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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 Hedge and Marsh Task

The Hedge and Marsh Task, also sometimes called the Reverse-Simon Task, is a choice reaction time task where there is dimensional overlap between the irrelevant stimulus and the response and between the relevant stimulus and the response, but there is no dimensional overlap between the two stimulus dimensions. This is accomplished by having two separate but correlated response dimensions. In the dimensional overlap taxonomy, it is considered a Type 5 task.

Hedge and Marsh (1975) examined a variation of the standard Simon task in which subject pressed a left key or a right key in response to the color of a stimulus (red or green), while the stimulus color appeared on the left or right side of the screen; in addition, however, they color-coded the response keys so that the response set not only had dimensional overlap with the irrelevant stimulus set (due to left-right position) but also with the relevant stimulus set (due to color). In addition to S-R consistency, therefore, the instructions given to subjects could be either congruent (e.g. “press the key with the same color as the stimulus”) or incongruent (“press the key with the opposite color from the stimulus”). There is no dimensional overlap between the relevant stimulus set (color) and the irrelevant stimulus set (location), and therefore there is no S-S consistency.

Hedge and Marsh Task

Because the Hedge and Marsh task has two types of overlap, there are two compatibility effects that can be obsereved.  First, the experiment showed a standard mapping effect: overall reaction times were much faster wth compatible (i.e congruent) mapping, i.e. when  each color stimulus was mapped to a correspondingly colored response (e.g. “press the key with the same color as the stimulus”) than when the mapping was incompatible, that is incongruent  (e.g. “press the key with the opposite color from the stimulus”).

The effect of irrelevant stimulus-response consistency, however, was unusual. Hedge and Marsh found the surprising result that the irrelevant S-R consistency effect reverses when the mapping instructions are incompatible. That is, when the instruction were to press the key with the same color as the stimulus, the subjects responded faster when the stimulus position was consistent with the response position (the normal S-R consistency effect); however, when the instructions were to press the key with the opposite color from the stimulus, subjects responded faster when the stimulus position was inconsistent with the response key position (a reversed S-R consistency effect). This effect of the irrelevant stimulus in a Hedge and Marsh task is called a Hedge and Marsh effect or a reverse-Simon effect.

The reverse-Simon effect was met with some initial skepticism. Simon, Sly and Vilapakkam (1981) suggested that the result might just be an artifact of the way that the display and the response keys were arranged: if the left key is green and the right key is red, then a display that shows a green patch on the left side or a red patch on the right side matches the arrangement of the keys. On the other hand, a display that shows a red patch on the left and a green patch on the right does not. They called this display-control correspondence, suggesting  that people reach faster when the displays and controls correspond than when they do not. This would give the appearance of a reverse irrelevant S-R consistency effect.

However, Kornblum and Stevens (1999) replicated the conditions for the Hedge and Marsh (1975) task with auditory stimuli and verbal responses. Stimuli were the words “boot” and “gate” spoken at either a high pitch or a low pitch. Subjects had to respond to either the pitch (making the word irrelevant) or the word (making the pitch irrelevant), by making one of two responses: saying the word “boot” at a high pitch or the word “gate” at a low pitch. This task has the same structure and dimensional overlap as the standard Hedge and Marsh task, making it a Type 5 task in the Dimensional Overlap Taxonomy. However, there was naturally no display and there were no controls in the experiment, and therefore there could be no display-control correspondence. Despite the fact that this task had no display or controls, both the regular S-R consistency effect (for compatible mappings) and the reversed S-R consistency effect (for incompatible mappings) were obtained. (See also DeJong, Liang, & Lauber, 1994, for another attempt to remove display-control correspondence from the task.)

Despite initial suspicions, the reverse S-R consistency effect has also been replicated under a wide variety of conditions and manipulations (e.g. Berbner, 1979; DeJong, Liang & Lauber, 1994; Hasbroucq & Guiard, 1991; Lu & Proctor, 1994; Smith & Brebner, 1983; Zhang, 1999). A number of explanations have been suggested to account for this reversal of the S-R consistency effect in the Hedge & Marsh task, although it is still a matter of much debate.

It should be pointed out that a number of studies have incorrectly claimed that they replicate the Hedge and Marsh task in the auditory domain (e.g. Arend & Wandmacher, 1987; Proctor & Pick, 1999;Ragot & Guiard, 1992). In these tasks, the relevant stimuli, irrelevant stimuli, and responses are all characterized by spatial location. For example, the word “left” or “right” might be spoken into the left or the right ear, requiring a response of a left or right key press. In these tasks, all three dimensions overlap with one another, including the two stimulus dimensions, which are both spatial. As a result, these are Type 8 tasks in the dimensional overlap taxonomy and should be considered variants of the Stroop task, not variants of the Hedge and Marsh task.

 


 

NOTE: Sometimes you will see researchers use the term “Simon task” to refer to this task. However, in the Dimensional Overlap taxonomy, the standard Simon task is not a Type 5 task: it is a Type 3 task. Although the standard Simon task does have an irrelevant stimulus dimension (usually location) that overlaps with the response, it does not have any overlap between the relevant stimulus dimension and the response. In a traditional Simon task, the mapping between stimulus and response is completely arbitrary. The dimensional overlap model therefore contends that the cognitive processing in the Simon task and the Hedge and Marsh task are fundamentally different, because of this difference in relevant stimulus-response overlap.

 
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The Stimulus-Response Compatibility Task

The Stimulus-Response Compatibility Task, also called the SRC Task  is the type of choice reaction time task where there is dimensional overlap between the relevant stimulus set and the response set.  In the dimensional overlap taxonomy, it is considered a  Type 2 task.

The results of performance with SRC tasks were first reported by Paul Fitts (Fitts & Seeger, 1953; Fitts & Deininger, 1954), who called them “Stimulus Response Compatibility Effects”.   In both papers the tasks  were eight-choice  reaction time tasks in which subjects had to move a stylus from a home position to one of eight target positions.  Since that time, many experiments have been run that have confirmed Fitts’ original results, and have used non-spatial stimulus and response attributes.  Thus was  the field of stimulus response compatibility born.

An example of this type of task is described next.  A subject is sitting at a table, on which  is a screen showing  four small,  horizontally arranged squares.  Inside each sqare is a small circle that functions as a light.   A stimulus consists of one of these lights going on.  In front of the screen are four keys.  The subject’s index and middle fingers of each hand are resting on these keys.  When the mapping instructions assign a response to its corresponding stimulus light (congruent mapping), people are much faster and more accurate than when the instructions assign a response to a non-corresponding stimulus light (incongruent mapping).

This effect is  extremely robust, and happens for a wide variety of stimuli and responses. People are slower to say “blue” in response to a red square than they are when saying “red” in response to a red square, even though there is no perceptual similarity between the stimulus and the response. The effect even shows up when the relationship is very abstract: for example, people can be told to respond to lights of different brightness by pressing buttons with different levels of force, and they are faster when they are told to press a button hard for a bright light than when they are told to press a button hard for a dim light.

The key factor that all mapping tasks have in common is the dimensional overlap between the relevant stimulus and the response.

 
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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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