05, ηp<sups>2</sups> = .258, respectively. The interaction again was not significant, F(1, 14) = 0.01, MSE = 2.91.

<h31 id="xhp-34-6-1372-d270e854">Results</h31>

<bold>Mean IC and IC(t) of CDFs</bold>

To see whether the two Type I and II distractors were processed concurrently on target-absent trials, mean interaction contrasts from the 15 participants were calculated individually and then averaged. When the target was absent, the mean IC was –19 (i.e., 553 – 630 – 624 + 682), which is in favor of parallel processing (all times are in milliseconds). The previous ANOVA result on target-absent trials showed that the interaction between Type I and II distractors was significant when the target was absent, which means that the mean IC was significantly less than 0.

Although our focus is on the target-absent condition, the pattern of mean response times in the target-present condition is also interesting. The mean IC from the target-present condition was also negative, as parallel processing would predict. This result should be interpreted with caution, because when the target is present, there is no guarantee that all four objects (or at least the two special distractors) are processed. Post hoc comparisons were performed with the familywise error rate controlled at the .05 level through the Bonferroni procedure. (The same post hoc procedure with the same familywise error rate is adapted in all experiments.) When the target was present, substitution of one special distractor (either Type I or Type II) for one green T or red O significantly increased mean response times (548 to 571 ms and 548 to 578 ms), t(14) = 3.98, p &lt; .005, and t(14) = 5.59, p &lt; .001, respectively. Of note, when one of the special distractors was already present, including the other special distractor did not change the mean response times significantly (571 to 579 ms and 578 to 579 ms), t(14) = 1.56 and t(14) = 0.15, respectively. With self-terminating parallel processing, one would not expect the presence of a special distractor to increase response time when the target is present, but this did not occur. The presence of each special distractor increased response time by about the same amount. With parallel exhaustive processing, one would expect response times with two special distractors to be larger than with only one, but this too was not observed. This pattern suggests that processing on target-present trials was neither self-terminating nor exhaustive. A short further discussion follows Experiment 2, which generated almost identical results.

The evidence for parallel processing is bolstered by the CDF results. To see whether the CDFs satisfy the important assumption of stochastic dominance, the four CDFs from the target-absent conditions were investigated. The CDFs were obtained by calculating 15 individual CDFs and then averaging them. The bin size was 1 ms; thus there are 1,800 equally divided bins from 200 ms to 2,000 ms (the number of bins varied from experiment to experiment depending on the range of response time data, but the bin size of 1 ms was the same). The top panel in Figure 4 shows those four average CDFs. The assumption of stochastic dominance was tested in the following way. First, the difference curve of two CDFs in question was calculated. If the stochastic dominance was satisfied between, say, the easy condition (baseline condition) and the one intermediate condition (Type I only), the difference curve of two CDFs from these conditions should always be greater than or equal to zero for all time t, when the upper CDF (baseline condition) is subtracted by the lower CDF (Type I only). Second, post hoc t tests, as were done in the target-present condition, were performed to see whether the two means of two different conditions in the target-absent condition were significantly different. A significant difference between two means implies not only that two CDFs from these conditions differ but also that the difference curve is not equal to zero for all time t. Note that for two random variables, such as response time, if two means are different, then two CDFs are also different, although the converse is not necessarily true.
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><anchor name="fig4"></anchor>

These two measures, difference curves of CDFs and t tests of the means, together help us investigate whether there is any violation of stochastic dominance. The middle panel in Figure 4 shows four difference curves: the baseline condition (represented as none) against two intermediate conditions (represented as Type I and Type II) and the most difficult condition (represented as both) against two intermediate conditions (there is no specific assumption for stochastic dominance between two intermediate difficulty conditions). As can be seen, the difference curves tended to be positive for all time t with a small dip at about 400 ms in the Type II–both pair, which was not significant. A t test showed that the difference value of the Type II–both CDF pair at time 396 ms was not significantly different from zero, t(14) = –1.94. Note that this is the largest dip in all the difference curves reported here. Also, post hoc t tests on the mean response times showed that the difference curves were not equal to zero for all time t. When the target was absent, the two means in each of two pairs of conditions (none–Type I and none–Type II) were all significantly different (553 vs. 630 ms and 553 vs. 624 ms), t(14) = 8.48, p &lt; .001, and t(14) = 7.42, p &lt; .001, respectively, which indicates that two CDFs in each pair of conditions did differ. Also the two means in two other pairs of conditions (both–Type I and both–Type II) were all significantly different (682 vs. 630 ms and 682 vs. 624 ms), t(14) = 9.89, p &lt; .001, and t(14) = 6.22, p &lt; .001, respectively. Clearly, the assumption of stochastic dominance was satisfied for all CDFs (stochastic dominance between none condition and both condition follows automatically).

