Measuring Reaction Time and Donders' Method of Subtraction

Cognitive Psychology

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Overview

Source: Laboratory of Jonathan Flombaum—Johns Hopkins University

The ambition of experimental psychology is to characterize the mental events that support the human ability to solve problems, perceive the world, and turn thoughts into words and sentences. But people cannot see or feel those mental events; they cannot be weighed, combined in test tubes, or grown in a dish. Wanting to study mental life, nonetheless, Franciscus Donders, a Dutch ophthalmologist in the early 1800s, came up with a property that he could measure—even back then: he measured the time it took for human subjects to perform simple tasks, reasoning that he could treat those measurements as proxies for the time it takes to complete the unobservable mental operations involved. In fact, Donders went one step further, developing a basic experimental paradigm known as the Method of Subtraction. It simply asks a researcher to design two tasks that are identical in nearly every way, excepting a mental operation hypothesized to be involved in one of the tasks and omitted in the other. The researcher then measures the time it takes to complete each task, and by subtracting the outcomes, he extracts an estimate of the time it takes to execute the one mental operation of interest. In this way, the method allows a researcher to isolate a mental operation. The time it takes to complete a task has become known as reaction time or latency. Even today, reaction time is by a wide margin the most prevalent dependent variable in experimental psychology.  

This video will demonstrate the measurement of reaction time using Donders’ Method of Subtraction.

Cite this Video

JoVE Science Education Database. Cognitive Psychology. Measuring Reaction Time and Donders' Method of Subtraction. JoVE, Cambridge, MA, (2017).

Procedure

1. Pick a task and material to implement it.

  1. To use Donders’ Method of Subtraction, one first needs a mental operation of interest, and a pair of tasks thought to differ in terms of the operation. For current purposes, this video explores the ability to resolve conflicts between different sources of information—an important aspect of the ability to exert self-control on behavior. The Stroop task is a good basis for measuring the time it takes to resolve a conflict between information sources.
  2. The Stroop task can easily be programmed on a computer, but one nice feature is that it can also be implemented with just a few index cards and magic markers.
  3. So, the first things needed are: four magic markers (one each in red, yellow, blue, and green), two large index cards, and a stopwatch.

2. Make the ‘No Conflict’ stimuli.

  1. Take one of the index cards, placing it in front of you so that the lines are horizontal. Fold it in half creating a vertical meridian for two columns of stimuli.
  2. On each line in the left column, write in clear, capital letters one of the four color-terms, ‘RED, YELLOW, BLUE, GREEN.’ Ink each word using its corresponding magic marker. Pick colors more-or-less randomly. It might be easier to do this by rolling a die with one of the four colors assigned to each number.
  3. Repeat 2.2 on each line of the right column, aligned with the crease in your card.
  4. You now have the stimuli for the ‘No Conflict’ condition of this classic experiment (Figure 1, left).

Figure 1A
Figure 1. Sample stroop stimuli, no conflict examples.

3. Make the ‘Conflict’ stimuli.

  1. Take your second index card, and repeat step 2.1.
  2. Now you are again going to write out a color term on each line and in each column. But crucially, ink each term with any marker, except for the corresponding color. In other words, create a conflict between the ink color and the word you write on each line. Again, you want to pick words and colors more or less randomly. If you are using a die, you can roll it once to pick your word, and again to pick your ink (rolling again if they happen to match). Or you can use two dice, of course.
  3. You now have the stimuli for your ‘Conflict’ condition (Figure 1, right). Note, your ‘Conflict’ and ‘No Conflict’ cards should have equal numbers of words.

Figure 1B
Figure 1. Sample stroop stimuli, conflict examples.

