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Taxonomy of DO Ensembles

The dimensional overlap model provides a useful way of talking about compatibility tasks (more info: Why study compatibility effects?). 

When all the individual stimuli used in a task vary on a common stimulus dimension (e.g. red and blue varying on the color dimension), and all the individual responses that are used in that task also vary on a common response dimension (e.g. left and right varying on spatial dimension), they form a stimulus set and a response set, respectively. When these two sets are put together in a larger set, that larger set is called an ensemble.

In addition to a relevant stimulus dimension and a response dimension, a task may also have one or more dimensions: irrelevant stimulus dimensions that subjects are instructed to ignore .

Different task may be characterized by the properties of the ensemble that they use.  If the individual sets in the task are similar, be they a stimulus set and response set, or two stimulus sets, then we speak of that ensemble as having dimensional overlap. (more info: What is Dimensional Overlap?)

This allows us to define a broad framework for classifying different types of ensembles, or tasks,  based on the dimensional overlap, or set-level similarity, of the ensembles in the task. Dimensional Overlap (i.e similarity) is of course a continuous property; however, we can talk about tasks that either do, or not  have overlap between their different components.  A framework with three possible dimensions (relevant stimulus, irrelevant stimulus, response), all of which can either overlap or not overlap, produces a taxonomy of eight possible dimensional overlap ensembles or tasks types.

These eight types constitute the dimensional overlap ensemble taxonomy.

Type Relevant S-R
Overlap?
Irelevant S-R
Overlap?
S-S
Overlap?
Example Tasks
1 no no no CRT task
2 yes no no Fitts task
3 no yes no Simon task
4 no no yes Flanker Task
Stroop-like Tasks
Cross-modal tasks
5 yes yes no Hedge and Marsh task
6 yes no yes (not possible?)
7 no yes yes SS x SR task
8 yes yes yes Stroop task

The first ensemble in the taxonomy is a Type 1 task, which is a standard Choice Reaction Time (CRT) task with no dimensional overlap. This is technically not a compatibility task at all: it contains no dimensional overlap between any of its components. However, it is often used as a “neutral” condition in compatibility experiments in order to establish a comparison point for measuring the benefit of consistency versus the cost of inconsistency (more info: Choice Reaction Time (CRT) tasks).

After the Type 1 task, the taxonomy enumerates all of the possible combinations of dimensional overlap among the three dimensions, all the way up to the Type 8 task, which has overlap among all the dimensions: relevant stimulus, irrelevant stimulus, and response. The well-known Stroop task is an example of a Type 8 task (more info: The Stroop Task).

Click on the links in the above table for a more detailed description of the experiments and results of tasks belonging to each ensemble.

As an easy reference, the table below shows some sample stimulus and response sets that could be used to produce tasks of each type in the taxonomy.

Type Relevant Stimulus
Dimension
Irrelevant Stimulus
Dimension
Response
Dimension
Instructions
1 color vertical
position
left/right
key-press
press the left key for a green stimulus
press the right key for a blue stimulus
2 color digit color  names say “green” for a green stimulus
say “blue” for a blue stimulus
or
say “blue” for a green stimulus
say “green” for a blue stimulus
3 color horizontal
position
left/right
key-press
press the left key for a green stimulus
press the right key for a blue stimulus
4 color color word digit names say “two” for a green stimulus
say “four” for a blue stimulus
5 color horizontal
position
colored left/right
key-press
press the blue key for a blue stimulus
press a green key for a green stimulus
or
press the green key for a blue stimulus
press a blue key for a green stimulus
6 (not possible?)
7 color horizontal position
and color word
left/right
key-press
press a left key for a green stimulus
press a right key for a blue stimulus
8 color color word color names say “blue” for a blue stimulus
say “green” for a green stimulus
or
say “green” for a blue stimulus
say “blue” for a green stimulus

 


 

NOTE: Although the above taxonomy represents the official taxonomy of the ensembles explored by the dimensional overlap model, it is possible to explore extensions of this taxonomy by examining new task dimensions.

For example, Stevens and Kornblum (2000, July) presented an extension of the taxonomy that distinguishes between the response dimension and the goal dimension in a task. The goal dimension is defined as the intended outcome of a response action, which may be different from the response action itself.

