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An Introduction to the Event-Related Potential Technique, second edition Steven J. Luck

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Luck, Steven J. (Steven John), 1963 – author.

An introduction to the event-related potential technique / Steven J. Luck — Second edition.

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Includes bibliographical references and index.

ISBN 978-0-262-52585-5 (pbk. : alk. paper)

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[DNLM: 1. Evoked Potentials. WL 102]

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10 9 8 7 6 5 4 3 2 1

2 A Closer Look at ERPs and ERP Components

Overview

This chapter provides a deeper analysis of the nature of ERPs, with the goal of helping you

understand how ERPs are generated in the brain and how the intracranial signals combine

together to create the waveforms we record on the surface of the scalp. The peaks that you see

in scalp ERP waveforms typically reflect the sum of multiple internal, underlying components,

and the conclusions of an experiment often require determining how these underlying compo-

nents differed across groups or conditions. However, as I mentioned in chapter 1 (and will

continue to emphasize throughout this book), it is very challenging to isolate and measure the

internal underlying components on the basis of the data that you actually record from the scalp.

This is called the superposition problem , and this chapter will explain how it arises and why it is so difficult to solve. This can be a little depressing, but don ’ t despair! Chapter 4 describes

some strategies you can use to solve this problem (or work around it), along with examples of

previous experiments that have successfully used these strategies to provide definitive answers

to important scientific questions. Chapter 3 provides a description of the specific ERP compo-

nents that are most commonly observed in typical experiments.

It is easy to confuse the peaks that we observe in our scalp waveforms with the internal

underlying brain components that sum together to create these peaks. In this chapter, I frequently

use the phrase underlying component to make it clear that I am talking about internal brain activity, not the observed peaks on the scalp.

This chapter will begin with a discussion of basic electrical concepts, followed by a detailed

discussion of the neural origins of ERPs and how they mix together in scalp recordings. We will

then discuss why it is so difficult to localize the internal generators of scalp ERPs. This will be

followed by a description of how the ERPs we record from scalp electrodes can radically mis-

represent the underlying components. We will then discuss how difference waves can be used

to solve this problem and isolate the underlying components. We will end by considering dif-

ferent ways of defining the term ERP component . You might think that it would be more logical to start with the definitions, but they will be much easier to grasp once you ’ ve spent some time

thinking concretely about the nature of the signals we record from scalp electrodes. The chapter

36 Chapter 2

ends with a general discussion of methods that can be used to identify the underlying components

that vary across groups or conditions in a given study.

This chapter is designed to provide you with a deep conceptual understanding of ERPs, and

it is therefore somewhat abstract. You need this kind of understanding to evaluate previous ERP

experiments and to design new ERP experiments. In fact, this chapter includes six specific

“ rules ” for interpreting ERP data. However, if you are in the middle of collecting or analyzing

data from an ERP experiment and you need to know the practical details of how to collect clean

data and perform appropriate analyses, you might want to skip ahead to chapters 5 – 10. You can

then come back to chapters 2 – 4 when you are ready to think more deeply about your results and

to design new experiments. But don ’ t forget to come back later, because chapter 2 is ultimately

the most important chapter in the entire book.

Basic Electrical Concepts

If you are going to measure electrical signals in your research, you need to know a little bit

about electricity. In this section, I will provide an overview of the most basic terms and concepts.

If you took physics in high school or college, you have already learned these terms and concepts

(although many people have told me that electricity was the part of physics they never really

understood). If you didn ’ t take physics, then don ’ t worry, because I didn ’ t either. When I was

in high school, I took shop classes on electronics rather than physics, because I was more inter-

ested in being able to fix my guitar amplifier than I was in learning to predict the velocity of a

ball rolling down a hill. Fortunately, the relevant concepts are pretty simple.

Current Current is the actual flow of electricity (charged particles) through a conductor. It is a measure of

the number of charge units (electrons or protons) that flow past a given point in a specific amount

of time. Current is measured in amperes, where 1 ampere is equal to 1 coulomb (6.24 × 10 18 ) of charge units moving past a single point in 1 second.

By convention, physicists and engineers refer to current flowing in the direction of positively

charged particles. For example, 1 coulomb of positively charged particles flowing from the left

hemisphere to the right hemisphere is viewed as being electrically equivalent to 1 coulomb of

negatively charged particles flowing from the right hemisphere to the left hemisphere. Thus, we

would talk about the current flowing from the left hemisphere to the right hemisphere in both

cases, regardless of whether it is positive charges moving from left to right or negative charges

moving from right to left.

When discussing the flow of electricity, it is useful to use the flow of water as an analogy.

Electrical current is analogous to the flow of water through a pipe or hose. Just as we can measure

the amount of water that passes a given point in a pipe in a given period of time (e.g., 3.6 liters

per minute), we can measure the amount of electricity that passes a given point in a conductor

in a given period of time (e.g., 3.6 coulombs per second).

A Closer Look at ERPs and ERP Components 37

Voltage People often get voltage and current mixed up, thinking that voltage is the actual flow of elec-

tricity. Current is the flow of electricity through a conductor, and voltage is the pressure that

pushes the electrical current through the conductor. A more precise term for voltage is electrical potential , because it is the potential for electrical current to flow from one place to another (and this is why ERPs are event-related potentials ). As an analogy, consider a tank of water at the top of a hill. There is a lot of potential for the water to flow from the tank to the bottom of the

hill, but little potential for the water to flow from the bottom to the top. Importantly, the potential

for water to flow downhill is present even if no water is flowing at a given moment (e.g., because

a valve is closed). Similarly, there is potential for electrical current to flow from one terminal

of a car battery to the other even if no current is flowing. Electrical potential is closely analogous

to water pressure: there can be a lot of water pressure in a hose even if the end of the hose is

closed and no water is actually flowing. However, once the end of the hose is opened, the pres-

sure will cause water to flow. Also, no water will flow out of the end of the hose unless there

is sufficient water pressure, just as no electrical current will flow without an electrical potential

to push it through the conductor.

Electrical potential is measured in units of volts (V). ERPs are so small that they are usually

quantified in microvolts ( μ V), where 1 microvolt is 1 millionth of a volt. You can imagine that the 120 V running through the video monitor in front of a subject could lead to significant

interference when you are looking for a 1 μ V experimental effect. This kind of interference will be discussed in more detail in chapter 5.

Resistance Resistance is the ability of a substance to keep charged particles from passing. It is the inverse

of conductance , which is the ability of a substance to allow charged particles to pass through it. Three main factors contribute to resistance: (1) the composition of the substance, (2) its length,

and (3) its diameter. Because of their molecular properties, some substances conduct electricity

better than others (e.g., copper is a better conductor than zinc). However, the ability of any

substance to conduct electricity will be reduced if it is very thin or very long. Resistance is

measured in ohms ( Ω ). To use yet another hydraulic example, consider a water filtration system in which the water

supply for a house passes through a large tank filled with carbon. If the carbon is tightly packed,

water will not easily flow through the tank, but if the carbon is loosely packed, water will flow

easily. This is analogous to the dependence of electrical resistance on the properties of the

substance. Now imagine water passing through a hose. If the hose is 100 m long and only 1

cm wide, it will resist the flow of water, and a great deal of pressure will be necessary to fill

a bucket in a short amount of time. However, if the hose is shorter (e.g., 1 m) or wider (e.g.,

10 cm), the bucket will fill quickly with only a moderate amount of water pressure. This

is analogous to the dependence of electrical resistance on the length and diameter of the

conductor.

38 Chapter 2

This last analogy also illustrates the relationship between voltage, current, and resistance. If

a thin hose is used, the volume of water that passes out of the end of the hose will be small rela-

tive to what would be obtained with a wider hose and the same water pressure. Similarly, if

voltage stays the same and the resistance increases, the current will decrease. However, if a thin

hose is used, a large volume of water can be obtained in a given time period by increasing the

water pressure. Similarly, it is possible to maintain a constant current when the resistance is

increased by increasing the voltage.

We will talk more about how resistance and its close cousin impedance influence EEG record- ings in chapter 5.