The bottom panel in Figure 4 shows CDF IC(t) calculated when the target was absent. The CDF IC(t) tended to be positive for all t. There was a small dip at around 850 ms, but the dip was negligible because its area was only about 0.15 ms. The pattern shows that objects are processed in parallel. Additional two-tailed t tests suggested by Schweickert and Giorgini (1999) indicated that the maximum value of CDF IC at time 523 ms was significantly different from zero, t(14) = 6.55, p &lt; .001, but the minimum at time 856 ms was not, t(14) = –0.37. This again supports the predicted pattern for parallel processing.

Experiment 2

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Experiment 1 found parallel processing in a search task claimed to require attention and serial processing because target identification required a conjunction of features (Treisman & Gelade, 1980). The evidence for parallel processing in Experiment 1, however, confirms more recent conclusions (e.g., Pashler, 1987; Treisman & Sato, 1990; Wolfe et al., 1989), but with a more conclusive method. Experiment 2 was designed to see whether parallel processing occurs in a search thought to require attention for a different reason, because featural similarity makes search inefficient.

According to Duncan and Humphreys (1989) and Wolfe et al. (1989), searching for an upright L among Ts rotated clockwise by 0°, 90°, 180°, and 270° is a very inefficient task because it produces a steep response time slope (about 20 ms/item). The standard conclusion is that stimuli in this task are examined in series (Bergen & Julesz, 1983; Wolfe et al., 1989). Experiment 2 uses this task. Another purpose of Experiment 2 is to address a concern remaining from Experiment 1, where substitution of new distractors not only changed the target–distractor similarity but also added new features to the target-absent display. In Experiment 2, new distractors that shared existing features were added. Unless noted, all other aspects of Experiment 2 (i.e., serial/parallel network models, logic of experimental manipulation, etc.) were the same as before.

Participants searched for an upright L among rotated Ts. For convenience, Ts rotated by 90°, 180°, and 270° are referred to as T90, T180, and T270, respectively. In the baseline target-absent condition, an upright T, a T180, and two Os were presented (Figure 5A). In one of the intermediate conditions, one O was replaced with a T90. In the other intermediate condition, one O was replaced with a T270 (Figure 5B and 5C). These substitutions are expected to change target–distractor discriminability, without adding a new type of feature to the display. In the most difficult condition, two Os were replaced with a T90 and a T270 (Figure 5D). When the target was present, either the upright T or the T180 was randomly replaced by the target letter L, with an exception explained in the Method section. The two manipulated factors were the presence or absence of a T90 and the presence or absence of a T270. These manipulations were aimed directly at altering the second attentive stage of two-stage models.
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><anchor name="fig5"></anchor>

<h31 id="xhp-34-6-1372-d270e1033">Method</h31>

<bold>Participants</bold>

Fourteen undergraduates (8 female and 6 male) from Purdue University participated in this experiment for course credit. All reported normal or corrected-to-normal vision.

<bold>Apparatus</bold>

The apparatus and its parameters were the same as in Experiment 1.

<bold>Stimuli</bold>

Figure 5 shows a display example when the target was absent. Each stimulus was 10 pixels wide and 10 pixels long to make lengths of vertical and horizontal strokes identical. The stimuli were white presented on a black background in a 2 × 2 imaginary array centered on the monitor. The visual angle was approximately 1.2°.

<bold>Procedure</bold>

The procedure was the same as in Experiment 1 except as noted. Sixty-four experimental trials with all possible combinations of factors (target presence, T90 presence, and T270 presence) plus six additional trials were randomly presented in each block. The additional trials were added to prevent an upright T and a T180 always occurring when the target was absent. In these six trials, either one upright T or one T180 was replaced by an O. These trials were not included in analyses.

<h31 id="xhp-34-6-1372-d270e1059">Results</h31>

<bold>ANOVA of Mean Response Times and Error Rates</bold>

Erroneous responses and outliers were removed as before. The mean error rate was 2.4% (the largest error rate among 14 participants was 7.0%). There were 1.93% outliers among the correct responses. Table 2 shows the mean response times and error rates. A 2 (target presence) × 2 (T90 presence) × 2 (T270 presence) ANOVA with repeated measures was carried out.
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><anchor name="tbl2"></anchor>

The ANOVA showed that main effects of the three experimental factors were all significant: target presence, F(1, 13) = 19.14, MSE = 5,141.60, p &lt; .005, ηp<sups>2</sups> = .595; T90 presence, F(1, 13) = 49.74, MSE = 413.64, p &lt; .001, ηp<sups>2</sups> = .793; and T270 presence, F(1, 13) = 132.26, MSE = 299.60, p &lt; .001, ηp<sups>2</sups> = .911. All two-way interactions were significant: target presence by T90 presence, F(1, 13) = 26.64, MSE = 254.85, p &lt; .001,ηp<sups>2</sups> = .672; target presence by T270 presence, F(1, 13) = 25.93, MSE = 318.34, p &lt; .001, ηp<sups>2</sups> = .666; and T90 presence by T270 presence, F(1, 13) = 24.59, MSE = 168.56, p &lt; .001, ηp<sups>2</sups> = .654. The three-way interaction was not significant, F(1, 13) = 0.00, MSE = 170.58.