Hommel (1993a) performed a variation of the Simon task in which subjects were told to light up a light by pressing a key when a stimulus appeared. In these tasks, subjects either needed to press a right key to light up a light on the right side, or press a left key to light up a key on the right side. Hommel (1993a) showed that this consistency between the response (key position) and goal (light position) had a measurable effect on reaction time. Stevens and Kornblum (2000, July) were able to extend the computational dimensional overlap model to include overlap with a “goal dimension” to account for this effect (more info: The Computational Model).

 

 
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The Stroop Task

The Stroop Task is a choice reaction time task where there is dimensional overlap between all three dimensions of the task: the relevant stimulus, the irrelevant stimulus, and the response.  In the dimensional overlap taxonomy, it is considered a Type 8 task.

Stroop (1935; see also Dyer, 1973; Lu & Proctor, 1995; MacLeod, 1991) studied the effects of an irrelevant color word in a color-naming task. In the simplest and most well-known version of the Stroop task, subjects are told to name the color of a stimulus (e.g. say the word “blue” when they see a blue stimulus). Along with the color, however, a color word (e.g. “blue” or “green”) is also presented. The color word can be either presented in the colors, or super-imposed on a colored background (see MacLeod, 1998). The color word is irrelevant, but it can be either consistent with the stimulus color and the response name (e.g. the word “blue” written in blue ink, requiring a response of “blue”) or inconsistent with the stimulus color and the response name (e.g. the word “green” written in blue ink, requiring a response of “blue”).

 

A simple Stroop task

 

Performance is slower and less accurate when the irrelevant stimulus word does not match the relevant stimulus and response, and faster and more accurate when it matches the relevant stimulus and response. The difference in reaction time is usually called the Stroop effect.

Stroop tasks permit a great deal of variation while still yielding the same basic consistency effect. This basic Stroop effect has been found using shapes and shape names (e.g. Irwin, 1978; Redding & Gerjets, 1977; Shor, 1971), pictures and picture names (e.g. Babbit, 1982; Dunbar, 1986; Rayner & Springer, 1986; Toma & Tsao, 1985) and spatial locations and their labels (e.g. Baldo, Shimamura, & Prinzmetal, 1998; Lu & Proctor, 1995; Palef, 1978; Seymour, 1973; Virzi & Egeth, 1985). Auditory Stroop tasks have also been studied, with typical stimuli being the words “left” and “right” spoken in the left and right ear (e.g. Green & Barber, 1981; McClain, 1983; Proctor & Pick, 1998; Ragot & Piori, 1994; Simon & Rudell, 1967). Although Stroop tasks have most commonly used conceptual dimensional overlap between dimensions (e.g. the learned associations between colors and their names) they have also used perceptual overlap (e.g. flanker stimuli) (e.g. Glaser & Glaser, 1982, 1989; Zhang & Kornblum, 1998).

In this standard version of the task, however, there is a problem: there is no way to determine whether this overall difference in reaction time is due to the S-S consistency or the irrelevant S-R consistency, or a combination of both.

Because there are three kinds of dimensional overlap in a Type 8 task, there are in principle three different compatibility effects that could appear: a mapping (relevant S-R) effect, an irrelevant S-R consistency effect, and an S-S consistency effect.

Zhang and Kornblum (1998) were able to measure each of these effects independently by constructing a four-choice Stroop task that included both a congruent and incongruent mapping. In this task, subjects responded to one of four words (“red”, “green”, “blue”, “yellow”) by saying one of four words from the same list. Above and below the target word appeared another irrelevant word from the same list. In the incongruent mapping condition, the words that appeared above and below the target could be either S-S inconsistent and S-R consistent (e.g. “blue” flanked by “blue” requiring a response of “green”), S-S inconsistent and S-R consistent (e.g. “blue” flanked by “green” requiring a response of “green”), or both S-S and S-R inconsistent (e.g. “blue” flanked by “red” requiring a response of “green”).