Electricity and Magnetism Electricity and magnetism are fundamentally related to each other, and it is important to under-

stand this relationship to understand how electrical noise is picked up in ERP recordings and

how MEG recordings are related to EEG recordings (which will be described in more detail

later). The flow of current through a conductor is always accompanied by a magnetic field that

flows around the conductor. Moreover, if a magnetic field passes through a conductor, it induces

an electrical current. These two principles are illustrated in figure 2.1 , which shows what happens

when a current is passed through one of two nearby conductors. The flow of current through

one of the conductors generates a magnetic field, which in turn induces current flow in the other

conductor. This is how electrical noise in the environment (e.g., the 120 V in the video display)

Current flows through conductor #1

Magnetic field induces current flow in conductor #2

Magnetic field generated around conductor #1

Conductor #1

Conductor #2

Figure 2.1 Relationship between electricity and magnetism. A current is passed through conductor #1, and this generates a magnetic

field that circles around conductor #1. As this magnetic field passes through conductor #2, it induces a small current in

conductor #2. This is how electrical devices located near the subject can induce artifactual electrical “ noise ” in the

electrodes or electrode wires. It is also the basic principle underlying magnetoencephalogram (MEG) recordings.

A Closer Look at ERPs and ERP Components 39

can induce electrical activity in an ERP subject, in the electrodes, or in the wires leading from

the electrodes to the amplifier (see chapter 5 for details).

The Neural Origins of ERPs

The neural origins of ERPs were described briefly in chapter 1, and here we take a much closer

look. We will also discuss why it is so difficult to localize ERPs on the basis of scalp recordings

(an even more detailed discussion of ERP localization is provided in online chapter 14). For a

more detailed description of the neural and biophysical events underlying the generation of EEG

and ERP signals, see the review by Buzs á ki, Anastassiou, and Koch (2012).

Electrical Activity in Individual Neurons Neurons produce two main types of electrical activity, action potentials and postsynaptic poten- tials . Action potentials are discrete voltage spikes that travel from the beginning of the axon at the cell body to the axon terminals, where neurotransmitters are released. Postsynaptic potentials

are the voltages that arise when the neurotransmitters bind to receptors on the membrane of the

postsynaptic cell, causing ion channels to open or close and leading to a graded change in the

voltage across the cell membrane. It is fairly easy to isolate the action potentials arising from a

single neuron by inserting a microelectrode into the brain, but it is virtually impossible to com-

pletely isolate a single neuron ’ s postsynaptic potentials in an in vivo extracellular recording (because PSPs from different neurons become mixed together in the extracellular space). Con-

sequently, in vivo recordings of individual neurons ( “ single-unit ” recordings) measure action potentials rather than postsynaptic potentials. When many neurons are recorded simultaneously,

however, it is possible to measure either their summed postsynaptic potentials or their action

potentials. Recordings of action potentials from large groups of neurons are called multi-unit recordings, and recordings of postsynaptic potentials from large groups of neurons are called

local field potential recordings. 1 In the vast majority of cases, action potentials cannot be detected by surface (scalp) electrodes

because of the timing of the action potentials and the physical arrangement of axons. When an

action potential is generated, current flows rapidly into and then out of the axon at one point

along the axon, and then this same inflow and outflow occur at the next point along the axon,

and so on until the action potential reaches a terminal. If two neurons send their action potentials

down axons that run parallel to each other, and the action potentials occur at exactly the same

time, the voltages from the two neurons will summate. However, if one neuron fires slightly

after the other, current will be flowing into one axon at the same time that it is flowing out of

the adjacent location on the other axon, and these signals will cancel. Because large populations

of neurons do not usually fire at precisely the same time (i.e., within microseconds of each

other), action potentials cannot usually be recorded from the scalp. As a result, ERPs almost

always reflect postsynaptic potentials rather than action potentials. The main exceptions to

this rule are peaks I and II of the brainstem auditory evoked response, which reflect precisely

40 Chapter 2

synchronized action potentials generated in the cochlea and passing through the auditory nerve

within a few milliseconds after a sudden sound onset (Pratt, 2012). You can safely assume that

any ERPs recorded from the scalp more than 20 ms after stimulus onset reflect postsynaptic

potentials rather than action potentials.

Notably, the neural events leading to the fMRI BOLD signal are more heterogeneous. Any-

thing that increases glucose or oxygen utilization can potentially lead to a change in regional

cerebral blood flow and impact the BOLD signal, whereas ERPs solely reflect postsynaptic

potentials. I like to think about this fact when I ’ m talking to a neuroimaging researcher who is

smug about having millimeter-level spatial resolution, but I try not to say it aloud.

Summation of Postsynaptic Potentials Whereas the duration of an action potential is only about a millisecond, postsynaptic potentials

typically last tens or even hundreds of milliseconds. In addition, postsynaptic potentials are

largely confined to the dendrites and cell body. Under certain conditions, these factors allow

postsynaptic potentials from multiple neurons to summate, making it possible to record them at

a great distance (i.e., at the scalp).

Figure 2.2 shows how postsynaptic potentials are thought to lead to electrical potentials that

can be recorded on the scalp. 2 Scalp ERPs are thought to arise mainly from pyramidal cells , the main input – output cells of the cerebral cortex. These cells have a set of basal dendrites and a

single apical dendrite (all of which branch out after leaving the cell body; see figure 2.2A ). The

overall spatial configuration of the cell body and dendrites looks like a pyramid (if you use a

lot of imagination). Cortical pyramidal cells are all oriented perpendicular to the cortical surface,

with the apical dendrite heading in the direction of the cortical surface and the cell body and

basal dendrites located closer to the white matter (see figure 2.2B ).

If an excitatory neurotransmitter is released at the apical dendrite of a cortical pyramidal cell,

as shown in figure 2.2A , an electrical current (in the form of positively charged ions) will flow

from the extracellular space into the cell, yielding a net negativity on the outside of the cell in

the region of the apical dendrites. To complete the circuit, current will also flow out of the cell

body and basal dendrites, yielding a net positivity in this area. This flow of current creates a

tiny dipole (a pair of positive and negative electrical charges separated by a small distance). If the postsynaptic potential is inhibitory rather than excitatory, this reverses the flow of current

and changes the polarity of the signal recorded on the scalp. If the postsynaptic potential occurs

at the cell body or basal dendrites rather than at the apical dendrite, this also changes the polarity

(see box 2.1 for a discussion of the meaning of an ERP component ’ s polarity).

The dipole from a single neuron is so small that it cannot be recorded from a scalp electrode,

but the dipoles from many neurons will sum together, making it possible to measure the resulting

voltage at the scalp. For the voltages from the individual neurons to summate and be recordable

at the scalp, they must be present at the same time across thousands or millions of neurons, and

the dipoles from the individual neurons must be spatially aligned. If the neurons are at random

orientations with respect to each other, then the positivity from one neuron may be adjacent to

A Closer Look at ERPs and ERP Components 41

Axons from presynaptic cells

Apical dendrite

Postsynaptic cell axon

Basal dendrites

Cell body

A Stimulated

region of cortex

Equivalent current dipoleSkull

CortexC

D E

Current dipole

Magnetic field

Skull

Magnetic Field leaving head

Magnetic field entering head

Cortical surface

White matter

Figure 2.2 Principles of ERP generation. (A) Schematic pyramidal cell during neurotransmission. An excitatory neurotransmitter

is released from the presynaptic terminals in the apical dendrite, causing positive ions to flow into this region of the

postsynaptic neuron. This creates a net negative extracellular voltage (represented by the “ – ” symbols) just outside the

apical dendrite. To complete the circuit, voltage will flow through the neuron and then exit in the region of the cell body

and basal dendrites (represented by the “ + ” symbols). This flow of current forms a small dipole. The polarity of this

dipole would be inverted if an inhibitory neurotransmitter were released rather than an excitatory neurotransmitter. It

would also be inverted if the neurotransmission occurred at the cell body or basal dendrites rather than at the apical

dendrite. (B) Folded sheet of cortex containing many pyramidal cells. When a region of this sheet is stimulated, the

dipoles from the individual neurons summate. (C) The summated dipoles from the individual neurons can be approxi-

mated by a single equivalent current dipole, shown here as an arrow. By convention, the arrowhead indicates the positive

end of the dipole. The position and orientation of this dipole determine the distribution of positive and negative voltages

recorded at the surface of the head. (D) Example of a current dipole with a magnetic field traveling around it. (E)

Example of the magnetic field generated by a dipole that lies just inside the surface of the skull. If the dipole is roughly

parallel to the surface, the magnetic field can be recorded as it leaves and enters the head; no field can be recorded if

the dipole is oriented radially (perpendicular to the surface). Reprinted with permission from Luck and Girelli (1998).

42 Chapter 2

the negativity from the next neuron, leading to cancellation. Similarly, if one neuron receives an

excitatory neurotransmitter and another receives an inhibitory neurotransmitter, the dipoles of

the neurons will be in opposite directions and will cancel. However, if the neurons all have a

similar orientation and all receive the same type of input, their dipoles will summate and may

be measurable at the scalp. This is much more likely to happen in cortical pyramidal cells than

in other cell types or in other brain structures, so ERPs mainly arise from the pyramidal cells.