Further analysis showed that when the target was present, the main effect of T90 presence was significant, F(1, 13) = 11.15, MSE = 167.14, p &lt; .01, ηp<sups>2</sups> = .462, as was the effect of T270 presence, F(1, 13) = 50.59, MSE = 115.74, p &lt; .001, ηp<sups>2</sups> = .796, and the interaction between presence of T90 and of T270 factors, F(1, 13) = 11.93, MSE = 173.77, p &lt; .005, ηp<sups>2</sups> = .478. Similarly, when the target was absent, both main effects and the interaction were significant: presence of T90, F(1, 13) = 50.86, MSE = 501.36, p &lt; .001, ηp<sups>2</sups> = .796; presence of T270, F(1, 13) = 83.68, MSE = 502.19, p &lt; .001, ηp<sups>2</sups> = .866; and interaction between presence of T90 and of T270, F(1, 13) = 12.53, MSE = 165.36, p &lt; .005, ηp<sups>2</sups> = .491.

The analysis of the error rates showed that the presence of the target did increase the error rates, F(1, 13) = 18.27, MSE = 14.01, p &lt; .001, ηp<sups>2</sups> = .584, as did the presence of the T270 distractor, F(1, 13) = 20.95, MSE = 0.98, p &lt; .001, ηp<sups>2</sups> = .617. However, the presence of the T90 distractor did not increase the error rates, and no higher order interactions were significant. Further ANOVA on error rates showed that when the target was present, the error rate increased only when the T270 distractor was present, F(1, 13) = 12.42, MSE = 1.99, p &lt; .005, ηp<sups>2</sups> = .490; no other effects were significant. When the target was absent, no effects were significant.

<h31 id="xhp-34-6-1372-d270e1255">Results</h31>

<bold>Mean IC and CDF IC(t)</bold>

For the means, the same patterns occurred as in Experiment 1. When the target was absent, the mean response time increased from the baseline condition to the two intermediate conditions and from the two intermediate conditions to the most difficult condition. The mean IC was –24 (i.e., 671 – 640 – 629 + 574). Parallel processing was supported in the target-absent condition by a significant interaction of the T90 and T270 factors, indicated in the previous ANOVA results. This showed that the mean IC is significantly less than 0.

Tests for stochastic dominance of four average CDFs when the target was absent were conducted in the same way as in Experiment 1. The four difference curves shown in the middle panel of Figure 6 tend to be nonnegative for all time t. Also, post hoc t tests confirmed that the different curves are not equal to zero for all time t. Two means in two pairs of conditions (none–T90 and none–T270) were significantly different (574 vs. 629 ms and 574 vs. 640 ms), t(13) = 9.40, p &lt; .0001, and t(13) = 9.67, p &lt; .0001, respectively. Also, two means in other pairs of conditions (both–T90 and both–T270) were both significantly different (671 vs. 629 ms and 679 vs. 640 ms), t(13) = 3.90, p &lt; .005, and t(13) = 6.19, p &lt; .001, respectively. Thus, stochastic dominance for all CDF pairs was satisfied.
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><anchor name="fig6"></anchor>

Next, we see that CDF IC(t) in Figure 6 (bottom panel) was positive for all times t, except for a small dip at 1,200 ms. It seems safe to ignore the dip because its negative area is a negligible 1 ms; further, it occurs in the upper tail, which is usually noisy. An additional two-tailed t test showed that the maximum CDF IC at time 542 ms was significantly different from zero, t(13) = 4.25, p &lt; .005. Also, the minimum CDF IC at time 1,192 ms was not significantly different from zero, t(13) = –2.04. These results support parallel processing on the target-absent trials.

When the target was present, the mean response time significantly increased from the baseline condition to the two intermediate conditions, but not from the intermediate conditions to the hardest condition. The same post hoc analysis as in Experiment 1 showed that the substitution of T90 or T270 for one of the Os in the baseline condition increased mean response times (546 to 570 ms and 546 to 579 ms), t(13) = 5.82, p &lt; .001, and t(13) = 6.71, p &lt; .001, respectively. However, when either the T90 or the T270 stimulus was already present, substitution of the other distractor did not increase response time significantly (570 to 578 ms and 579 to 578 ms), t(13) = 1.97 and t(13) = –0.11, respectively. Though the pattern could be a consequence of Type I and Type II errors of statistical tests, it has occurred in two experiments and is thus worthy of note. As in Experiment 1, if processing is independent and parallel, a self-terminating search would not lead to a significant effect of the presence of a special distractor, but an exhaustive search would not lead to the effect of two special distractors being about the same as the effect of only one.