4. Test a participant.

  1. You are now ready to test your first participant. You can also test yourself—but you’ll need someone to run the stopwatch.
  2. Place either one of your index cards face down on a table in front of your participant.
  3. Set your stopwatch to 0.
  4. Explain to the participant that when you say go, she can turn over the card, and as quickly as possible she should look at each line of the index card, working her way down the left column and then the right column, saying out loud the color of the ink. In other words, she should not read the word, only report its ink color. Emphasize that she must report each line correctly before moving on to the next, but that she should try to go as quickly as possible. She should say ‘DONE’ after reporting the final line.
  5. You say go, activate the timer, and get ready to stop the timer when your subject says, ‘DONE.’
  6. Write down the time it took.
  7. Now repeat 4.5-4.8, but with the other index card. You want the participant to do the task once with the ‘No Conflict’ stimuli, and once with the ‘Conflict’ stimuli. Order does not matter. But if you were to run multiple participants, you would want to counterbalance, with half the participants doing one order and the remaining half doing the other.

5. Analysis

  1. You should now have two reaction times: the time it took for your participant to get through the ‘Conflict’ card, and the time she took with the ‘No Conflict’ card. Subtract the ‘No Conflict’ time from the ‘Conflict’ time. If the number is positive, it is a sign that resolving the conflict between ink color and written words is a step that is involved in the ‘Conflict’ condition and not the ‘No Conflict’ condition. And the difference is an estimate of how long resolving the conflict takes.
  2. Note that each card included several words. But because the two cards included the same number of words, the difference between your conditions can be used to derive an estimate of the time to resolve a single instance of conflict. Since the difference between the cards is the difference between the sums of several instances that included a conflict and as many that did not, just divide the time difference between the two cards by the number of words on each card. The result is an estimate of the time to resolve a single conflict.

The ambition of experimental psychology is to characterize the mental events that support the human ability to solve problems, perceive the world, and turn thoughts into words and sentences.

But people can't see or feel those mental events; they can't be weighed, combined in test tubes, or grown in a dish.

Wanting to study mental life, nonetheless, Franciscus Donders, a Dutch ophthalmologist in the early 1800s, came up with a property that he could measure-even back then; he measured the time it took for human subjects to perform simple tasks, reasoning that he could treat those measurements as proxies for the time it takes to complete the unobservable mental operations involved.

In fact, Donders went one step further, developing a basic experimental paradigm known as the Method of Subtraction.

This method simply asks the experimental psychologist to design two tasks that are identical in nearly every way, except that one task involves a hypothesized mental operation and the other does not.

The researcher then measures the time it takes to complete each task, and by subtracting the outcomes, she extracts an estimate of the time it takes to execute the one mental operation of interest.

In this way, the method allows the researcher to isolate a mental operation. The time it takes to complete a task has become known as 'reaction time' or 'latency.' Today, reaction time is the most prevalent dependent variable in experimental psychology.

This video will demonstrate the measurement of reaction time using Donders' Method of Subtraction.

To use Donders' Method of Subtraction, one first needs a mental operation of interest, and a pair of tasks thought to differ in terms of the operation. This video will use the Stroop task to explore the ability to resolve conflicts between different sources of information-an important aspect of the ability to exert self-control on behavior.

The Stroop task is a good basis for measuring the time it takes to resolve a conflict between information sources. Here the conflict arises between reading the name of the color and viewing the color in which the word is written.

The Stroop task can easily be programmed on a computer, but one nice feature is that it can also be implemented with just a few index cards and colored pencils. So, the first things needed are four colored pencils, one each in red, orange, blue, and green, and also two large index cards, a stopwatch, and six-sided dice.

Take one of the index cards, placing it in front of you so that the lines are horizontal. Fold it in half, creating a vertical meridian for two columns of stimuli.

On each line in the left column, write in clear, capital letters one of the four color-terms. For each word use its corresponding colored pencil. You want to pick colors more-or-less randomly. It might be easier to do this by rolling a die with one of the four colors assigned to each number.

Repeat the same procedure on each line of the right column, aligned with the crease in your card.

Take your second index card, and again place it in front of you so that the lines are horizontal. Again, fold it in half creating a vertical meridian for two columns of stimuli.

