Within and cross dimensions 1 Running Head: WITHIN AND CROSS DIMENSIONS Response Selection modulates Visual Search Within And Across Dimensions

In feature search tasks, uncertainty about the dimension on which targets differ from the surrounding nontargets hampers search performance relative to a situation in which this dimension is known in advance. Typically these cross-dimensional costs are associated with less efficient guidance of attention to the target. In the present study participants either had to perform a visual search task, i.e., search for a withinor cross-dimensional target element or had to perform a nonsearch task, i.e., respond to a withinor cross-dimensional target element presented at the center of the visual field. The results showed similar effects both in search and non-search conditions: preknowledge of the target-defining dimension gave faster response times than when the dimension was unknown. Similar results were found using a trial-by-trial cueing. It is concluded that effects that typically have been attributed to early top-down modulation of attentional guidance may represent effects that occur later in processing possibly related to response selection factors. Within and cross dimensions 3 Response Selection Modulates Search Within And Across Dimensions. How do we select information from the environment? This has been a topic of research for the last twenty years. Typically, the paradigm of visual search is one of the most widely used methods to study the way we select information from the environment. In this paradigm, participants have to detect one defined target that is presented among a variable number of nontarget elements. In most versions of this paradigm, the target either differs from nontargets in one dimension (i.e., a feature search task), or it differs in two (or more) dimensions (i.e., a conjunction search task). Typically, observers detect the presence or absence of the target. Time to detect the target is plotted as a function of the number of items in the display (set size). For the simple feature searches, detection of the target is independent of the number of nontargets, as shown by a flat function relating set size to reaction times (RTs). This result is taken as evidence for a parallel, efficient search process in order to detect the target. Feature search is sometimes referred to as singleton search or pop-out target detection. In a conjunction search, however, the corresponding function is linearly increasing. This pattern has been taken as evidence for a serial, inefficient search process (Treisman & Gelade, 1980). Typically, in feature search both the target dimension (e.g., color) and the target feature value in this dimension (e.g., red) are constant and known to the observer. For example, observers consistently search for red amongst green items. Recently, there has been a renewed interest in feature search (e.g., Cohen & Magen, 1999; Müller, Heller, & Ziegler, 1995; Treisman, 1988; Wolfe, Butcher, Lee, & Hyle, 2003). Instead of keeping the target identity the same across trials, the identity of the target varies across trials. For example, the target may be a red horizontal line or a green horizontal line amongst a variable number of gray horizontal lines (within-dimensional search) or the target may be a red horizontal line or a gray vertical line among gray horizontal lines (cross-dimensional search). The consequence of varying the target identity randomly across trials is Within and cross dimensions 4 that observers do not know what target is going to be presented on the next trial. Usually, feature value uncertainty is compared with dimensional uncertainty. Treisman (1988) was the first to investigate these two types of uncertainty. In a withindimensional search condition, the target dimension was constant (e.g., orientation), but the target feature value was unpredictable (left-oriented, right-oriented or horizontal). In a cross-dimensional search, the target dimension was unpredictable (color, orientation, or size), but the feature value within a particular dimension was constant (e.g., in color dimension the target is always red). A cross-dimensional cost of about 100 ms was found relative to within-dimensional search. Müller, Heller, and Ziegler (1995) replicated the cross-dimensional cost and explained their findings by assuming that pop-out target detection must be based on the output of dimension-specific saliency maps. Furthermore, Found and Müller (1996) described a dimension-specific intertrial facilitation effect: if a target was preceded by a target defined along the same dimension, detection was faster relative to a preceding target defined along a different dimension. To explain these effects, Müller and colleagues (Krummenacher, Müller, & Heller, 2001, 2002; Müller et al., 1995; Müller, Reimann, & Krummenacher, 2003) proposed a dimension-weighting account of visual search, according to which master map units compute the weighted sum of dimension-specific saliency signals in parallel. If the dimension of the target is known in advance, that dimension is assigned a larger weight than the