Discussion of Experiments 1 and 2

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The results did not support the proposition that each stimulus was attended to in series as suggested by two-stage models such as feature integration theory (Treisman & Gelade, 1980; Treisman & Sato, 1990) and guided search (Wolfe, 1994; Wolfe et al., 1989). The search task in Experiment 2 is typically inefficient (Wolfe, 1998) and usually produces a large set-size effect (Bergen & Julesz, 1983; Duncan & Humphreys, 1989); nonetheless, a serial processing account was rejected. This is another validation of the warning of Townsend (1971, 1972) that set-size effects by themselves should not be interpreted as evidence for a serial system even if the magnitude of the effect size is large.

The conclusion here is that a search with a steep slope for response time as a function of set size is not necessarily serial and can be parallel. It seems that simple parallel self-terminating or exhaustive models would not work either. Discussion of implications for visual search models follows Experiment 3.

Experiment 3

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Bundesen (1990) and Bricolo, Gianesini, Fanini, Bundesen, and Chelazzi (2002) argued that serial search occurs when and only when there is an extreme set-size effect. The reasoning, in brief, is that both serial and parallel processing can operate in search. Items may be processed more slowly in parallel than in series, but with serial processing, time is also required to shift attention from one item to another. Details of when serial processing is optimal vary from one model to another, but generally the critical comparison favors serial processing when the time to process one item in series exceeds the time to shift attention. The time to shift attention internally from one item to another is unknown, but as a guide Hoffman (1979) estimated the time to shift attention from one display location to another as between 80 and 250 ms (see also Bundesen, 1996). We may thus expect serial processing when slopes are in the range of 80 to 250 ms per item, or greater, rather than when slopes are merely greater than the 30 ms per item that has been a traditional borderline between serial and parallel processing (e.g., Treisman & Gelade, 1980).

Experiment 3 was designed to see whether the method of selective influence would find evidence for serial processing when there is an extreme set-size effect. Single-character items were specially designed to produce very high similarity between the target and the distractors. This makes the search very difficult (Duncan & Humphreys, 1989), so an extreme set-size effect is expected.

An example of single-character items producing an extremely large set-size effect is found in a study by Bricolo, Gianesini, Fanini, Bundesen, and Chelazzi (2002). In their experiments, participants were asked to find a T-shaped target rotated in a specific way (either upright or rotated by 90°, 180°, or 270°). The T-shaped target was somewhat similar to a plus sign because the cross stroke of the T was shifted slightly toward the middle of the stem. Distractors were exactly the same shapes as the target but rotated in different ways from the target; for example, if a target was rotated 90°, distractors were upright or rotated by 180° or 270°. Therefore, participants were asked to locate a shape rotated in a specific way. The slope in the target-present condition was about 250 ms/item, a very extreme response time slope. Bricolo et al. concluded that highly inefficient search indeed recruits serial processing, which was confirmed by analyses of response time distributions from two different experiments. According to this study, a single simple parallel model could not explain the results of two experiments in a consistent way.

The stimuli used in Experiment 3 are similar to those of Bricolo et al. (2002) in that one stroke of the letter T was slightly shifted in the distractors. Participants were asked to find an ordinary letter T rotated by 0°, 90°, 180°, or 270° among Ts whose stems were shifted slightly from center by two pixels. These shifted-stem T distractors were rotated in the same directions as the target. Displays were similar in format to those in Experiment 2. Figure 7 shows example displays when the target was absent. To avoid confusion with the labels for the distractors used in Experiment 2 (rotated Ts), the shifted-stem T distractors used in the current experiment are abbreviated as sT0, sT90, sT180, and sT270.
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><anchor name="fig7"></anchor>

To determine whether the new stimuli chosen here indeed produced an extreme set-size effect, a short preliminary experiment was done (see Appendix). The set-size effect observed in the search task using these stimuli was 128 ms/item for the target-present trials, which was a very large slope. Thus the stimuli chosen were suitable for the purpose of Experiment 3. Also, the slope ratio between the target-present and target-absent conditions was 2.1:1, which is very close to 2:1, the ratio commonly found in experiments with inefficient search.

The basic manipulations and predictions in Experiment 3 were the same as in Experiments 1 and 2. A substitution of a new distractor (sT90 or sT270) for an O was expected to have the same effect as the prolongation of a processing time for the substituted stimulus (e.g., Figure 7A and 7B), and the effects of two such independent substitutions on the response time distributions were expected to generate the different patterns of mean IC and CDF IC(t), depending on the organization of the processes (e.g., Figure 3) for the stimuli.