 

complete Stroop task and effects

 

When the mapping was incongruent, the reaction times were fastest for S-S consistent and S-R inconsistent flankers, intermediate for S-S inconsistent and S-R consistent flankers, and slowest for S-S and S-R inconsistent flankers. This demonstrates that both S-S consistency and S-R consistency contribute independent and separately measurable effects in the Stroop task, as predicted by the dimensional overlap model.

 

 

 
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The SS x SR Task

The SS x SR Task, or SS x SR Factorial-Combination Task, is a choice reaction time task with two different irrelevant stimulus dimensions, where one has dimensional overlap with the relevant stimulus and the other has dimensional overlap with the response. This allows an examination of both an S-S consistency effect and an irrelevant S-R consistency effect in the same task. In the dimensional overlap taxonomy, it is considered a Type 7 task.

Stoffels and van der Molen (1988) were the first to explore a factorial combination task, by integrating an auditory Simon task with a Flanker task in the same experimental design. Subjects responded to the letter “H” or the letter “S” with a left or right key-press. These targets were presented with either “H” or “S” flankers on both sides, and an auditory tone presented in either the left or the right ear. The flankers could be S-S consistent or S-S inconsistent, while the tone could be either S-R consistent or S-R inconsistent. The S-S and S-R consistency had additive effects: the S-S consistency effect was the same regardless of S-R consistency, and the S-R consistency effect was the same regardless of S-S consistency.

A number of studies have also combined a visual Simon task with the Stroop-like task (Simon & Berbaum, 1990; Kornblum, 1994; Hommel, 1998; Kornblum et al., 1999). In these studies, subjects were told to respond to a stimulus color with a left or right key-press. The stimulus color was presented on the left or the right side of the display, either with a color word super-imposed on a colored rectangle or with the color itself spelling out the color word. Both the position of the color and the color word are irrelevant. Several of these experiments showed additive effects of S-S and S-R consistency.

Factorial Combination Task

These tasks have played an important role in the debate over the locus of the S-S consistency effect in cognitive processing. Specifically, Kornblum et al. (1999) used the computational dimensional overlap model to demonstrate that both the additivity and the different time-courses of S-S and S-R effects can be explained by assuming that stimulus and response processing occur in discrete stages and that S-S and S-R dimensional overlap impact different processing stages.

 

 
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Cross-Modal Tasks

Cross-modal Tasks are a type of choice reaction time task that use structural overlap between stimulus dimensions of different sensory modalities. As a result, there is dimensional overlap between the irrelevant stimulus and the relevant stimulus, but no dimensional overlap with the responses. In the dimensional overlap taxonomy, these are considered to be Type 4 tasks. Other Type 4 tasks include the Flanker task and the Stroop-like task.

Robert Melara and Lawrence Marks (1990; Marks, 1987; Melara, 1989) are two of the first to study stimulus-stimulus consistency effects using cross-modal tasks. In a typical cross-modal task, subjects are told to press a left key or a right key depending on the brightness of a stimulus light. In conjunction with the stimulus light, subjects hear a tone of either a high or a low pitch, or a loud or a soft volume. The stimulus dimensions of brightness, pitch, and volume are not perceptually similar, and no specific level of brightness has an associative link with any particular pitch or loudness of sound. However, all of these dimensions can be rank-ordered from “low” to “high” along a continuum. As a result, the relationship between the elements of the relevant stimulus set (high and low brightness) and the relationship between the elements of the irrelevant stimulus set (high or low pitch or volume) allows them to be paired. Thus, although the tone is irrelevant to the task, it can be either consistent (e.g. a bright light paired with a loud sound) or inconsistent (e.g. a bright light paired with a soft sound) with the light. Responses are faster and more accurate for consistent stimuli than inconsistent stimuli.

Cross-Modal Task

This type of task validates the generality of the dimensional overlap theory. If the stimulus-stimulus consistency effect only appeared in Flanker tasks, a theory could be proposed that the effect was caused directly by a perceptual mechanism. If the stimulus-stimulus consistency effect only appeared in Stroop-like tasks, a theory could be put forth that was based on individual learned associations (such as the learned association between a color and its color word). The fact that the effect appears in cross-modal tasks, however, demonstrates that it is truly the dimensional overlap–in the most abstract sense–between the two stimulus dimensions that is key to the appearance of the consistency effect.