The summation of the individual dipoles is complicated by the fact that the cortex is not flat,

but instead has many folds. Fortunately, however, physicists have demonstrated that the summa-

tion of many nearby dipoles is essentially equivalent to a single dipole formed by averaging the

orientations of the individual dipoles. 3 This averaged dipole is called an equivalent current dipole . It is important to note, however, that whenever the individual dipoles are more than 90 ° from each other, they will cancel each other to some extent, with complete cancellation at 180 ° .

For example, the orientation of the neurons in the basal ganglia is largely random, making it

difficult or impossible to record basal ganglia activity from the scalp.

An important consequence of these facts about ERP generation is that only a fraction of brain

processes will produce a scalp ERP “ signature. ” To produce a measurable signal on the scalp,

the following conditions must be met:

• Large numbers of neurons must be activated at the same time.

• The individual neurons must have approximately the same orientation.

• The postsynaptic potentials for the majority of the neurons must arise from the same part of

the neurons (either the apical dendrite or the cell body and basal dendrites).

• The majority of the neurons must have the same direction of current flow to avoid cancellation.

Box 2.1 What Does the Polarity of an ERP Component Mean?

I am often asked whether it “ means something ” if a component is positive or negative. My response

is that polarity depends on a combination of four factors:

• Whether the postsynaptic potential is excitatory or inhibitory

• Whether the postsynaptic potential is occurring in the apical dendrite or the basal dendrites and

cell body

• The location and orientation of the generator dipole with respect to the active recording electrode

• The location of the reference electrode (which will be discussed in chapter 5)

If you know three of these factors, then the polarity of the ERP can be used to infer the fourth

factor. But we don ’ t usually know three of these factors, so the polarity doesn ’ t usually tell us

anything. Polarity at a given site is meaningful only insofar as most components will have a constant

polarity over a given region of the head, and the polarity of a component can help us determine

which component we are seeing. But it cannot ordinarily be used to determine whether the compo-

nent reflects excitation or inhibition.

A Closer Look at ERPs and ERP Components 43

Volume Conduction When a dipole is present in a conductive medium such as the brain, current is conducted through

that medium until it reaches the surface. This is called volume conduction and is illustrated in figure 2.2C . I should note, however, that I don ’ t like the term volume conduction very much because it might be taken to imply that we are recording charged particles that pass from the

neurons all the way to the scalp electrodes. That isn ’ t the way it works. By analogy, when

electricity is generated in a power plant and flows through power lines, the electrons don ’ t go

all the way from the power plant to your house. Instead, one electron pushes the next one,

which pushes the next one, and so forth. Similarly, when a dipole is active in the brain, you

don ’ t have to wait for charged particles to move all the way from the dipole to the surface.

Instead, a postsynaptic potential in a set of neurons creates an essentially instantaneous voltage

field throughout the entirety of the head, with no meaningful delay. And don ’ t forget that you

are measuring voltage, which is the potential for current to flow and not the actual flow of

current.

Electricity does not just run directly between the two poles of a dipole in a conductive medium,

but instead spreads out across the conductor. Consequently, ERPs do not appear only at an

electrode located directly above the dipole but are instead picked up by electrodes located all

over the head. The high resistance of the skull causes the voltage to be even more widely dis-

tributed. Consequently, the scalp distribution of an ERP component is usually very broad.

Figure 2.2C illustrates a very important fact about ERP scalp distributions. For any dipole

location, the voltage will be positive over one portion of the scalp and negative over the remain-

der of the scalp, with an infinitesimally narrow band of zero that separates the positive and nega-

tive portions. In many cases, one of these portions will fall over a part of the head where you

don ’ t have any electrodes (e.g., the face or the bottom of the brain), so you might not see both

sides of the dipole. In other cases, you will be able to see both the positive and negative sides

of the dipoles. 4 The zero band that separates the positive and negative sides of the head will be

in a different place for each different dipole, and no single zero band will be present when

multiple dipoles are active. Thus, there is no place on the head that consistently has zero voltage

(see chapter 5 for additional discussion).

Relationship between Dipoles and Components An equivalent current dipole represents the summed activity of a large number of nearby neurons.

How is this related to the concept of an ERP component ? We will define the term ERP component more carefully later in this chapter, but we can make a simple link to the concept of a dipole at

this time. Specifically, when an equivalent current dipole represents the activity of a single

functional brain region, this dipole can be considered to be the same thing as an ERP component.

The moment-by-moment changes in the magnitude of the dipole (sometimes called the dipole ’ s

source waveform ) constitute the time course of the ERP component. As will be described soon, all of the different dipoles in the brain sum together to give us the complex pattern of positive

and negative peaks that we record from our scalp electrodes.

44 Chapter 2

Magnetic Fields The blurring of voltage caused by the high resistance of the skull can be largely circumvented

by recording magnetic fields instead of electrical potentials. As illustrated in figure 2.2D , an

electrical dipole is always surrounded by a magnetic field of proportionate strength, and these

fields summate in the same manner as voltages. Thus, whenever an ERP is generated, a magnetic

field is also generated, running around the ERP dipole. Moreover, the skull is transparent to

magnetism, so the magnetic fields are not blurred by the skull, 5 leading to much greater spatial

resolution than is possible with electrical potentials. The magnetic equivalent of the EEG is

called the magnetoencephalogram (MEG), and the magnetic equivalent of an ERP is an event- related magnetic field (EMRF).

As illustrated in figure 2.2E , a dipole that is parallel ( tangential ) to the surface of the scalp will be accompanied by a magnetic field that leaves the head on one side of the dipole and enters

back again on the other side. If a highly sensitive probe called a SQUID (superconducting

quantum interference device) is placed next to the head, it is possible to measure the magnetic

field as it leaves and reenters the head. However, if the dipole is perpendicular to the surface of

the head (a radial dipole), the magnetic field running around the dipole will not leave the head, and it will be “ invisible ” to the SQUID. For orientations that are between tangential and radial,

the strength of the magnetic field that is recorded from outside the head gets weaker and weaker

the more radial the dipole is. Similarly, the strength of the extracranial magnetic field becomes

very weak for deep dipoles. Thus, MEG recordings are primarily sensitive to superficial, tan-

gential dipoles.

Because magnetic fields are not as widely dispersed as electrical potentials, they can provide

more precise localization. However, as will be discussed in online chapter 14, the combination

of ERP and ERMF recordings provides even better localization than ERMF recordings alone.

Unfortunately, three factors make magnetic recordings very expensive: the SQUID is expensive;

the coolant must be continually replenished; and an expensive magnetically shielded recording

chamber is necessary to attenuate the earth ’ s magnetic field, which is orders of magnitude larger

than the MEG signal. Thus, MEG/ERMF recordings are much less common than EEG/ERP

recordings.

The Forward Problem and the Superposition of Components on the Scalp

If I tell you the locations and orientations of a set of dipoles in a brain, along with the shape

and conductances of the brain, skull, and scalp, then it would be possible for you to use a

relatively simple set of equations to compute the distribution of voltage that would be observed

for those dipoles. This is called the forward problem, and it is relatively easy to solve. In this section, I will spend some time explaining how the forward problem is solved in a little bit of

detail, because it will help you to understand exactly how the ERP components generated in the

brain become mixed together in the scalp electrodes. This creates the superposition problem,

which I described briefly in chapter 1 and which is often the biggest impediment in ERP studies.

A Closer Look at ERPs and ERP Components 45

Describing the forward problem in detail requires me to introduce a little bit of math, but only

a very little bit (see box 2.2 ).

The forward problem is illustrated in figure 2.3 , which shows the ERP waveforms for three

hypothetical generator locations. These are called source waveforms , and they show the time course of voltage for the components. For any given electrode location on the scalp, a fixed percent-

age of the source waveform from a given internal generator will propagate to the electrode. That

is, X% of the voltage from a given generator will be propagated to a given electrode site, where X

has a different value for each combination of internal generator and external scalp electrode. The

percentage of the voltage that is propagated will depend on the position and orientation of the

generator with respect to the position of the electrode, along with the conductivity of the various

tissues within the head. For example, a high percentage of the voltage from a superficial radial

dipole will propagate to an electrode on the scalp right over the top of the generator, and a smaller

(and inverted) percentage will propagate to an electrode on the opposite side of the head.