<h31 id="xhp-34-6-1372-d270e1433">Method</h31>

<bold>Participants</bold>

Sixteen undergraduate students (5 female and 11 male) from Purdue University participated in this experiment for course credit. All reported normal or corrected-to-normal vision.

<bold>Stimuli</bold>

Each character was 10 pixels × 10 pixels. They were presented in an imaginary 2 × 2 array (approximately 1.2° of visual angle) centered on the monitor. Four items were presented on each trial, as in Experiments 1 and 2. The stimuli were white presented on a black background.

<bold>Apparatus and procedure</bold>

The apparatus and procedure were exactly the same as in Experiment 2, including the additional trials of stimuli presentation. Only the stimuli were different.

<h31 id="xhp-34-6-1372-d270e1447">Results</h31>

<bold>ANOVA of Mean Response Times and Error Rates</bold>

Erroneous responses and outliers were removed as before. Table 3 shows mean response times along with error rates. The mean error rate was 4.6% (the largest error rate among 16 participants was 9.7%). There were 1.28% outliers among the correct responses. A 2 (target presence) × 2 (sT90 presence) × 2 (sT270 presence) ANOVA with repeated measures showed that main effects of the three experimental factors were all significant: target presence, F(1, 15) = 89.40, MSE = 16,825.10, p &lt; .001, ηp<sups>2</sups> = .856; sT90 presence, F(1, 15) = 284.77, MSE = 6,760.59, p &lt; .001, ηp<sups>2</sups> = .950; and sT270 presence, F(1, 15) = 392.83, MSE = 4,390.30, p &lt; .001, ηp<sups>2</sups> = .963. Two two-way interactions were significant: target presence by sT90 presence, F(1, 15) = 158.36, MSE = 1,808.05, p &lt; .001, ηp<sups>2</sups> = .913; and target presence by sT270 presence, F(1, 15) = 182.94, MSE = 1,657.97, p &lt; .001, ηp<sups>2</sups> = .924. No other effects were significant.
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><anchor name="tbl3"></anchor>

Further analysis showed that when the target was present, the presence of distractor sT90 significantly increased mean response time, F(1, 15) = 130.36, MSE = 2,787.37, p &lt; .001, ηp<sups>2</sups> = .897, as did the presence of distractor sT270, F(1, 15) = 218.34, MSE = 1,331.53, p &lt; .001, ηp<sups>2</sups> = .936. The interaction between presence of sT90 and of sT270 was not significant, F(1, 15) = 1.36, MSE = 800.93. Similarly, when the target was absent, the presence of sT90 and of sT270 significantly increased mean response time, F(1, 15) = 319.70, MSE = 5,781.27, p &lt; .001, ηp<sups>2</sups> = .955, and F(1, 15) = 368.32, MSE = 4,716.74, p &lt; .001, ηp<sups>2</sups> = .961, respectively. Again, however, the interaction between these two factors was not significant, F(1, 15) = 2.47, MSE = 637.33. This indicates that the mean IC for the target-absent condition was not significantly different from 0.

The results from the target-present condition showed a different pattern of mean response times from the previous experiments. The same post hoc analysis as in Experiments 1 and 2 for the target-present conditions showed that substitution of sT90 or sT270 distractors for an O, when the other distractor was not present, increased mean response times significantly (918 to 1,061 ms and 918 to 1,046 ms), t(15) = 11.38, p &lt; .001, and t(15) = 10.51, p &lt; .001, respectively. However, unlike the results from Experiments 1 and 2, substitutions of sT90 or sT270 when the other distractor was already present also increased the mean response times significantly (1,061 to 1,208 ms and 1,046 to 1,208 ms), t(15) = 12.98, p &lt; .001, and t(15) = 9.30, p &lt; .001, respectively. The interaction between the presence of sT90 and of sT270 was not significant. On the basis of the results from the target-absent and target-present conditions, we can conclude that participants searched for the target by examining each stimulus one by one, even though there were only four stimuli presented.

The analysis of error rates showed that only the main effect of target presence was significant. Participants made more errors when there was a target present than when it was absent, F(1, 15) = 30.78, MSE = 28.92, p &lt; .001, ηp<sups>2</sups> = .672. A two-way interaction between sT90 presence and sT270 presence was significant, F(1, 15) = 5.82, MSE = 1.90, p &lt; .05, ηp<sups>2</sups> = .280. The three-way interaction also was significant: target presence by sT90 presence by sT270 presence, F(1, 15) = 5.67, MSE = 2.33, p &lt; .05, ηp<sups>2</sups> = .274. No other effects were significant.