 
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The Stroop-like Task

The Stroop-like Task is illustrated by a choice reaction time task that uses color-word stimuli written in colored ink, the ink  is usually the relevant stimulus, but assigns them to key-press responses. As a result, there is dimensional overlap between the irrelevant and the relevant stimulus, but no dimensional overlap with the responses. In the dimensional overlap taxonomy, it is considered a Type 4 task. Other Type 4 tasks include the Flanker task and Cross-Modal tasks.

A number of researchers have explored performance in Stroop-like tasks (e.g. Hommel, 1998, exp. 1; Kahneman & Henick, 1981; Keele, 1972; Kornblum, 1994; Kornblum et al., 1999; Simon & Berbaum, 1990; Simon, Paullin, Overmyer & Berbaum, 1985, exp. 2). Typically, subjects are told to press a left key or a right key depending on the color of the stimulus. The color word is irrelevant, but can be either consistent (e.g. “blue” written in blue ink) or inconsistent (e.g. “green” written in blue ink) with the color. Responses are faster and more accurate for consistent stimuli than for inconsistent stimuli.

Stroop-like task

Unlike in the Flanker task, where the relevant and irrelevant stimuli are perceptually similar, this task only contains conceptual overlap between the two stimulus sets: color and color words are only linked through a learned symbolic association.

This task is called “Stroop-like” because the stimuli used in the task are the same as the stimuli first used by Stroop (1935) for the Stroop task. However, these tasks are different from actual Stroop tasks, because in Stroop tasks there is also overlap between the stimulus dimensions and the response dimension. You will sometimes see papers describing these tasks as “Stroop tasks”, disregarding the fact that the responses in these tasks have no overlap with color. According to Dimensional Overlap model, this difference is critical: cognitive processing in Stroop-like tasks and Stroop tasks is fundamentally different, based on the presence or absence of dimensional overlap with the response dimension.

 
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What is Consistency?

While dimensional overlap (DO) is a property of sets, consistency is a property of individual trials in a task.  The different ways that elements from overlapping dimensions can be combined to construct individual trials gives rise to a variety of types of consistency.

S-S consistency: Consider an ensemble with dimensional overlap between a relevant and an irrelevant stimulus set.  Trial draws on the same value from each dimension, then that trial has S-S consistency.   For example: in a task where the relevant stimulus is color and the irrelevant stimulus is a color word, the relevant and irrelevant stimulus sets overlap on the dimension of color.

On a trial where the color BLUE is presented with the word “BLUE” the stimulus is S-S consistent. On a trial where the color BLUE is presented with the word “GREEN”, on the other hand, the stimulus is S-S inconsistent.

Irrelevant S-R consistency: Consider an ensemble with a relevant and an irrelevant stimulus set, plus a response set,  with dimensional overlap between the irrelevant stimulus and the response. For example, suppose a blue or green light can appear on the left or right side, and the color of the light is assigned to a left or right key press. In this task, the irrelevant stimulus and the response overlap on the dimension of left-right position.

On a trial where the color assigned to a left key press also appears on the left side, the trial is S-R consistent. On a trial where the color assigned to a left key press also appears on the right side, the trial is S-R inconsistent.

Relevant S-R consistency (Congruent/Incongruent mapping): Consider an ensemble with a relevant stimulus and a response set (there may or may not also be an irrelevant stimulus set), and the relevant stimulus and response sets have dimensional overlap. A trial which on which one of the relevant stimuli and now mapped onto one of the responses is called Relevant Consistent.

In the case of relevant S-R consistency, if the instructions map the stimuli onto their corresponding response (e.g. “respond to the left light with the left key, and to the right light with the right key”) that mapping is said to be congruent. If the instructions map the stimuli onto non-corresponding responses keys (e.g. respond to the left light with the right key,and to the right light with the left key), that mapping is said to be incongruent.

 

The different types of consistencies reflects the functional role that Dimensional Overlap plays at the level of trials. The different patterns of DO found in ensembles, results in different types of tasks.  This is captured in the DO taxonomy.

 
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Debate: What is the locus of the S-S Overlap Effect?

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