Now, you are again going to write out a color term on each line and in each column. But crucially, print each term with any pencil except for the corresponding color. In other words, create a conflict between the lead color and the word you write on each line.

Again, you want to pick words and colors more or less randomly. If you are using a die, you can roll it once to pick your word, and again to pick your pencil color, rolling again if they happen to match. Or you can use two dice, of course.

You now have the stimuli for your 'Conflict' condition. Note, your 'Conflict' and 'No Conflict' cards should have equal numbers of words.

You are now ready to test your first participant.

Place either one of your index cards face down on a table in front of your participant.

Set your stopwatch to 0, and explain the task to the participant.

After the participant confirms that they understand the task, start the timer and say...

The participant should look at each line on the left side of the index card and say out loud the color of the word as quickly as possible. That is, they should not read the word by name, only the color it's printed in.

The participant must report each line correctly before moving on to the next.

After the colors on the left side of the card have been reported, the participant should repeat the procedure with the colors on the right side of the card.

The participant says "DONE" after reporting the final line, and you stop the timer.

Now repeat the timed test, but with the other index card.

You want the participant to do the task once with the 'No Conflict' stimuli, and once with the 'Conflict' stimuli. Order does not matter. But if you were to run multiple participants, you would want to 'counterbalance,' with half the participants doing one order, and the remaining half doing the other.

You should now have two reaction times: the time it took for your participant to get through the 'Conflict' card, and the time she took with the 'No Conflict' card.

Subtract the 'No Conflict' time from the 'Conflict' time. If the number is positive, it is a sign that resolving the conflict between printed color and word names is a step that is involved in the 'Conflict' condition, and not the 'No Conflict' condition. And the difference is an estimate of how long resolving the conflict takes.

Note that each card included several words, so the reaction time difference is the difference between the total time it takes to get through each card. By dividing that difference by the number of words on the card, you can get an estimate of how long it takes to resolve each individual instance of word-color conflict.

It is hard to draw conclusions from a single subject, and so an experiment typically tests many subjects, around 20 for the Stroop task, aggregating their results to draw reliable conclusions. For each participant, you end up with two reaction times: one from the 'Conflict' and one from the 'No Conflict' condition. On a spreadsheet, you would organize the results something like this.

These results can be summarized with a simple graph of the average reaction time across all participants in each condition. As seen here, participants read through the card with the No Conflict stimuli about 11.6 sec faster than they read through the card with the Conflict Stimuli. In terms of Donders' method, this suggests that resolving the conflict between print color and reading takes about 11.6 sec per card. Since each card in this experiment had 12 words written on it, this means that, on average, resolving the conflict between print color and reading takes about 1 sec per word.

Donders' Method of Subtraction can be used with reaction time measures in a variety of areas in experimental psychology, not just with Stroop or conflict paradigms.

In addition, the Method of Subtraction underpins the basic logic for a wide array of approaches to experimental psychology with dependent variables beyond reaction time. These include measures as diverse as how long an infant glares at a stimulus, and the blood-oxygen-level-dependent (BOLD) response measured in the human brain by sophisticated fMRI machines.

In many fMRI experiments, researchers obtain patterns of brain activity from two experimental conditions that are identical, excepting the involvement of a mental process of interest, such as the conflict and no conflict trials of the Stroop task. By subtracting one pattern from the other they can isolate brain areas involved in that process of interest.

You've just watched JoVE's introduction to Donders' Method of Subtraction. Now, you should have a good understanding of how to conduct a simple Stroop task in order to determine the time it takes to resolve conflicts and presented stimuli. There are numerous ways to apply to technique. So go out there and make Donders proud.

Results

It is hard to draw conclusions from a single subject, and so an experiment typically tests many subjects, aggregating their results to draw reliable conclusions. For this Stroop experiment, you would test 20 or so participants just the way you tested one. For each participant, you end up with two reaction times, one from the ‘Conflict’ and one from the ‘No Conflict’ condition (Table 1). These results can be summarized with a simple graph of the average reaction time across all participants in each condition (Figure 2).