other dimensions, allowing a faster detection of the target. However, if the target-defining dimension is not known in advance, a particular dimension can not be given preferential treatment and thus the master map salience signal might stay longer below threshold required for response. Thus, fast target detection requires the target dimension be weighted sufficiently to amplify the saliency signal generated within this dimension above the detection threshold. Dimension change incurs a cost because attentional weight must be shifted from the old to the new dimension. Within and cross dimensions 5 Müller and colleagues found besides a dimension-specific intertrial effect, also a featurespecific intertrial effect for color targets: detection of a color singleton (e.g. red) was facilitated when a color singleton defined by the same color (red) was detected in the previous search trial(s) relative to when another color singleton (e.g. blue) was detected (see also Hillstrom, 2000; Kumada, 2001). They explained this by dividing the color dimension in relatively independent subdimensions, each computing feature contrast within separate ‘wavelength’ channels. The dimensional weighting account can be applied in these sub-dimensions in the same way as in the broader dimensions, e.g. in the dimension shape (Found & Müller, 1996). In line with these results, Maljkovic and Nakayama (1994) have demonstrated also featurespecific intertrial effects for color targets. They referred to this phenomenon as priming of pop-out. Maljkovic and Nakayama (1994) showed that even though participants knew the upcoming target feature, this did not influence the repetition effect. They argued that these repetition effects are passive and autonomous, and not influenced by top-down control. However, Hillstrom (2000) found also a feature-specific intertrial effect, but with responses faster to trials in an alternating sequence (in which the participants knew the color of the target on each trial) relative to a random sequence. This suggests that there can be a top-down modulation on the feature repetition effect. Indeed, in a recent study of Müller, Reimann and Krummenacher (2003), observers were precued either to the most likely target-defining dimension or to the most likely feature value. This trial-by-trial cueing procedure reduced, but did not abolish, the intertrial effects. Müller and colleagues argued that topdown dimensional control can modulate stimulus-driven processes in the detection of pop-out signals. Closely related to the dimensional weighting theory is the Guided Search account of Wolfe (1994). Guided Search assumes that visual stimuli are analyzed into basic features in different dimension-specific modules (e.g., color, orientation). The activation for each stimulus is calculated, Within and cross dimensions 6 separately in each dimension module. This activation is based on differences between the items (bottom-up) and on task demands (top-down). These activations are summed onto an activation map. In visual search, focal attention is guided to the location with the most activation. In a recent study, Wolfe, Butcher, Lee and Hyle (2003) investigated the contributions of topdown and bottom-up processes in feature search tasks, by means of varying the uncertainty about the target’s feature value and dimension. They used a fully mixed condition in which both the target dimension and the target feature value were uncertain from trial to trial. Also, items that were targets on one trial can appear as distractors an another. For example, on one trial the target could be a red horizontal line with green horizontal lines as distractors, whereas on a next trial the target could be a green horizontal line with red horizontal lines as distractors. This method increased uncertainty about the feature and dimension of the target, in order to obtain less top-down information. Note that Wolfe et al. (2003) used the term top-down guidance even though this effect is typically referred to as stimulus identity (e.g., Posner, 1978). Wolfe et al. (2003) reasoned that implicit knowledge of what happened on a previous trial can help tuning the sensory systems for the next trial. Whereas Wolfe and colleagues called these intertrial effects the result of top-down guidance, Maljkovic and Nakayama (1994) considered these very same effects as the result of passive bottom-up priming and not influenced by top-down control. Wolfe et al. (2003, Experiment 3) showed that intertrial effects are based more strongly on target than on distractor identity. Furthermore, the results revealed a cost for cross-dimensional relative to within-dimensional search. Wolfe and colleagues suggested that these RT differences might be based on the salience of the difference between the target and the non-targets. The activation of the target is considered as the signal; the activation of the non-targets as distracting noise. This signal to noise ratio (S/N ratio) is a hypothetical measure of the size of the signal guiding attention to the target among its non-targets. Top-down processes act to set weights to Within and cross dimensions 