When the target was present, the interaction of sT90 and sT270 presence was significant, F(1, 15) = 8.27, MSE = 2.93, p &lt; .05, ηp<sups>2</sups> = .355, but no other effects were significant. When the target was absent, although Table 3 shows a tendency of increasing error rates, only sT270 presence significantly increased error rate, F(1, 15) = 7.72, MSE = 6.19, p &lt; .05, ηp<sups>2</sups> = .340. No other effects were significant.

<h31 id="xhp-34-6-1372-d270e1659">Results</h31>

<bold>Mean IC and CDF IC(t)</bold>

For the response times, on target-absent trials, the mean interaction contrast was –18 (i.e., 1,613 – 1,288 – 1,277 + 934). This was not significantly different from 0, F(1, 15) = 2.47, MSE = 637.33. This additivity is evidence of serial processing of sT90 and sT270 distractors.

For the response time CDFs, the top panel in Figure 8 shows no violations of stochastic dominance, which is confirmed by the difference curves (Figure 8, middle panel) and the post hoc t tests for the pairs of means. Two means in two pairs of conditions (none–sT90 and none–sT270) were significantly different (934 vs. 1,277 ms and 934 vs. 1,288 ms), t(15) = 16.53, p &lt; .0001, and t(15) = 18.26, p &lt; .0001, respectively. Also, the means of the other two pairs of conditions (both–sT90 and both–sT270) were significantly different (1,613 vs. 1,277 ms and 1,613 vs. 1,288 ms), t(15) = 17.53, p &lt; .0001, and t(15) = 17.76, p &lt; .0001, respectively. The bottom panel of Figure 8 shows the CDF IC(t) was positive in the beginning and became negative. Two t tests for the maximum (.231) and minimum (–.115) of CDF IC, at times 752 and 1,422 ms, respectively, show that they are each significantly different from zero, t(15) = 10.48, p &lt; .0001, and t(15) = –6.90, p &lt; .0001. The CDF IC(t) clearly showed the pattern expected if the two sT90 and sT270 distractors were processed in series.
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><anchor name="fig8"></anchor>

<h31 id="xhp-34-6-1372-d270e1716">Discussion</h31>

Experiment 3 shows that evidence for serial attentive processing can be found for stimuli producing a large slope in visual search, even when the set size is small. Although CDF IC(t) and mean IC only show directly the serial process organization of sT90 and sT270 distractors, it is a reasonable extrapolation to conclude that all four shifted-stem T distractors were processed sequentially, because all four distractors are about equally similar to the targets (upright and rotated Ts; see Figure 7D).

Furthermore, the pattern of mean response times from the target-present condition suggests that the target itself was not easily discriminated from the distractors. When the target was present, substitution of sT90 or sT270 distractors for Os significantly increased mean response time regardless of the presence of the other distractor, sT270 or sT90, respectively. Also, there was no interaction between sT90 presence and sT270 presence when the target was also present. This additivity indicates serial processing of the sT90 and sT270 distractors on target-present trials. As before, it is reasonable to extrapolate and conclude that in the hardest condition on target-present trials, all stimuli including the target were processed in series.

The results of Experiment 3 along with a supplementary experiment (see Appendix) support the hypothesis of Bundesen (1990) and of Bricolo et al. (2002), that stimuli producing an extremely high set-size effect are processed in series.

General Discussion

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Historically, two-stage models of selection have been developed to explain why some searches are parallel and others serial, as is the case in the experiments reported here. The second, serial stage in such models is assumed to be used by stimuli requiring attention. Serial searches have been proposed at one time or another for targets defined by a conjunction of features (Treisman & Gelade, 1980) and searches producing a large set-size effect (Wolfe et al., 1989).

Here, a conjunction search (for a target defined by color and form) was found to be parallel using experimental manipulation that selectively influences the second stage of two-stage models. There was also evidence for parallel search when there was a moderately large set-size effect (over 20 ms/item). On the other hand, serial processing was found for a search with an extremely large set-size effect (over 100 ms/item). A small set size (four items) is neither necessary nor sufficient for parallel processing. The results indicate a need to refine the notion of which stimuli require serial processing and attention. Overall, the results are in agreement with the hypothesis that serial search occurs when and only when the set-size effect is extremely large (i.e., very inefficient search), an implication of Bundesen (1990, 1996) and of Bricolo et al. (2002).

In the previous experiments, discussed earlier, where the visual quality of stimuli (contrast and/or brightness) was manipulated (Egeth & Dagenbach, 1991; Pashler & Badgio, 1985; Townsend & Nozawa, 1995), the parallel processing stage of two-stage models has been confirmed. These results suggested that the change of contrast and/or brightness of stimuli would have effects in the early parallel stage. However, the evidence for serial processing using the same experimental manipulation was also found in Egeth and Dagenbach (1991). Clearly, if one accepts that the changes in stimulus contrast selectively influence only the parallel stage and not the later serial stage of two-stage models, then the contradictory result of Egeth and Dagenbach is inexplicable.