Figure 2
Figure 2. Reaction time as a function of conflict condition. Participants read through the card with the no conflict stimuli about 11.6 s faster than they read through the card with the conflict stimuli. 

Subject Conflict RT (ms) No Conflict RT (ms)
1 17240 6189
2 18345 7194
3 17734 5238
4 16221 5715
5 19334 8273
6 14322 4718
7 18845 6293
8 17240 6189
9 18345 7194
10 17734 5238
11 16221 5715
12 19334 8273
13 14322 3654
14 18845 6293
15 17735 6497
16 16944 6227
17 15893 5265
18 19115 7836
19 18931 8110
20 16241 5578

Table 1. Reaction times by subject. Reaction time data are reported across condition for each subject.

Applications and Summary

Donders’ Method of Subtraction can be used with reaction time measures in a variety of areas in experimental psychology, not just with Stroop or conflict paradigms. In addition, the Method of Subtraction underpins the basic logic for a wide array of approaches to experimental psychology with dependent variables beyond reaction time. These include measures as diverse as how long an infant glares at a stimulus, and the blood-oxygen-level-dependent (BOLD) response measured in the human brain by sophisticated fMRI machines. In many fMRI experiments, researchers obtain patterns of brain activity from two experimental conditions that are identical, excepting the involvement of a mental process of interest. By subtracting one pattern from the other, they can isolate brain areas involved in that process. Indeed, the Stroop is a classic example. Participants have their brains scanned during conflict and no conflict trials. Many brain areas are involved in each kind of trial, including visual cortex and regions involved in reading. But when the no conflict scans are subtracted from the conflict ones, fairly isolated frontal regions of the brain—especially one called the anterior cingulate cortex—appear to be critically active in only the no conflict trials. This makes sense! Those frontal regions are often associated with the ability to control one’s own behavior under difficult conditions.   

1. Pick a task and material to implement it.

  1. To use Donders’ Method of Subtraction, one first needs a mental operation of interest, and a pair of tasks thought to differ in terms of the operation. For current purposes, this video explores the ability to resolve conflicts between different sources of information—an important aspect of the ability to exert self-control on behavior. The Stroop task is a good basis for measuring the time it takes to resolve a conflict between information sources.
  2. The Stroop task can easily be programmed on a computer, but one nice feature is that it can also be implemented with just a few index cards and magic markers.
  3. So, the first things needed are: four magic markers (one each in red, yellow, blue, and green), two large index cards, and a stopwatch.

2. Make the ‘No Conflict’ stimuli.

  1. Take one of the index cards, placing it in front of you so that the lines are horizontal. Fold it in half creating a vertical meridian for two columns of stimuli.
  2. On each line in the left column, write in clear, capital letters one of the four color-terms, ‘RED, YELLOW, BLUE, GREEN.’ Ink each word using its corresponding magic marker. Pick colors more-or-less randomly. It might be easier to do this by rolling a die with one of the four colors assigned to each number.
  3. Repeat 2.2 on each line of the right column, aligned with the crease in your card.
  4. You now have the stimuli for the ‘No Conflict’ condition of this classic experiment (Figure 1, left).

Figure 1A
Figure 1. Sample stroop stimuli, no conflict examples.

3. Make the ‘Conflict’ stimuli.

  1. Take your second index card, and repeat step 2.1.
  2. Now you are again going to write out a color term on each line and in each column. But crucially, ink each term with any marker, except for the corresponding color. In other words, create a conflict between the ink color and the word you write on each line. Again, you want to pick words and colors more or less randomly. If you are using a die, you can roll it once to pick your word, and again to pick your ink (rolling again if they happen to match). Or you can use two dice, of course.
  3. You now have the stimuli for your ‘Conflict’ condition (Figure 1, right). Note, your ‘Conflict’ and ‘No Conflict’ cards should have equal numbers of words.