It ’ s actually possible to estimate the percentage of propagation from each possible generator

location to each electrode site in a given subject by creating a model of the subject ’ s head from

a structural MRI scan, combined with normative conductivity values for the different tissues that

constitute the head (e.g., brain, skull, scalp). There are software packages that can provide the

propagation factors if you provide a structural MRI scan.

Box 2.2 Four Kinds of Math

ERP waveforms are sequences of numbers, so you can ’ t escape a little bit of math if you want to

understand ERPs. If you are a “ math person, ” then you are probably looking forward to seeing some

mathematical formalisms as you read the book. But if you are not a math person, the last thing

you ’ ll want to see is a lot of equations. There will be some equations in the following chapters, but

they will be very simple. And I promise not to write something like “ As will be obvious from equa-

tion 6.4 … ” because I don ’ t usually find that an equation makes something obvious.

I am not a math person. I managed to get through a year of calculus in my freshman year of

college, but that ’ s as far as I got. And I remember almost nothing I learned that year. So this book

contains no calculus.

It turns out that you can understand all the key mathematical concepts involved in ERP research

without any calculus. In fact, everything I will describe can be boiled down to addition, subtraction,

multiplication, and division. If you are not a math person, you can use these four simple mathemati-

cal operations to understand things like Fourier analysis, time – frequency analysis, and how filters

work. This will require that you spend some time looking at simple equations that combine these

four simple operations in interesting ways, but ultimately it ’ s all just arithmetic that anyone can

understand.

If you are a math person, I think you will find that boiling things down in this way allows you

to find a new appreciation for the logic that underlies the mathematics. And you will probably

discover that there are some important things about Fourier analysis, time – frequency analysis, and

filtering that you did not fully appreciate before.

46 Chapter 2

Figure 2.3 Relation between the underlying component waveforms and the observed scalp waveforms. In this example, three

components are present (C1, C2, C3), each of which has a source waveform (time course of voltage, shown at the bottom

left) and a generator location (represented by the arrows in the head). The contribution of each component waveform

to the observed waveform at a given electrode site is determined by a weighting factor that reflects the location and

orientation of the generator relative to that electrode, along with the conductivity of the tissues that form the head. The

table shows the weighting factors between the three components, and the three electrode sites are given in the table (but

note that these are made-up values, not the actual weighting factors from a real head). The observed waveform at a given

electrode site (shown at the bottom right) is equal to the sum of each of the component waveforms, multiplied by the

weighting factor between each component and that electrode site. The weights are indicated by the w ’ s on the arrows between the component waveforms and the observed waveforms (e.g., w 2,3 represents the weighting factor between component 2 and electrode 3). Adapted with permission from Kappenman and Luck (2012). Copyright 2012 Oxford

University Press.

A Closer Look at ERPs and ERP Components 47

The proportion of the voltage that is propagated from a given generator location to a given

electrode site is called the weight between the generator and the electrode. There is a separate weight for each combination of generator location and electrode site. In figure 2.3 , the weights

are denoted as w x,y , where x is the generator location and y is the electrode site. For example, the weight from generator 2 to electrode 1 is denoted w 2,1 . I just made up the weights shown in figure 2.3 — they are not the actual weights. For example, real weights would be much less than

1.0, because only a small proportion of the generator voltage makes it all the way out to the

scalp electrodes. The real weights would be provided by a software package on the basis of a

subject ’ s structural MRI data. Note that the weights are proportions (between – 1 and +1), not

percentages.

The “ fake ” weights shown in figure 2.3 make it easy to see how the waveforms at a given

electrode site reflect the weighted sum of the internal underlying components. For example, the

waveform at electrode E1 is simply the C1 waveform plus 25% of the C2 waveform plus 50%

of the C3 waveform (because the weights from components C1 – C3 to electrode E1 are 1.0, 0.25,

and 0.50, respectively). If you think this seems very simple, you ’ re right! The waveform at a

given electrode site is always just the weighted sum of all the source waveforms. This simplicity

arises from the fact that voltages simply add together in a simple conductor like the human head.

Note that the voltage at a given electrode site is a weighted sum of all the underlying com- ponents. The weights will be negative on one side of the head and positive on the other, with

a narrow band where the weights are zero at the transition between the positive and negative

sides of the dipoles. And the weights may be quite small near this band. However, a given

electrode site picks up at least some voltage from almost every component in the brain. This

means that almost all of the components are mixed together at every electrode site. How many

different components are likely to be mixed together in a given experiment? It is difficult to

know for sure, but dozens may be present in a typical experiment. For example, evidence for

at least 10 different sources was found in the brief period from 50 to 200 ms after the onset of

an auditory stimulus in a simple target detection task (Picton et al, 1999), and many more are

presumably active when a longer time range is examined and when the subject is engaged in

a complex task.

In most cases, we are interested in measuring individual components, not the mixture that we

record at a given scalp electrode. Unfortunately, there is no foolproof way to recover the under-

lying components from the recordings obtained at the scalp. There are many different methods

that attempt to recover the underlying components (see box 2.3 ), but all of them are based on

assumptions that are either known to be false or are not known to be true. The mere fact that

each of these techniques will arrive at a different solution is an indication that most (or all) of

them are incorrect.

As this chapter progresses, we will see why this superposition problem makes life so difficult

for ERP researchers. You may find this depressing, but keep in mind that we will eventually

discuss a set of strategies for overcoming the superposition problem. And the online supplement

to chapter 4 describes some excellent examples of previous studies that have overcome the

48 Chapter 2

Box 2.3 Unmixing the Components

The mixing of underlying components in scalp recordings is such an important problem that many

different mathematical procedures have been developed to unmix them. The best known and most

widely used procedures are dipole localization methods, principal component analysis, independent

component analysis, Fourier analysis, and time-frequency analysis. All of these will be covered in

some detail later in the book.

Although these techniques seem very different from each other, they all share a fundamental

underlying structure, and it is worth understanding this structure. Specifically, they all assume that

the waveforms recorded at the scalp consist of the weighted sum of a set of underlying basis func- tions . However, they make different assumptions about the nature of these basis functions. For example, Fourier analysis assumes that the basis functions are sine waves, but it makes no assump-

tions about the pattern across the scalp; in contrast, dipole localization methods make no assumptions

about the time course of the basis functions, but they assume that the scalp distribution reflects the

conductivity of the brain, skull, and scalp. These techniques also differ widely in the mathematical

approach that is used to unmix the observed waveforms. However, it is useful to keep in mind that

they all assume that the observed waveforms consist of the sum of a relatively small set of basis

functions.

superposition problem and made important contributions to our understanding of the mind and

brain.

The Challenges of ERP Localization

This section provides a brief discussion of the challenges involved in localizing ERPs. A more

complete discussion is provided in online chapter 14.

As noted in the description of the forward problem, it is relatively easy to compute the dis-

tribution of voltage on the scalp if you know the locations and orientations of the dipoles (and

have a structural MRI scan). However, if I provide you with an observed voltage distribution

from the scalp and ask you to tell me the locations and orientations of the dipoles, you will not

be able to provide an answer with 100% confidence. This is the inverse problem , and it is what mathematicians call an “ ill-posed ” or “ underdetermined ” problem. This simply means that there

are multiple different sets of dipoles that can perfectly explain a given voltage distribution, and

there is no way to tell which is the correct one. In fact, it has been known for more than 150

years that an infinite number of different dipole configurations can produce any given voltage

distribution (Helmholtz, 1853; Nunez & Srinivasan, 2006; see also Plonsey, 1963). It is impos-

sible to know with certainty which one of these configurations is the one that is actually respon-

sible for producing the observed voltage distribution (unless you have other sources of

information, such as lesion data).

Figure 2.4 illustrates some of the challenges involved in localizing ERPs. When a single dipole

is present just under the skull and points directly outward (a superficial, radial dipole), a very

A Closer Look at ERPs and ERP Components 49

Figure 2.4 Scalp distributions (left) produced by different dipole configurations (right). See the text for descriptions of panels A – D

Psychological Association.

50 Chapter 2

focal voltage distribution is observed on the scalp, with the maximum voltage directly over the

location of the dipole ( figure 2.4A ). If this dipole is moved laterally even a small amount (e.g.,

1 cm), the voltage distribution will be noticeably different. Consequently, a dipole such as this

can be localized quite accurately simply by comparing the observed voltage distribution with

the distribution that would be produced by a single hypothetical dipole with various different

positions and orientations and selecting the dipole that best fits the observed data. Noise in the

data will distort the observed scalp distribution somewhat, but it is still possible to localize a

single superficial dipole like the one shown in figure 2.4A with reasonable accuracy as long as

the noise is not too large (and assuming you know for certain that it is a single superficial dipole). Multiple-dipole configurations also exist that can produce exactly the same distribution of

voltage as a single superficial dipole. Thus, we can localize a single superficial dipole with

considerable precision (assuming very low levels of noise in the average ERP waveforms), but

we cannot know from the scalp distribution that only a single superficial dipole is present.