7 optimize the S/N ratio. In a cross-dimensional condition, all features are comparable and thus receive equal weight. In a within-dimensional condition, however, one dimension receives the strongest weight. Consequently, this gives an advantage for the within-dimensional condition. Cohen and Magen (1999) suggested another explanation for the cross-dimensional cost. They argued that this effect reflects response stage processes and not perceptual processes as proposed by Müller and colleagues (Müller et al., 1995; Found & Müller, 1996) and Wolfe et al. (2003). They also compared withinand cross-dimensional search. However, they changed the stimulus-to-response mapping from a present/absent task (as in Müller et al., 1995) to a discrimination task (either between two features in one dimension, or between two dimensions). They reasoned that if perceptual processes caused the difference between the two conditions, a different stimulus-to-response mapping should not affect the cross-dimensional cost. Instead, if such a difference would be obtained, the results should be attributed to response selection processes. They found that cross-dimensional search was at least as efficient as within-dimensional search. To explain these results, they refer to the response selection model of Cohen and Shoup (1997). In this model, visual stimuli are analyzed into features in different dimension maps (see also Cave & Wolfe, 1990; Cohen, 1993; Treisman & Sato, 1990). More importantly, they assume that after visual selection, the response assignments to single features are determined separately within each dimension module. In other words, there is not a single response selection mechanism, but there is one for each dimension module (see also Mordkoff & Yantis, 1993). Recently, the model was elaborated by Cohen and Feintuch (2002), resulting in a visual system linking perception and action, referred to as the dimensional action system. However, these results can also be explained by the dimension-weighting theory. In the intra-dimensional task, the target’s identity had to be determined, whereas in the cross-dimensional task, only the target’s dimension was necessary for a correct response. This resulted in an advantage for the cross-dimensional condition. This was also Within and cross dimensions 8 pointed out by Cohen and Magen (1999, p.306). The hypothesis that it is easier to detect a dimension of the target than the target feature, was directly put to test and confirmed by Mortier & Theeuwes (submitted). The aim of this study was to distinguish between a search-based account and a responsebased account. Guided Search (Wolfe et al., 2003) assumes that cross-dimensional costs and intertrial facilitation are due to speeding up or slowing down the actual search for the singleton target. In other words, this theory assumes that the within-dimensional search is faster because the actual search for the feature target becomes faster. Also, intertrial facilitation occurs because the search for the singleton target is speeded. Recent work by Theeuwes, Reimann & Mortier (submitted) suggests that these effects may have nothing to do with actual search. In the present study we examined cross-dimensional costs and intertrial facilitation (dimension-specific or featurespecific) in conditions in which there was no search at all. If these effects occur in a non-search task, this would indicate that these effects cannot be attributed to search processes. If these effects are not present when the search component is removed, then it is fair to argue that crossdimensional costs and intertrial facilitation are related to the actual search process. In Experiment 1 and 2 participants either had to perform a visual search task, i.e., search for a withinor cross-dimensional target element or had to perform a non-search task, i.e., respond to a withinor cross-dimensional target element presented at the center of the visual field. Experiment 3 and 4 used a trial-by-trial cueing procedure in a non-search task. Experiment 1 We examined whether a cross-dimensional cost was specific for search processes. One way to determine this is to eliminate search. Consequently, there is no need to guide attention to the target. We compared a classic feature search task, in which participants have to discern the presence or absence of the target, with a non-search task. In this non-search task only one stimulus is presented and observers had to indicate whether the stimulus is a target or not. Both tasks had two Within and cross dimensions 9 conditions: a within-dimensional condition, in which the dimension of the target is known in advance and a cross-dimensional condition, in which the dimension of the target is uncertain. Method Participants. Eight undergraduates, ranging in age from 19 to 23 years participated as paid volunteers. All participants had normal or corrected-to-normal vision and were naive as to the purpose of the experiment. Apparatus and Stimuli. Participants were seated in front of a computer monitor with their heads fixed on a chinrest. Viewing distance was approximately 75 cm. All participants were