Figure 1B
Figure 1. Sample stroop stimuli, conflict examples.

4. Test a participant.

  1. You are now ready to test your first participant. You can also test yourself—but you’ll need someone to run the stopwatch.
  2. Place either one of your index cards face down on a table in front of your participant.
  3. Set your stopwatch to 0.
  4. Explain to the participant that when you say go, she can turn over the card, and as quickly as possible she should look at each line of the index card, working her way down the left column and then the right column, saying out loud the color of the ink. In other words, she should not read the word, only report its ink color. Emphasize that she must report each line correctly before moving on to the next, but that she should try to go as quickly as possible. She should say ‘DONE’ after reporting the final line.
  5. You say go, activate the timer, and get ready to stop the timer when your subject says, ‘DONE.’
  6. Write down the time it took.
  7. Now repeat 4.5-4.8, but with the other index card. You want the participant to do the task once with the ‘No Conflict’ stimuli, and once with the ‘Conflict’ stimuli. Order does not matter. But if you were to run multiple participants, you would want to counterbalance, with half the participants doing one order and the remaining half doing the other.

5. Analysis

  1. You should now have two reaction times: the time it took for your participant to get through the ‘Conflict’ card, and the time she took with the ‘No Conflict’ card. Subtract the ‘No Conflict’ time from the ‘Conflict’ time. If the number is positive, it is a sign that resolving the conflict between ink color and written words is a step that is involved in the ‘Conflict’ condition and not the ‘No Conflict’ condition. And the difference is an estimate of how long resolving the conflict takes.
  2. Note that each card included several words. But because the two cards included the same number of words, the difference between your conditions can be used to derive an estimate of the time to resolve a single instance of conflict. Since the difference between the cards is the difference between the sums of several instances that included a conflict and as many that did not, just divide the time difference between the two cards by the number of words on each card. The result is an estimate of the time to resolve a single conflict.

The ambition of experimental psychology is to characterize the mental events that support the human ability to solve problems, perceive the world, and turn thoughts into words and sentences.

But people can't see or feel those mental events; they can't be weighed, combined in test tubes, or grown in a dish.

Wanting to study mental life, nonetheless, Franciscus Donders, a Dutch ophthalmologist in the early 1800s, came up with a property that he could measure-even back then; he measured the time it took for human subjects to perform simple tasks, reasoning that he could treat those measurements as proxies for the time it takes to complete the unobservable mental operations involved.

In fact, Donders went one step further, developing a basic experimental paradigm known as the Method of Subtraction.

This method simply asks the experimental psychologist to design two tasks that are identical in nearly every way, except that one task involves a hypothesized mental operation and the other does not.

The researcher then measures the time it takes to complete each task, and by subtracting the outcomes, she extracts an estimate of the time it takes to execute the one mental operation of interest.

In this way, the method allows the researcher to isolate a mental operation. The time it takes to complete a task has become known as 'reaction time' or 'latency.' Today, reaction time is the most prevalent dependent variable in experimental psychology.

This video will demonstrate the measurement of reaction time using Donders' Method of Subtraction.

To use Donders' Method of Subtraction, one first needs a mental operation of interest, and a pair of tasks thought to differ in terms of the operation. This video will use the Stroop task to explore the ability to resolve conflicts between different sources of information-an important aspect of the ability to exert self-control on behavior.

The Stroop task is a good basis for measuring the time it takes to resolve a conflict between information sources. Here the conflict arises between reading the name of the color and viewing the color in which the word is written.

The Stroop task can easily be programmed on a computer, but one nice feature is that it can also be implemented with just a few index cards and colored pencils. So, the first things needed are four colored pencils, one each in red, orange, blue, and green, and also two large index cards, a stopwatch, and six-sided dice.

Take one of the index cards, placing it in front of you so that the lines are horizontal. Fold it in half, creating a vertical meridian for two columns of stimuli.