Now consider the somewhat deeper dipole shown in figure 2.4B . The distribution of voltage

over the scalp is broader than that observed with the superficial dipole, and moving the dipole

laterally by a given amount won ’ t have as large of an effect on the scalp distribution for the

deeper dipole as it would for the superficial dipole. All else being equal, the deeper the dipole,

the smaller and more broadly distributed the voltage will be on the scalp, and the less accurately

it can be localized. An even more important problem arises in this situation, because it becomes

difficult to tell the difference between a deep but focal generator and a superficial generator that

extends across a large region of cortex. For example, the error-related negativity has a fairly

broad distribution that is consistent with a single deep generator in the anterior cingulate cortex

(Dehaene, Posner, & Tucker, 1994), but it is also consistent with the activation of a large patch

of superficial cortex.

Figure 2.4C shows a situation in which two dipoles are simultaneously active. Voltages arising

from different generators simply sum together, so the scalp distribution of the two simultaneous

dipoles is simply equal to the sum of the scalp distributions of the individual dipoles. In this

particular example, the two dipoles are both superficial, and they are quite far apart. It would be

possible for you to localize the dipoles quite accurately in this situation, assuming that the data

were not distorted by much noise and that you already knew that exactly two dipoles were active.

Figure 2.4D shows a different situation in which two dipoles are simultaneously active (the

dipoles from figure 2.4A and B ). This is a “ nightmare scenario ” for people who want to localize

ERPs, because the scalp distribution of the sum of the two dipoles is nearly indistinguishable

from the scalp distribution of the superficial dipole alone. Given even a small amount of noise,

it would be impossible to know whether the data were the result of a single superficial dipole

or two dipoles that are aligned in this fashion. The problem would still be bad even if the two

dipoles were not perfectly aligned. Moreover, imagine an experiment in which these two dipoles

were present, and an experimental manipulation led to a change in the amplitude of the deep

dipole with no effect in the superficial dipole. It is very likely that an experimental effect of this

nature would be attributed to the superficial dipole rather than the deep dipole.

A Closer Look at ERPs and ERP Components 51

As more and more simultaneous dipoles are added, the likelihood of dipoles aligning in this

manner increases, and it becomes more and more difficult to determine how many dipoles are

present and to localize them accurately. This problem becomes even worse when the data are

noisy. Under these conditions, a set of estimated dipole locations that matches the observed scalp

distribution can be quite far from the actual locations.

The examples shown in figure 2.4 are cause for both optimism and pessimism. You should be

optimistic because ERPs can be localized accurately if you can be certain that you have a single

dipole or that you have two to three dipoles that are not aligned in a way that makes them dif-

ficult to localize. But you should also be pessimistic because it will be difficult to localize ERPs

unless you know that you have a single dipole or that you have two to three dipoles that are not aligned in a way that makes them difficult to localize. Fortunately, there are some things you

can do to increase the likelihood that only a single dipole is active (e.g., performing localization

on difference waves that isolate a single component).

In many experiments, the number of dipoles could be very large ( > 10), and localizing ERPs solely on the basis of the observed scalp distribution would be impossible to do with confidence.

The only way to localize ERPs in this case is to add external constraints, and this is how existing

procedures for localizing ERPs solve the non-uniqueness problem. As will be discussed in detail

in online chapter 14, some common procedures allow the user to specify a fixed number of

dipoles (Scherg, 1990), whereas other procedures use structural MRI scans and constrain the

dipoles to be in the gray matter (Dale & Sereno, 1993; H ä m ä l ä inen, Hari, Ilmonieni, Knuutila,

& Lounasmaa, 1993) or choose the solution that best minimizes sudden changes from one patch

of cortex to the next (Pascual-Marqui, Esslen, Kochi, & Lehmann, 2002). Although each of these

methods produces a unique solution, they do not necessarily produce the correct solution. And

they may produce quite different solutions, further reducing our confidence that any of them has

found the correct solution.

The most significant shortcoming of mathematical procedures for localizing ERPs is that they

do not typically provide a well-justified margin of error. That is, they do not indicate the probabil-

ity that the estimated location falls within some number of millimeters from the actual location.

For example, I would like to be able to say that the N2pc component in a particular experiment

was generated within 9 mm of the center of the lateral occipital complex and that the probability

that this localization is incorrect is less than 0.05. I am aware of no mathematical localization

technique that is regularly used to provide this kind of information. 6 Without a margin of

error, it is difficult to judge the credibility of a given localization estimate. In most cases, the

strongest claim that can be made is that the observed data are consistent with a given generator

location.

Although it is usually impossible to definitively localize ERPs solely on the basis of the

observed scalp distributions, this does not mean that ERPs can never be localized. Specifically,

ERPs can be localized using the general hypothetico-deductive approach that is used throughout

science. That is, a hypothesis about the generator location for a given ERP effect leads to a set

of predictions, which are then tested by means of experiments. One prediction, of course, is that

52 Chapter 2

the observed scalp distribution will be consistent with the hypothesized generator location.

However, confirming this prediction is not usually sufficient to have strong confidence that the

hypothesis about the generator location is correct. Thus, it is important to test additional predic-

tions. For example, one could test the prediction that damage to the hypothesized generator

location eliminates the ERP component. Indeed, researchers initially hypothesized that the P3

component was generated in the hippocampus, and this hypothesis was rejected when experi-

ments demonstrated that the P3 is largely intact in individuals with medial temporal lobe lesions

(Polich, 2012). Similarly, one could predict that an fMRI experiment should show activation in

the hypothesized generator location under the conditions that produce the ERP component (see,

e.g., Hopf et al., 2006). It is also possible to record ERPs from the surface of the cortex in

neurosurgery patients, and this can been used to test predictions about ERP generators (see, e.g.,

Allison, McCarthy, Nobre, Puce, & Belger, 1994). This hypothesis-testing approach has been

quite successful in localizing some ERP components.

As was discussed in chapter 1, the main advantages of the ERP technique are its high temporal

resolution, its relatively low cost, its noninvasiveness, and its ability to provide a covert and

continuous measure of processing. Spatial resolution is simply not one of the strengths of the

ERP technique, and it is therefore sensible that this technique should mainly be used in studies

designed to take advantage of its strengths and that are not limited by its weaknesses.

Waveform Peaks versus Underlying ERP Components

Now that you understand how the underlying components become mixed together in scalp

electrodes — and why it is so difficult to recover the underlying components from the observed

scalp waveforms — it is time to consider why this is such a big problem in most ERP studies. In

this section, I will show a set of simple artificial waveforms that demonstrate how the superposi-

tion problem can easily lead to misinterpretations of ERP data, along with a set of “ rules ” for

avoiding these misinterpretations. In general, the goal of this section is to get you to look beyond

the ERP waveforms that you have recorded from the scalp and think about the underlying com-

ponents that might give rise to these surface waveforms. Even though you cannot usually localize

the underlying components, you can learn to make educated guesses about the underlying com-

ponents from the observed scalp waveforms.

The term ERP component will be described more formally later in this chapter. For now, you can just think of a component as electrical activity within a given region of the brain

that reflects some neural process occurring in that region, which then propagates to our scalp

electrodes.

To understand the underlying “ deep structure ” of a set of ERP waveforms, the first thing you

need to do is understand how the peaks in the observed ERP waveforms can provide a mislead-

ing representation of the underlying components. To make this clear, I created some simple

simulated components using Excel and then summed them together to create simulated scalp

ERP waveforms. The results are shown in figure 2.5 . This is a busy and complicated figure, but

A Closer Look at ERPs and ERP Components 53

Baseline

Peak1

200

– 400 600 800 1000 ms

Peak1

Peak2

Peak3

C1'

C2'

C3'

A D

B E

C F

Peak1

Peak2

Peak3

Decrease in amplitude of C2'

in Condition X Observed ERP

Waveform

One possible set of underlying components

Another possible set of underlying components

Increase in amplitude of C3 in Condition Z

Increase in amplitude of C1 in Condition Y

Condition X minus

Baseline

Condition Y minus

Baseline

Condition Z minus

Baseline

Condition X Condition Y Condition Z

Figure 2.5 Examples of the complications that arise when underlying components sum together to form an observed ERP waveform.