According to the hypothesis discussed here (e.g., Bundesen, 1990), when visual searches become serial or parallel is determined by the attentional demand of a given task. In Bundesen’s analysis (1990, 1996) the rule for when serial processing is optimal is based on a comparison of the time to process a single item with the time to shift attention from one item to another. It is intuitively obvious that conditions that make processing an item extremely difficult will lead to attention being devoted to one item at a time—that is, to serial processing. Thus, the reason for observing rather contradictory results in Egeth and Dagenbach (1991) is fairly straightforward in this conceptualization. The change of contrast in the search for rotated Ls among rotated Ts, which would be expected to have effects in the early parallel stage, instead makes processing a single item very attention demanding and thereby a serial process.

<h31 id="xhp-34-6-1372-d270e1798">Implication for Search Models</h31>

The experiments reported here were designed to test a specific assumption of two-stage models, but further implications about search models can be drawn. Although the results supported parallel processing in Experiments 1 and 2, independent parallel channel models such as that of Shiffrin and Gardner (1972) have a problem in interpreting the mean response time patterns from the target-present conditions. The problem is that response time increased when one special distractor was present but did not increase further when two special distractors were present. This asymmetric change in mean response time is not compatible with the independent parallel models with either self-terminating or exhaustive search stopping rules. Details about how searches are terminated when the target is present are usually obtained from the effects of changing set size, but changes in set size were not needed here with the method of selective influence. Set size was changed in an additional experiment (see Appendix) for Experiment 3, however, to estimate the set-size effect. In that experiment, the slope for the target-absent trials was approximately twice that for the target-present trials. This is evidence against exhaustive processing and consistent with self-terminating processing (Sternberg, 1966; Van Zandt & Townsend, 1993). The search in Experiment 3 was determined to be serial, so the stopping rule for it may be different from that of the parallel searches in the other experiments.

Two-stage models such as feature integration theory (Treisman & Gelade, 1980; Treisman & Sato, 1990) and guided search (Wolfe, 1994; Wolfe et al., 1989) explain processing that is neither self-terminating nor exhaustive in a natural way. In the revised version of feature integration theory (Treisman & Sato, 1990) some items are inhibited after early processing. In guided search, stimuli may have different activation levels as a result of top-down and bottom-up processing, and in the second stage, attention is given to each stimulus in a prioritized sequence. For example, if a subgroup of stimuli can be distinguished by a salient feature associated with the target, such as color, then participants search those stimuli first (Egeth, Virzi, & Garbart, 1984; Kaptein, Theeuwes, & van der Heijden, 1995). Although it is natural for these models to explain why some items are processed in the second level and some are not, to account for the data here, models must still explain why special distractors would sometimes be processed in the second level and sometimes not.

One post hoc possibility for Experiments 1 and 2 is a parallel attentive search, prioritized as in revised feature integration theory or guided search. Suppose in the second stage two items are selected as a group on the basis of their likelihood, processed in parallel, and if the target is not found, two further items are selected, processed in parallel, and so on. Suppose that the processing within a group of two items is exhaustive, but if the target is found, no further groups are processed. This accounts for the parallel processing found for target-absent trials in Experiments 1 and 2. If one or two special distractors occur on a target-absent trial, they are processed in parallel in the first group and behave as ordinary parallel processes. Suppose one or two special distractors occur on a trial with the target present. The target and one special distractor will have priority; they are processed exhaustively in parallel, the target is found, and processing stops. This accounts for an effect of one special distractor on target-present trials but no further effect of a second special distractor. Also, the serial processing found in Experiment 3 can be explained by allowing only one item to be processed at a time in the second stage, which is the basic structure of two-stage models that assume serial attentive processing. Note that the current discussion is confined to the models, including two-stage models, that fall within the category of serial/parallel network (Schweickert, Giorgini, & Dzhafarov, 2000) under the assumption that the selective influence worked as intended. Models beyond this scope, such as models allowing the violation of selective influence, which may be plausible, are not pursued here.

The explanation presented here is a modification of those of Bundesen (1990, 1996) and Fisher (1982, 1984). The common idea across these models is that the items can be processed in groups, where items in the same group are processed in parallel and the number of such groups (or the number of items in a group, equivalently) varies depending on the task demand. In Bundesen’s (1990) version of a limited-capacity parallel model, multiple objects can be processed together and serial processing is thought to occur only in the extreme situation where the number of objects that can be processed at a time becomes one. And, as other limited-capacity parallel models assume (e.g., Townsend & Ashby, 1983; Ward & McClelland, 1989), processing capacity is divided and assigned to each concurrent process, which determines the duration of a process. In Fisher’s (1982, 1984) queuing models, it is assumed that stimuli arrive at the visual system sequentially but can be processed concurrently up to a certain number of processes, which is greater than one (therefore serial processing is not a part of the model). Also it is assumed that the system has a limited processing capacity.