On each line in the left column, write in clear, capital letters one of the four color-terms. For each word use its corresponding colored pencil. You want to pick colors more-or-less randomly. It might be easier to do this by rolling a die with one of the four colors assigned to each number.

Repeat the same procedure on each line of the right column, aligned with the crease in your card.

Take your second index card, and again place it in front of you so that the lines are horizontal. Again, fold it in half creating a vertical meridian for two columns of stimuli.

Now, you are again going to write out a color term on each line and in each column. But crucially, print each term with any pencil except for the corresponding color. In other words, create a conflict between the lead color and the word you write on each line.

Again, you want to pick words and colors more or less randomly. If you are using a die, you can roll it once to pick your word, and again to pick your pencil color, rolling again if they happen to match. Or you can use two dice, of course.

You now have the stimuli for your 'Conflict' condition. Note, your 'Conflict' and 'No Conflict' cards should have equal numbers of words.

You are now ready to test your first participant.

Place either one of your index cards face down on a table in front of your participant.

Set your stopwatch to 0, and explain the task to the participant.

After the participant confirms that they understand the task, start the timer and say...

The participant should look at each line on the left side of the index card and say out loud the color of the word as quickly as possible. That is, they should not read the word by name, only the color it's printed in.

The participant must report each line correctly before moving on to the next.

After the colors on the left side of the card have been reported, the participant should repeat the procedure with the colors on the right side of the card.

The participant says "DONE" after reporting the final line, and you stop the timer.

Now repeat the timed test, but with the other index card.

You want the participant to do the task once with the 'No Conflict' stimuli, and once with the 'Conflict' stimuli. Order does not matter. But if you were to run multiple participants, you would want to 'counterbalance,' with half the participants doing one order, and the remaining half doing the other.

You should now have two reaction times: the time it took for your participant to get through the 'Conflict' card, and the time she took with the 'No Conflict' card.

Subtract the 'No Conflict' time from the 'Conflict' time. If the number is positive, it is a sign that resolving the conflict between printed color and word names is a step that is involved in the 'Conflict' condition, and not the 'No Conflict' condition. And the difference is an estimate of how long resolving the conflict takes.

Note that each card included several words, so the reaction time difference is the difference between the total time it takes to get through each card. By dividing that difference by the number of words on the card, you can get an estimate of how long it takes to resolve each individual instance of word-color conflict.

It is hard to draw conclusions from a single subject, and so an experiment typically tests many subjects, around 20 for the Stroop task, aggregating their results to draw reliable conclusions. For each participant, you end up with two reaction times: one from the 'Conflict' and one from the 'No Conflict' condition. On a spreadsheet, you would organize the results something like this.

These results can be summarized with a simple graph of the average reaction time across all participants in each condition. As seen here, participants read through the card with the No Conflict stimuli about 11.6 sec faster than they read through the card with the Conflict Stimuli. In terms of Donders' method, this suggests that resolving the conflict between print color and reading takes about 11.6 sec per card. Since each card in this experiment had 12 words written on it, this means that, on average, resolving the conflict between print color and reading takes about 1 sec per word.

Donders' Method of Subtraction can be used with reaction time measures in a variety of areas in experimental psychology, not just with Stroop or conflict paradigms.

In addition, the Method of Subtraction underpins the basic logic for a wide array of approaches to experimental psychology with dependent variables beyond reaction time. These include measures as diverse as how long an infant glares at a stimulus, and the blood-oxygen-level-dependent (BOLD) response measured in the human brain by sophisticated fMRI machines.

In many fMRI experiments, researchers obtain patterns of brain activity from two experimental conditions that are identical, excepting the involvement of a mental process of interest, such as the conflict and no conflict trials of the Stroop task. By subtracting one pattern from the other they can isolate brain areas involved in that process of interest.

You've just watched JoVE's introduction to Donders' Method of Subtraction. Now, you should have a good understanding of how to conduct a simple Stroop task in order to determine the time it takes to resolve conflicts and presented stimuli. There are numerous ways to apply to technique. So go out there and make Donders proud.

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