Panels B and C show two different sets of underlying components that sum together to produce the observed waveform

shown in panel A. Panels D, E, and F show three simulated experiments in which one component differs between a

baseline condition and three comparison conditions. In panel D, component C2 ′ is decreased in condition X compared to the baseline condition. In panel E, component C1 is increased in condition Y compared to the baseline condition,

which creates an apparent shift in the latencies of both peak 1 and peak 2. In panel F, component C3 is increased in

condition Z relative to the baseline condition, influencing both the amplitude and the latency of peak 2. Panels G, H,

and I illustrate difference waves for conditions X, Y, and Z, respectively.

54 Chapter 2

the next several sections will walk you through the different parts. This is probably the most

important figure in the whole book, so it ’ s worth taking your time and understanding each panel

of the figure.

Voltage Peaks Are Not Special Our eyes are naturally drawn to the peaks in a waveform, but the peaks often encourage incorrect

conclusions about the underlying components. This is illustrated in panels A and B of figure

2.5 , which show how three very reasonable components sum together to create the ERP wave-

form that we observe at the scalp. If you look carefully, you can see how the peaks in the observed

waveform do a poor job of representing the underlying components. First, notice that the first

positive deflection in the observed waveform (panel A) peaks at 50 ms, whereas the first under-

lying component (C1 in panel B) peaks at 100 ms. Similarly, the third underlying component

(C3 in panel B) begins at 100 ms, but there is no obvious sign of this component in the observed

waveform until approximately 200 ms.

It is natural for the human visual system to focus on the peaks in the waveform. However,

the points in an ERP waveform where the voltage reaches a maximally positive or maximally

negative value do not usually have any particular physiological or psychological meaning, and

they are often completely unrelated to the time course of any individual underlying component.

The peaks in the observed waveform are a consequence of the mixture of components, and they

typically occur at a different time than the peaks of the underlying components. For example,

the latency of a given peak in the observed waveform may differ across electrode sites (because

of the different weights from the underlying components at the different electrode sites),

whereas an underlying component has exactly the same time course at every electrode site

(because the voltage propagates instantaneously to all electrodes). Sometimes the peak in the

observed waveform occurs at the same time as the peak in an underlying component (e.g., when

the underlying component is much larger than the other components). However, even in these

cases it is not clear that the peak of activity tells us anything special about the underlying

process. That is, theories of cognition or brain processes do not usually say much about when

a process peaks. Instead, these theories usually focus on the onset of a process, the duration of

the process, or the integrated activity over time (see, e.g., Pashler, 1994; Usher & McClelland,

2001).

This leads to our first and most important “ rule ” about interpreting ERP data:

Rule 1: Peaks and components are not the same thing. There is nothing special about the point

at which the voltage in the observed waveform reaches a local maximum.

In light of this fundamental rule, I am always amazed at how often peak amplitude and

peak latency are used to measure the magnitude and timing of ERP components. These

measures often provide a highly distorted view of the amplitude and timing of the underlying

components. Chapter 9 will describe better techniques for quantifying ERP data that do not rely

on peaks.

A Closer Look at ERPs and ERP Components 55

Peak Shapes Are Not the Same as Component Shapes Panel C of figure 2.5 shows another set of underlying components that also sum together to

equal the ERP waveform shown in panel A. These three components are labeled C1 ′ , C2 ′ , and C3 ′ . From the single observed waveform in panel A, there is no way to tell whether it was actu- ally created from components C1, C2, and C3 in panel B or from C1 ′ , C2 ′ , and C3 ′ (or from some other set of underlying components). There are infinitely many sets of underlying compo-

nents that could sum together to produce the ERP waveform in panel A (or any other ERP

waveform).

If the observed waveform in panel A actually consisted of the sum of C1 ′ , C2 ′ , and C3 ′ , the peaks in the observed panel would be a very poor indicator of the shapes of the underlying

components. For example, the relatively short duration of peak 2 in panel A bears little resem-

blance to the long duration of component C2 ′ in panel C. If you saw a waveform like panel A in an actual experiment, you probably wouldn ’ t guess that a very long-duration negative com-

ponent like C2 ′ was a major contributor to the waveform. This leads to our second rule:

Rule 2: It is impossible to estimate the time course or peak latency of an underlying ERP com-

ponent by looking at a single ERP waveform — there may be no obvious relationship between

the shape of a local part of the waveform and the underlying components.

In a little bit, we will talk about how difference waves can sometimes be used to determine

the shape of an underlying ERP component. You can also gain a lot of information by looking

at the waveforms from multiple scalp sites because the time course of a given component ’ s

contribution to one electrode site will be the same as the time course of its contribution to the

other electrode sites (because ERPs propagate to all electrodes instantaneously).

The Time Course and Scalp Distribution of an Effect Panels D – F of figure 2.5 show three simulated experiments in which a “ baseline ” condition is

compared with three other conditions, named X, Y, and Z. The waveform for the baseline condi-

tion is the same as that shown in panel A, which could be the sum of either components C1, C2,

and C3 from panel B or components C1 ′ , C2 ′ , and C3 ′ from panel C. I am calling this a “ base- line ” condition only because I am using it for comparison with conditions X, Y, and Z.

In the simulated experiment shown in panel D, we are assuming that the observed waveform

for the baseline condition is the sum of components C1 ′ , C2 ′ , and C3 ′ and that component C2 ′ is decreased by 50% in condition X relative to the baseline condition. However, if you just saw

the waveforms in this panel, and you didn ’ t know the shapes of the underlying components, you

might be tempted to conclude that at least two different components differ between the baseline

condition and condition X. That is, it looks like condition X has a decrease in the amplitude

of a negative component peaking at 300 ms and an increase in the amplitude of a positive com-

ponent peaking at 500 ms. You might even conclude that condition X had a larger positive

component peaking at 100 ms. This would be a very misleading set of conclusions about the

56 Chapter 2

underlying components because the effect actually consists entirely of a decrease in the ampli-

tude of a single, broad, negative component (C2 ′ ). These incorrect conclusions arise from our natural inclination to assume that the peaks in the observed waveform have a simple and direct

relationship to the unknown underlying components. This leads us to conclude that the increased

amplitude in peak 3 in panel D reflects an increase in the amplitude of a long-latency positive

component, when in fact it is a result in of a decrease in the amplitude of an intermediate-latency

negative component.

Panel E shows a simulated experiment comparing the baseline condition with condition Y.

This time, we ’ re assuming that the underlying components are C1, C2, and C3 (rather than C1 ′ , C2 ′ , and C3 ′ ). Condition Y is the same as the baseline condition except for an increase in the amplitude of component C1. However, if you saw these observed waveforms, you might be

tempted to conclude that condition Y has an increase in the amplitude of an early positive com-

ponent peaking at 100 ms followed by a decrease in a negative component that peaks at 300 ms.

Similarly, panel F shows a simulation in which the amplitude of component C3 is increased

in condition Z compared to the baseline condition. Although only this late positive component

differs across conditions, the observed waveform for condition Z appears to exhibit a reduction

of a negative component at 300 ms as well. However, this is just a consequence of the fact that

component C3 overlaps in time with component C2.

In panels D – F, a change in the amplitude of a single component caused a change in the

amplitude of multiple peaks, making it likely that the researcher will falsely conclude that mul-

tiple underlying components differ across conditions. I have seen this general pattern of wave-

forms countless times, and people often misinterpret the effects in exactly this way. This leads

to our third rule:

Rule 3: An effect during the time period of a particular peak may not reflect a modulation of

the underlying component that is usually associated with that peak.

Difference Waves as a Solution Difference waves can often be used to provide a better estimate of the time course and scalp dis-

tribution of the underlying components. Difference waves are a very simple concept: You simply

take the voltage at each time point in one ERP waveform and subtract the voltage from a different

ERP waveform at the corresponding time points. The result gives you the difference in voltage

between the two waveforms at each time point. In an oddball experiment, for example, you can

subtract the frequent-trial waveform from the rare-trial waveform (rare-minus-frequent), and the

resulting difference wave will show the difference in voltage between these trial types at each

point in time (see, e.g., figure 1.4 in chapter 1). The difference wave from a given electrode site

is analogous to a difference image in an fMRI experiment, except that differences are computed

at each time point in an ERP difference wave and at each voxel in an fMRI difference image.