instructed not to move their eyes during the trials. The display background was black (0.6 cd/m). In the search task, the display contained stimuli on an imaginary circle drawn around the center of the display with a radius of 3.6 degrees of visual angle. The display size existed of 3, 6 or 9 items. The position of each element was randomly chosen, the only restriction being that distances between neighboring display elements were equal. In the non-search task, the display contained only one stimulus, which appeared randomly on the imaginary circle to keep the displays similar. Both tasks had two conditions, a withindimensional condition and a cross-dimensional condition. In the within-dimensional condition the target was a colored circle, either yellow, green or red. In the cross-dimensional condition, the target could be a gray triangle (shape), or a big gray circle (size) or a red circle (color). The nontargets in the search task were gray circles. A target-absent trial in the non-search task was one gray circle. All stimuli (yellow, green, red and gray) were equiluminant (approximately 9.0 cd/m). Procedure. Participants began each trial by fixating a central fixation cross. After 700 ms, the stimulus display was presented during 200 ms on a black background (see Figure 1). Observers had 2 seconds to respond. The intertrial interval was 800 ms. The three possible targets were mapped onto one response button and the target-absent trials were mapped onto the other response Within and cross dimensions 10 button. Participants were told to respond as quickly as possible with either left response (“z”button) or right response (“/”-button). When the observers made an error, a tone (300 Hz ) was presented for 100 ms. ------------------------------------Insert Figure 1 about here ------------------------------------Design. All observers participated in the searchand the non-search task. These two tasks were blocked and presented in counterbalanced order. Each task consisted of two conditions, a within-dimensional condition and cross-dimensional condition. For each task, the conditions were also blocked and presented in counterbalanced order. Each task consisted of 1080 experimental trials, with each condition 540 trials. Each condition comprised 6 experimental blocks, with each block consisting of 90 trials. For each condition, there were 270 target-present trials and 270 targetabsent trials. On the target-present trials, each of the three targets was presented equally often. Only in the search task, the display size was varied, with the three display sizes equally often presented. Within each condition, all types of trials were randomly varied. Participants received 18 practice trials before each condition. At the end of each block there was a short break in which the participants received feedback on their accuracy and reaction times (RTs). The response mapping was counterbalanced across participants. Results RTs of incorrect responses in response to the red target (4.76 %) and RTs longer than 1100 ms (0.04 %) were excluded from the analysis. Reaction Times. The main interest is the comparison of mean RTs for the identical target present in within-dimensional condition and cross-dimensional : the response to the red circle. Only the data in response to this target were analyzed. Within and cross dimensions 11 First, we determined whether in the search-task search for the red target was performed in parallel. An ANOVA was performed on the mean reaction times in the search task with display size and condition as factors. There was no display size effect, [F(2,14) = .32], with the average slope 0.7 ms per item, indicating that the search-task was indeed a pop-out search task. There was a main effect of condition, F(1,7) = 33.28, p < .01. There was a significant interaction between display size and condition, F(2, 14) = 5.74, p < .05. Note however, that this interaction is only due to the deviating pattern at display size 3, in which RTs for the cross-dimensional condition were slower then for the other display sizes, whereas in the within-dimensional condition, the RTs were faster with display size 3 relative to the other display sizes. If display size 3 was excluded from the analysis, then there was no significant interaction, F < 1 (see Figure 2). ------------------------------------Insert Figure 2 about here ------------------------------------Second, a repeated measures ANOVA was performed on the individual mean reaction times of the target present trials with task (search or non-search) and condition (within dimension or across dimensions) as factors. Since only the red circle was present in both conditions, we only analyzed these results. The main effect of task was not significant, F (1,7) = 1.06. Importantly, there was a main effect of condition: F(1,7) = 71.73, p < .0001. The interaction task x condition was not significant, F (1,7) = .34 (see Figure 3). ------------------------------------Insert Figure 3 about here ------------------------------------Within and cross dimensions 12 A separate analysis was performed on the target-absent trials, with task and condition