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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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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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What is Dimensional Overlap?

Dimensional Overlap (DO) is a property of sets.

A set is a collection of items.  When these items have one or more attributes in common they form a category (cf. Kornblum, Hasbroucq & Osman; Kornblum & Lee).  This category is identified by the common attribute which is also the dimension of that category.  When two or more sets are included in a larger set this larger set is called an ensemble.

Dimensional Overlap is the degree to which a stimulus set, and a response set, or two or more stimulus sets are perceptually, structurally or conceptually similar.  Similarity is a continuous variable, going from “almost identical” to “they have nothing to do with each other”, and different levels of  similarity are carried over to differences in degrees of DO. These differences are dealt with in the computational model as different strengths of the “automatic association lines” between different mental representation units. (More info: The Computational Model)

The best way to understand the ideas of perceptual, conceptual, and structural similarity is to consider some examples of tasks with dimensional overlap  based on such similarities.

A.  An experimental subject is sitting in front of a screen.  On the screen is the outline drawing of two outstretched hands.  The subject has his own outstretched hands positioned on eight response keys, and he is instructed to press the key under the finger that corresponds to the finger outline on the screen, when an “X” appears in the tip of that finger.  The stimulus set (i.e. the outline drawing of the hands with an X in any fingertip), and the response set (i.e. the set of potential key presses with one of the fingers) are perceptually similar, giving that ensemble dimensional overlap.

B.  In this task, the subject must press the left key when he hears a sound in the left ear, and the right key when he hears a sound in the right ear.  Laterality is the attribute, or dimension, that the stimulus and the response sets have in common, and which makes them perceptually similar, thus giving the ensemble dimensional overlap.

C.  In this task, the subject says the name of a color that is presented (e.g. when you see Blue you say “Blue”, and when you see Green, you say “Green”). Here, the attribute that the stimulus set (Blue and Green) and the response set (“Blue” and “Green”) have in common is COLOR.  These two sets are conceptually similar, thus giving this SR ensemble Dimensional Overlap.

D.  Take the set of symbols 1, 2, 3, 4, 5. They form a category called “integers”; it could also be called “digits”, or any of several other names.  Next, take the set of words “one”, “two”, “three”, “four”, “five”…They form a category called “digit name”.  Both of these sets are tokens for numerals, and are conceptually similar.  The ensemble comprising these two sets, therefore, has dimensional overlap.

In this case, as well as in the case of colors (in C above),  the correspondence between the elements of the stimulus set and the response set are so exact as to give their similarity level (hence the level of DO) an especially high value.

E.  The set of symbols B, C, D, F, G…are members of a category called “consonants”.  Likewise, the set of symbols A, E, I, O, U are members of a category called “vowels”.  Both of these sets are sets of “letters”.  Letters may, therefore, be viewed as the attribute that they have in common, on which they overlap, and makes them conceptually similar.  An ensemble with both of these sets has dimensional overlap.

F.  Now let us consider the set of integers (1, 2, 3, 4, 5…), and the set of letters (A, B, C, D, E,).  Both of these sets share the property of being the first consecutive elements of two sequential series (the alphabet and the integers).  Thus making them structurally similar, and giving them dimensional overlap.

G.  Finally, consider a set of weather reports: “hot, mild, cold, and freezing”.  To the extent that this set may also be viewed as consecutive items on an abstract sequential series of items (this would be true whether high and low temperatures are indicated by a numeric scale, or in some other way), this set of weather reports is similar to the set of digits, and the set of letters, and to the extent that all three sets share the same dimension, they are all structurally  similar to one another, and together would form an ensemble with dimensional overlap.  This particular pattern of DO is at the basis of what we have called “cross modal” tasks.  (More info: Cross-Modal Tasks)

 

Relevant and Irrelevant Stimuli

In all the tasks that we have used to illustrate different sorts of similarities, the stimulus set that overlaps with the response set has always been a set of relevant stimuli. (cf, “Why Study Compatibility”)   Relevant stimuli are those that the subject is instructed to attend to, and respond to.  Of course, any “stimulus” has many features that could, in principle, be selected to play that role.  However, in the mapping instructions for all tasks, specific features are selected for that precise purpose, while other features are explicitly excluded and are to be ignored by the subject.  Those “to be ignored” features are the irrelevant stimuli.  The correlation between the relevant stimuli and the response, is 1.0,  the correlation between the irrelevant stimuli and the response is zero.

Even though they are irrelevant to the task, and the subject is told to ignore them, irrelevant stimuli are sometimes difficult to ignore.  For example, let’s go back to the experimental set up we used in case B above, and introduce a small change: Instead of presenting the same tone to the left and the right ear, let the tone now be either a high or low pitch tone.  Again, it will be randomly presented to the left or the right ear, just as in B above..  However, this time, instead of mapping the side of the ear to the key, the subject is instructed to make a left or right key-press according to the pitch of the tone, and to ignore in which ear the tone was presented: “press the right key to the high pitch tone, the left key to the low pitch tone, and ignore the ear to which the tone is presented”.  With these instructions, and the experimental set up, pitch is the relevant stimulus, and ear is the irrelevant stimulus. When these irrelevant (i.e. “to be ignored”) stimuli have dimensional overlap with the response, or with some other aspects of the tasks, it results in significant changes in performance.

The eight combinations of the presence/absence of relevant/irrelevant, stimulus-response ensembles, and stimulus-stimulus ensembles are presented in the Taxonomy of DO Ensembles.  (More info: Taxonomy of DO Ensembles)

 

Consistency and Inconsistency

When the relevant and the irrelevant stimuli denote the same attribute, this gives rise to S-S Consistency / Inconsistency.  For example: if the color BLUE is the relevant stimulus, and the name of the color “BLUE” is the irrelevant stimulus, the dimension on which they overlap is COLOR, and the fact that they both represent the same feature (i.e. BLUE) makes this an S-S CONSISTENT  pair of stimuli.

If this match between the color and the name does not hold, then this is an S-S INCONSISTENT pair.

When the irrelevant stimulus and the response denote the same attribute, this gives rise to S-R Consistency / Inconsistency. For example, if the color of a light is the relevant stimulus, and a left/right key-press is the response, and the light can be turned on either on the left or on the right, then the location of the lights (left or right) and the position of the response keys (left or right) make this ensemble S-R CONSISTENT.  The dimension on which they overlap is “lateral position in space”.

If the match between the location of the lights and the position of the response key does not hold, then this is an S-R INCONSISTENT pair. (More Info: What is consistency?)

 

Dimensional Overlap is a GENERAL mental phenomenon

Some sets sometimes seem so physically different from other sets – for instance when the sensory channel for the one is vision and for the other is audition – that the similarity (the DO) between them seems far fetched.  Yet, they give rise to compatibility effects in performance, which verifies that there is some set-level similarity between the mental representations (cf. Robert Melara and Lawrence Marks (1990; Marks, 1987; Melara, 1989).

 
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