Panels G – I of figure 2.5 show difference waves from the three simulated experiments shown

in panels D – F. The baseline waveform has been subtracted from the waveforms for conditions

A Closer Look at ERPs and ERP Components 57

X, Y, and Z. These difference waves are very helpful in showing us the nature of the experimental

effects. They make the time course of the effects very clear, showing that they are different from

the time course of the peaks in the observed waveforms. Indeed, under these conditions — in

which the experimental effects consist entirely of a change in the amplitude of a single underly-

ing component — the difference waves reveal the time course and scalp distribution of the under-

lying component that differs across conditions. That is, if you compare the difference wave in

panel G to the underlying components in panel C, you will see that the difference wave has

exactly the same time course as component C2 ′ . And because the difference waves in these examples subtract away everything except the one component that differs across conditions, the

difference waves will have the same topography as the underlying component.

You cannot be guaranteed that a difference wave will contain only a single component. For

example, the rare-minus-frequent difference waves from the oddball paradigm that were dis-

cussed in chapter 1 (see figure 1.4) contained both an N2 wave and a P3 wave. However, there

is a good chance that you will have a single component in your difference waves if you compare

conditions that are very subtly different.

How can you know if a broad effect in a difference wave consists of a change in a single

underlying component or a sequence of two or more components? First, you can look at the

scalp distribution of the difference wave, collapsed across the entire duration of the effect, to

see if the scalp distribution is too complex to be explained by a single dipole. Second, you can

compare the scalp distributions of the early and later parts of the difference wave. If they are

the same, then you probably have a single component; if they are different, then you have at

least two components. Difference waves are discussed in more detail later in this chapter.

Interactions between Amplitude and Latency Although the amplitude and latency of an underlying component are conceptually independent,

they can become confounded when the underlying components become mixed together at the

scalp. For example, panel F of figure 2.5 illustrates the effect of increasing the amplitude of

component C3. Because component C3 overlaps with peak 2, this change in the amplitude of

component C3 causes a shift of approximately 20 ms in the peak latency of peak 2 in condition

Z relative to the baseline condition. This leads to our next rule:

Rule 4: Differences in peak amplitude do not necessarily correspond with differences in com-

ponent size, and differences in peak latency do not necessarily correspond with changes in

component timing.

This is a somewhat depressing rule, because the most obvious virtue of the ERP technique is

its temporal resolution, and it is unpleasant to realize that estimates of component timing can

be distorted by changes in the amplitude of temporally overlapping components. Keep in mind,

however, that this sort of temporal distortion mainly happens when a large change in a large

component overlaps with a smaller component, leading to a small latency change in the smaller

component. If you think carefully about a given effect and spend some time looking at the

58 Chapter 2

difference waves, you should be able to determine whether the latency differences could plau-

sibly be a result of amplitude changes (or vice versa). In addition, chapters 3 and 4 will discuss

how this problem can be completely avoided by looking at the onset time of a difference wave.

Distortions Caused by Averaging In the vast majority of ERP experiments, the ERP waveforms are isolated from the background

EEG by means of signal averaging. It ’ s tempting to think of averaging as a process that simply

attenuates the nonspecific EEG, allowing us to see what the single-trial ERP waveforms look like.

However, to the extent that the single-trial waveform varies from trial to trial, the averaged ERP

may provide a distorted view of the single-trial waveforms, particularly when component latencies

vary from trial to trial. This is illustrated in figure 2.6 . Panel A illustrates three single-trial ERP

waveforms (without any EEG noise), with significant latency differences across trials, and panel

B shows the average of those three single-trial waveforms. The averaged waveform differs from

the single-trial waveforms in two significant ways. First, it is smaller in peak amplitude. Second,

it is more spread out in time. As a result, even though the waveform in panel B is the average of

the waveforms in panel A, the onset time of the averaged waveform in panel B reflects the onset

time of the earliest single-trial waveform and not the average onset time. In other words, the onset

time in the average waveform is not equal to the average of the single-trial onset times (see chapter

8 and online chapter 11 for additional discussion). This leads to our next rule:

Rule 5: Never assume that an averaged ERP waveform directly represents the individual wave-

forms that were averaged together. In particular, the onset and offset times in the averaged

waveform represent the earliest onsets and latest offsets from the individual trials or individual

subjects that contribute to the average.

Fortunately, it is often possible to measure ERPs in a way that avoids the distortions created

by the averaging process. For example, the area under the curve in the averaged waveform shown

in figure 2.6A is equal to the average of the area under the single-trial curves in figure 2.6B .

Similarly, it is possible to find the time point that divides the area into two equal halves, and

this can be a better measurement of latency than peak measures. These methods are described

in detail in chapter 9.

Comparisons across Experiments It can be very difficult to determine whether an ERP effect in one experiment reflects the same

underlying component as an ERP effect in another experiment. For example, imagine that you ’ ve

conducted an experiment in which you recorded ERPs from bilingual speakers of two languages,

Xtrinqua and Kirbish, focusing on the N400 component elicited by words in these two languages.

You found that the N400 was larger (more negative) for proper nouns in Xtrinqua than for proper

nouns in Kirbish. You therefore conclude that processing proper nouns requires more work in

Xtrinqua than in Kirbish. However, this assumes that the effect you have observed actually

reflects a change in the same N400 component that was observed in prior studies of semantic

A Closer Look at ERPs and ERP Components 59

integration. Perhaps you are instead seeing a smaller P3 rather than a larger N400. Because the

P3 is related to the amount of cognitive resources devoted to processing a stimulus, this would

suggest that it is actually easier to process Xtrinqua proper nouns than Kirbish proper nouns.

This is nearly the opposite of the conclusion that you would draw if the effect was an increase

in N400 amplitude rather than a decrease in P3 amplitude. This type of problem has come up

many times in the language ERP literature (see review by Swaab, Ledoux, Camblin, & Boudewyn,

2012), and analogous problems arise in other ERP domains. Scalp distribution can sometimes

be used to rule out a given component, but this only works when the scalp distributions of two

components are easily distinguished (which is not the case for P3 and N400).

This leads to our final rule of ERP interpretation:

Rule 6: An ERP effect observed in one experiment may not reflect the same underlying brain

activity as an effect of the same polarity and timing in previous experiments.

Solutions to this problem will be described in the final section of this chapter.

Some General Comments about the Component Structure of ERP Waveforms The six rules of ERP interpretation presented in this chapter have been violated in a very large

number of published ERP experiments (including some of my own papers!). Violations of these

rules significantly undermine the strength of the conclusions that can be drawn from these

experiments, so you should look for violations when you read ERP papers. If you are relatively

new to the ERP technique, it would be worth looking back through old ERP papers that you ’ ve

previously read and identifying any violations of these rules. This will be good practice, and it

may cause you to reevaluate your conclusions about some prior findings.

This section of the book can be depressing, because it focuses on the most difficult challenges

that face ERP researchers. But don ’ t despair! Chapter 4 provides some strategies for overcoming

these challenges.

A BP3 wave on 3 different trials

Average of the 3 trials

Figure 2.6 Illustration of the distortions in an averaged ERP waveform that arise from trial-to-trial latency variation. (A) A single-

trial component at three different latencies, representing trial-to-trial variations in timing. (B) The average of these three

single-trial waveforms. The average waveform is broader than the single-trial waveforms and has a smaller peak ampli-

tude. In addition, the onset time and offset time of the average waveform reflect the earliest onset and latest offset times,

not the average onset and offset times.

60 Chapter 2

Also, many of these problems are not nearly as bad when you consider the waveforms

recorded at multiple scalp sites. Because the ERP waveforms at different scalp sites reflect

exactly the same components, but scaled by different weighting factors (as shown in figure 2.3 ),

you can rule out many alternative explanations by looking at the data from multiple electrodes.

Consider, for example, the simulated experiment shown in figure 2.7 (which is based on the C1 ′ , C2 ′ , and C3 ′ components in figure 2.5 ). In this imaginary experiment, ERPs were recorded from the Fz, Cz, and Pz electrode sites in condition A and condition B. If you just saw the data from

the Cz electrode site, you might conclude that the P3 wave was larger and earlier for condition

B than for condition A. However, you can rule out this conclusion by looking at the scalp dis-

tribution of the waveforms (both the parent waveforms and the difference waves). From the

whole set of data, you can see that the P3 wave is largest at Pz, a little smaller at Cz, and quite

a bit smaller at Fz (which is the usual pattern). The experimental effect, however, is largest at

Fz, smaller at Cz, and near zero at Pz, and it extends from approximately 150 to 450 ms. Both

the timing and the scalp distribution of the experimental effect are inconsistent with a modula-

tion of the P3 wave and are more consistent with a frontal N2 effect. You should also note that

the scalp distribution of the effect is the same throughout the time course of the effect, suggest-

ing that it really does consist of a single component that extends from approximately 150 to 450

ms, rather than consisting of separate early and late effects. Thus, a careful examination of the

data from multiple electrode sites, including the difference waves, will allow you to avoid making

na ï ve mistakes in interpreting your data. Moreover, as you gain more experience with ERPs,

you will be able to do a better job of figuring out the underlying components (see box 2.4 ).