as within-subjects factors. There was no main effect of task, F < 1 (search task: 407 ms, non-search task: 406 ms). There was a main effect of condition, F(1,7) = 89.17, p < .001, with slower RTs in the cross-dimensional condition (439 ms) relative to the within-dimensional condition (374 ms). The interaction between task and condition was not significant, F(1,7) = 1.74, p > .05. Intertrial effects. An ANOVA was performed on the trials containing the red circle as target with task (search or non-search), condition (within dimension or across dimensions) and intertrial transition (same target or different target on the previous trial) as factors. Trials were excluded of which the previous trial was a target-absent trial. There was a main effect of condition, F(1, 7) = 46.76, p < .001 (within: 374 ms, cross: 412 ms). There was no effect of task, F(1, 7) = 1.11 (search: 389 ms, non-search: 397 ms). Importantly, there was a main effect of intertrial transition, F(1, 7) = 17.47, p < .01, with target-repeating trials (382 ms) being faster than target-alternating trials (404 ms). There were reliable interactions between intertrial transition and condition, [F(1, 7) = 11.26, p < .05] and between intertrial transition and task, F(1, 7) = 5.52, p = .051. There was a significant three-way interaction between condition, task and intertrial transition, F(1, 7) = 19.32, p < .01. Planned comparisons showed that there was no significant difference between target-repeating trials (379 ms) and target-alternating trials (381 ms) in the within-dimensional condition of the non-search task, F(1, 7) < 1. Whereas there was a significant difference between the target-repeating trials (387 ms) and the target alternating trials (439) in the cross-dimensional condition of the non-search task, F(1,7) = 26.7 p <.01. In the search task, there was a significant difference between target-repeating trials and target-alternating trials, as well in the within-dimensional condition, F(1,7) = 7.13, p < .05 (targetrepeating trials: 361 ms, target-alternating trials: 374 ms), as in the cross-dimensional condition F(1,7) = 7.8, p< .05 (target-repeating trials: 402 ms, target-alternating trials: 422 ms). Within and cross dimensions 13 Error analysis. The total number of errors in response to the red circle and to target-absent trials was 4.8 % (target misses 4.76 %, false alarms 4.85 %). The errors were calculated for each condition of each task for each participant. An ANOVA was performed on these totals with type of error (target miss or false alarm), task and condition as within-subject variables. There were no main effects: type of error, F <1; task, F(1,7) = 2.04; condition, F < 1. Only the interaction between type of error and condition was significant, F(1,7) =16.24, p <.01, with more target misses (5.3 %) and fewer false alarms (4.2 %) in the within-dimensional condition than in the cross-dimensional condition (target misses 4.2 %, false alarms 5.5%). Therefore speed accuracy trade-off effects were not apparent in the data. Discussion Relative to responding to a target of which the dimension is known but the feature value is not known, a cost was found in the feature search task for responding to a target of which the dimension is uncertain. In other words, if participants had to search for a target, they were faster to detect the target if they knew the dimension in advance. These results basically replicate previous obtained results (e.g., Müller et al., 1995; Treisman, 1988). More importantly, however, exactly the same results were obtained in the condition where there was nothing to search. In the non-search condition, there was only one element in the display and exactly the same cross-dimensional costs were found. Indeed, the interaction between type of task (search vs. nonsearch) and condition (cross vs. within) was not reliable (F<1) and 48 ms cost in the search task was comparable with the 42 ms cost in the non-search task. It might be that the main effect of task was obscured, since half of the participants performed first the search-task and then the non-search task, and half in reversed order. In the non-search task, the task was to identify the color of the target in order to discriminate it from the non-target. In the search task, however, only detection of the target was needed. It could be that the participants who first performed the non-search task, carried over this identity analysis to the Within and cross dimensions 14 search task. If this would be the case, it would be difficult to find an effect of task. However, there was no reliable difference, not even a tendency, between this group and the group which performed first the non-search task, F < 1. Rts were faster if the target was repeated relative to when the target was different from the previous trial. This effect is similar to previous results (Found & Müller, 1996; Hillstrom, 2000). However, this effect was absent in the within-dimensional condition of the non-search task. It remains unclear why this absence occurred (see the results of Experiment 2, which did show this effect. These results suggest that the cross-dimensional