To account for the present results, I propose a literal fusion of these two models. As has been demonstrated in experiments reported here and in Fisher (1982), the number of concurrent processes may be one (serial processing; Experiment 3) or two or three (parallel processing; Experiments 1 and 2; Fisher, 1982), depending on the task difficulty. Whether multiple items can be processed concurrently is assumed to be determined by the attentional demand of the task and the fixed amount of attentional resource. If a task is very inefficient and the target is not easily discriminated from the distractors, the system may limit the optimal number of processes to one so that the whole attentional resource is devoted to a single process at a time (i.e., Bundesen, 1990). On the other hand, if a target can be efficiently discriminated from distractors, multiple processes can be executed concurrently because each process requires less attentional resource than before.

Note that, as in Fisher (1982, 1984), the proposed modification does not require any functional relationship between the system’s resources and process durations. That is not because the assumption is rejected but because the proposed alternative does not require such an assumption to explain the current results. In many limited-capacity parallel models (e.g., Bundesen, 1990; Townsend & Ashby, 1983; Ward & McClelland, 1989), the process durations are inversely related to the assigned processing capacity, which is a typical way of explaining the set-size effect. As has been shown in Fisher (1982), however, such an assumption may not be necessary to explain the set-size effect when the objects are processed in a small number of groups. This claim that there is no functional relation between process duration and processing capacity does not necessarily entail the stochastic independence between process durations. It is assumed here, however, that process durations are independent or at least conditionally independent (Dzhafarov, 2003; Dzhafarov et al., 2004), which is feasible either way when process durations are not dependent on processing capacity.

<h31 id="xhp-34-6-1372-d270e1908">Conclusion</h31>

The results are clear about when serial and parallel processing occur in the experiments reported here. The data from three experiments together support an implication of the model of Bundesen (1990, 1996), that serial search occurs when and only when the set-size effect is extremely large, and parallel search occurs when the task difficulty is less extreme. Thus, the traditional criterion about when searches become serial needs to be redefined. Also, an implication for the parallel models is that the set-size effect can be effectively explained by allowing stimuli to be processed in small number of groups, which is determined by the system’s processing capacity and task demand, as suggested by Fisher (1982, 1984).

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<h31 id="xhp-34-6-1372-d270e3199">APPENDIX</h31> <anchor name="A"></anchor> <h31 id="xhp-34-6-1372-d270e3200">APPENDIX A: Pilot Experiment for Experiment 3</h31>

The purpose of the experiment was to determine whether the stimuli used in Experiment 3 indeed generate a very large set-size effect. In order to calculate the set-size effect, 8 and 12 stimuli were presented.

Four undergraduate students (2 male and 2 female) from Purdue University participated in the experiment for course credit. All reported normal or corrected-to-normal vision.

Stimuli were the same as in Experiment 3 (see Figure 7). On each trial 8 or 12 characters were presented in randomly selected positions among 16 possible positions of an imaginary 4 × 4 array. The array was about 2 cm × 2 cm, centered on the monitor (approximately 2.29° of visual angle). Stimuli were white on a black background.

The same apparatus was used as in the previous experiments. Participants were asked to find the target (an upright or rotated T) among rotated shifted-stem T-shaped distractors. This is the most difficult condition of Experiment 3 (i.e., Figure 7D). There was a single session of eight blocks of trials including a practice block. There were 48 trials in each block. All other procedures were the same as in the previous experiments.

A repeated measures ANOVA was performed using the mean response times of the 4 participants as input, after removing errors and outliers (as defined in Experiment 1). Experimental factors were target presence and set size. Mean error rate was 9.6%, and the largest error rate among the 4 participants was 12.7%. Participants responded faster when the target was present than when it was absent, F(1, 3) = 30.96, MSE = 380,182.71, p &lt; .05, ηp2 = .912. They also responded faster when the set size was 8 rather than 12, F(1, 3) = 150.06, MSE = 16,344.51, p &lt; .005, ηp2 = .980. The difference in mean response times between the target-present and target-absent conditions was much bigger when the set size was 12 than when it was 8, as indicated by a significant interaction between target presence and set size, F(1, 3) = 35.14, MSE = 8,416.01, p &lt; .01, ηp2 = .921.

Table A1 shows mean response times, error rates, and response time slopes for target-present and target-absent conditions for each set size. The response time slope for the target-present condition was 128 ms/item, indicating the task was extremely inefficient. The slope ratio between the target-present and target-absent conditions was 2.1:1. This is an indication that the search was self-terminating (Sternberg, 1966; Van Zandt & Townsend, 1993).

Submitted: July 1, 2005 Revised: February 5, 2008 Accepted: February 9, 2008