effect as typically is found in visual search tasks, may have nothing to do with attentional guidance. However, one may argue that in Experiment 1 there was still some guiding of spatial attention in the non-search task. Indeed, the exact location of the single target element varied from trial to trial. Thus, even though there were no nontargets, one could claim that it was possible that attention was guided to the target. Experiment 2 was designed to investigate this issue. Experiment 2 In Experiment 2, the uncertainty of the target location in the non-search task in Experiment 1 was removed. In this experiment the target was always placed at the same location (i.e. in the middle of the screen). In this way, observers knew the location of the target, and there is no need for localizing the target. Method Participants. Eight undergraduates, ranging in age from 19 to 26 years participated as paid volunteers. All participants had normal or corrected-to-normal vision and were naive as to the purposes of the experiment. Within and cross dimensions 15 Apparatus, Stimuli and Procedure. The apparatus was the same as in Experiment 1. The stimuli were the same as in the non-search condition of Experiment 1. The procedure was identical to the one in Experiment 1 with two changes. First, there was only a non-search task. Second, the target was always placed in the center of the screen. Design. All observers participated in the within-dimensional condition and the crossdimensional condition. These two conditions were blocked and presented in counterbalanced order. Participants received 18 practice trials before each condition. Each condition comprised 4 experimental blocks, with each block consisting of 45 trials. This resulted in a total of 360 experimental trials. For each condition, there were 90 target-present trials and 90 target-absent trials. On the target-present trials, each of the three targets were presented equally often. Within each condition, all types of trials were randomly varied. At the end of each block there was a short break in which the participants received feedback on their accuracy and reaction times. Results The analysis performed on the results was the same as in Experiment 1. Only the results of the response to the red circle were analyzed. Reaction times from incorrect response trials in response to the red circle (4.4 %) and reaction times more than 1100 ms (0.4 %), were excluded from the analysis. Reaction Times and Error Analysis. We compared the mean reaction times of the responses to the red target in the within-dimension (color) condition with those in the cross-dimensional condition by means of a paired t-test. The average difference of 59 ms was significant, t(7) = 3.8, p < .01 (valid: 340 ms versus invalid: 399 ms). As in Experiment 1, a strategy effect needs to be excluded. There was a main effect of type of trial (target present vs. target absent), F(1,7)=18.58, p <.01. However, the RTs for target absent (391 ms) were slower relative to target present trials (370 ms). Within and cross dimensions 16 The total number of errors in response to the red circle and to target-absent trials was 5.2 % (target misses 4.4 %, false alarms 5.9 %). The errors were calculated for each condition for each participant. An ANOVA was performed on these totals with type of error (target miss or false alarm) and condition as within-subject variables. There were no main effects: condition, F < 1; type of error, F(1,7) = 2.59, ns. The interaction was not significant, F < 1. This indicates that the results of the reaction times cannot be attributed to a speed-accuracy trade-off. Table 1 gives the RTs and error percentages of Experiment 2. ------------------------------------Insert Table 1 about here ------------------------------------Intertrial effects. A two-way ANOVA was performed on the trials containing a red circle as target with condition (within dimension or across dimensions) and intertrial transition (same target or different target on the previous trial) as factors. Trials were excluded of which the previous trial was a target-absent trial. There was a main effect of condition, F(1, 7) = 18.9, p < .01, as was also shown in the reaction time analysis. There was also a main effect of intertrial transition, F(1, 7) = 9.89, p < .05, with target-repeating trials (342.5 ms) faster responded to than target-alternating trials (391.5 ms). The interaction was not significant, F(1, 7) = 1.59. Discussion Experiment 2 replicated the results of the non-search task of Experiment 1. A significant cost of 59 ms was found in responding to a target defined in an uncertain dimension relative to a known target-dimension. The intertrial effect was significant for both the within-dimensional condition and the cross-dimensional condition. This is in contrast with Experiment 1, in which the intertrial effect was absent in the within-dimensional condition of the non-search task. It is unclear why this difference occurred. Within and cross dimensions 17 Since the target was consistently located in the center of the screen there was clearly no need to search. Taking together, the results of Experiment 1 and 2 show cross-dimensional costs and intertrial effects as have been reported in previous studies (e.g., Found and Müller, 1996; Müller et al., 1995), yet these effects occur in a task in which there is no need to guide attention to the target. The presence of cross-dimensional costs and intertrial effects under conditions in which there is no search, indicates that search processes are not necessary to induce these effects. A general framework which can explain these findings both under search and non-search conditions is the dimensional action model of Cohen and Shoup (1997; Cohen and Magen, 1999). These findings indicate that when the dimension one has to respond to does not vary from trial to trial (i.e., the within-dimensional condition), the response selection mechanism of a particular dimension (in our case, color) may get primed by the previous trial. In the cross-dimensional condition, there is no priming of just one dimension specific response selection mechanism, since both the color-specific and the shape-specific response selection mechanisms were necessary to perform the task. Even though these findings suggest that the previously reported cross-dimensional costs may have nothing to do with search processes, one may argue that active trial-by-trial dimensional cueing may allow participants to set-up a top-down setting that enables to facilitate attentional guidance to the featural singleton. In a recent study, Müller et al. (2003) employed a trial-by-trial dimensional cueing procedure. Before each trial, a verbal cue (the word “color” and “shape”) indicated the likely target-defining dimension. It is assumed that the cue allows participants to actively set themselves for the likely upcoming stimulus dimension. In terms of the dimensional weighting account (Müller et al., 2003) or guided search (e.g., Wolfe et al., 2003) it is assumed that participants use the advance cue to allocate attentional weight to the likely target dimension. In experiments 3 and 4, we used the same trial-by-trial procedure as Müller et al. (2003). However, Within and cross dimensions 18 instead of using a search task we used a non-search task in which only one element was presented in the display. Experiment 3 In Experiment 3, identical to Müller et al (2003), a symbolic (verbal) cue indicated with 80 % probability the dimension of a single stimulus, presented in the middle of the screen: ‘color’ or ‘shape’. This resulted in two different types of trials: a valid dimension trial, in which the cue indicates validly the dimension of the target (e.g., the cue is ‘color’ and the target is a red circle); and an invalid dimension trial, in which the cue indicates a different dimension as the target dimension (e.g., the cue is ‘color’ and the target is a gray triangle). The main interests w ere the validity effects and the intertrial effects. Participants. Twelve undergraduates, ranging in age from 18 to 27 years participated as paid volunteers. All participants had normal or corrected-to-normal vision and were naive as to the purposes of the experiment. Apparatus and Stimuli. The apparatus was the same as in Experiment 1. The target could be a red or a green circle, a gray triangle or a gray square. The non-target was a gray circle. Procedure. Initially, a verbal cue (“color” or “shape”) w as presented at the center of the screen for 700 ms (see Figure 4). The cue was replaced by a fixation cross. After 850 ms, the stimulus was presented in the center of the screen for 200 ms. Participants had 2 seconds to make a response. When the observers made a error, a tone (300 Hz ) was presented for 100 ms. The intertrial interval was 800 ms. The task was to respond as quickly as possible to the target with either left response (“z” -button) or right response (“/”). The four possible targets were mapped onto one response button and the target-absent trials were mapped onto the other response button. The response mapping was counterbalanced across participants. ------------------------------------Insert Figure 4 about here Within and cross dimensions 19 ------------------------------------Design. Participants received 100 practice trials, followed by 20 experimental blocks, each consisting of 50 trials. There was a total of 1000 experimental trials. Forty percent of the trials were target-absent trials and sixty percent target-present. On target-present trials, half the targets were defined in the color and half in the form dimension. The color targets were half red and half green; and the form targets were half triangle and half square. On target-absent trials, a gray circle was presented. In target-present trials, the cue indicated with 80 % probability the dimension of the target. All types of trials were randomly varied. At the end of each block there was a short break in which the participants received feedback on their accuracy and RTs. The independent variables were target (present, absent), and for target-present trials, cue validity (valid, invalid dimension), target dimension and, depending on the target dimension, target feature value (red, green, square,