Although I am not a big fan of mathematical techniques for determining the underlying com-

ponents in ERP experiments, they can certainly be useful for generating plausible hypotheses

and for showing that some hypotheses are inconsistent with the data. For example, if you were

to perform source localization on the difference waves shown in figure 2.7 (with many more

electrode sites, of course), this would make it clear that the effect is not consistent with the likely

generators of the P3 wave. Source localization would also make it clear that a single generator

source could account for both the early and late portions of the effect. Thus, even though you

should be skeptical about the three-dimensional coordinates of the effect that would be provided

by source localization techniques, these techniques are still valuable for testing more general

hypotheses about the component structure of your data. This is especially true if you combine

source localization with the use of difference waves (see box 2.5 for an example of my own

rather lame attempt at using math to understand the underlying component structure of an

experiment).

Difference Waves as a Tool for Isolating Components

In this section, I want to spend some additional time discussing the value of difference waves

in addressing the problems caused by the mixing of components in our observed ERP wave-

forms. As shown in figures 2.5 and 2.7 , difference waves can sometimes reveal the time course

A Closer Look at ERPs and ERP Components 61

300150 450 750600

Condition A

Parent Waveforms Difference Waves

Condition B Minus Condition A Condition B

Figure 2.7 Simulated experiment in which three underlying components (similar to components C1 ′ , C2 ′ , and C3 ′ in figure 2.5 ) propagate to electrode sites Fz, Cz, and Pz with different weighting factors. The amplitude of a negative-going component

(C2 ′ ) is reduced in condition B compared to condition A. Because the weighting from this component is greatest at Fz, intermediate at Cz, and smallest at Pz, the difference between conditions A and B is greatest at Fz, intermediate at Cz,

and smallest at Pz. This can be seen in the parent waveforms from the individual conditions (left column) and in the

difference waves (right column). Note that because the difference waves were formed by subtracting condition A from

condition B rather than vice versa, the difference waves show a positive deflection rather than a negative deflection.

62 Chapter 2

Box 2.4 Experience Matters

It appears that people can learn to make good inferences about the underlying components when

examining ERP data. Many years ago, Art Kramer conducted a study in which he created artificial

ERPs from a set of realistic underlying components (Kramer, 1985). He then gave these waveforms

(from multiple conditions at multiple electrode sites) to eight graduate students and two research

associates who had between 1 and 10 years of experience with ERPs. There was a strong effect of

experience: the experienced ERP researchers were able to figure out the nature of the underlying

components, whereas the people who were new to ERPs could not reliably determine the underlying

component structure of the data. Of course, there are limits to this conclusion. It was based on a

small sample of researchers from one particular lab who were shown one type of data, and there is

no guarantee that a given experienced researcher will always (or even usually) reach a correct

interpretation. When writing a journal article, you couldn ’ t cite your years of experience with ERPs

as evidence that your interpretation of the underlying component structure is correct. However, once

you gain enough experience with ERPs (and learn to apply everything you have read in this chapter),

you should be able to figure out the likely pattern of underlying ERP components from a given

experiment with some confidence.

and scalp distribution of an underlying ERP component. A well-constructed difference wave

(i.e., one based on a well-controlled and relatively subtle experimental manipulation) will always

contain fewer components than the parent waveforms from which the difference wave was constructed. And fewer components means less opportunity for confusion due to the mixing of

components.

Given that I ’ m a big fan of difference waves, it ’ s a bit ironic that the first published use of

difference waves to assess the component structure of an experiment were in a paper by Risto

N ä ä t ä nen and his colleagues (N ä ä t ä nen, Gaillard, & Mantysalo, 1978) that was designed to

question the interpretation of a previous study by my graduate mentor, Steve Hillyard (Hillyard,

Hink, Schwent, & Picton, 1973). However, Jon Hansen and Steve Hillyard responded with a

paper in which they embraced the difference wave approach and fought back with their own

difference waves (Hansen & Hillyard, 1980).

The logic behind difference waves is very simple. As shown in figure 2.3 , the ERP waveform

at a given electrode site is the weighted sum of a set of underlying source waveforms (recall

that source waveform is just another term for the time course of an ERP component at the gen- erator site). If two conditions differ in some of the source waveforms and not in others, then the

difference wave created by subtracting one condition from the other will eliminate the source

waveforms that are identical in the two conditions, making it possible to isolate the components

that differ. This is completely reasonable because ERPs from different sources simply sum

together.

As described earlier in this chapter, figures 2.5 and 2.7 show how difference waves can

help reveal the time course of an effect. To see how difference waves can help reveal the scalp

A Closer Look at ERPs and ERP Components 63

When I was making the simulated waveforms shown in figure 2.7 , I realized that these waveforms

looked a lot like the data from one of the first experiments I conducted in graduate school (Luck,

Heinze, Mangun, & Hillyard, 1990). In this experiment, subjects attended either to the left or the

right side of a bilateral visual display, and we wanted to see if the P1 and N1 components would

be larger over the hemisphere contralateral to the attended side (relative to the ipsilateral hemi-

sphere). The waveforms are shown in the illustration that follows.

As you can see, we found that the waveform was more positive over the contralateral hemisphere

from approximately 80 to 200 ms, including the time ranges of the P1, N1, and P2 components.

From visual inspection of the data, it was not clear whether this broad attention effect was a single

component or a modulation of separate P1 and P2 components. Because I thought of myself as a

statistics hotshot at that time, I decided that I would use principal component analysis (PCA) to

answer this question. PCA produced nice results indicating that the attention effect consisted of

modulations of separate P1 and P2 components. However, the more I thought about the results, the

more I realized that they could be an artifact of PCA assumptions. Also, Steve Hillyard was not as

impressed by fancy mathematical techniques as I was (for reasons that I now appreciate). Our com-

promise was to put the PCA results into an appendix in the published paper. Fortunately, the conclu-

sions of the paper did not hinge on the PCA results.

Box 2.5 My Own Experience with Mathematical Approaches

100 200 300 400

Contralateral to attended location

Ipsilateral to attended location

+0.5 µV

–0.5 µV

distribution of an effect, consider the N170 component shown in figure 2.8 . As discussed in

chapter 1, the N170 is larger in response to pictures of faces than pictures of non-face objects such

as cars (for a review, see Rossion & Jacques, 2012). If you simply measure the scalp distribution

at 170 ms for trials on which faces were presented, the distribution will reflect face-specific pro-

cessing plus all of the nonspecific activity that is present at 170 ms. However, if you first construct

face-minus-nonface difference waves and then measure the scalp distribution, you will see the

topography of face-specific brain activity, uncontaminated by the nonspecific activity.

Bruno Rossion ’ s lab conducted a study in which they examined the development of the N170

(Kuefner, de Heering, Jacques, Palmero-Soler, & Rossion, 2010), and this study showed the

importance of measuring scalp distributions from difference waves. In this study, ERPs were

recorded from children between 4 and 17 years of age while they viewed images of faces,

64 Chapter 2

scrambled faces, cars, and scrambled cars. When the scalp distribution was measured at the time

of the N170 component from the ERPs elicited by faces, the scalp distribution changed markedly

over the course of development. Previous studies had found similar effects and concluded that

the neuroanatomy of face processing changed during this period of development. However, these

changes in scalp distribution could instead be a result of distortion from other ERP components

that are also present at 170 ms and that change in relative amplitude over the course of develop-

ment. To test this, Kuefner et al. constructed difference waves in which they subtracted the ERPs

elicited by scrambled faces from the ERPs elicited by intact faces, removing any activity that

was not face specific. The scalp distribution of the resulting difference wave was virtually identi-

cal from 4 to 17 years, indicating that the face-specific processing had the same neuroanatomical

locus across this developmental period.

Difference waves can also help you avoid a visual illusion that sometimes causes people to

misperceive ERP effects. Figure 2.9 shows a simulated experiment in which this illusion arises.

In this experiment, the difference between condition A and condition B is exactly the same at

the Fz and Cz electrode sites. However, because this effect is superimposed on the steeply rising

edge of the P3 wave at the Cz site, the effect looks smaller at Cz than at Fz. The difference wave

shows that the effect is exactly the same at these sites. The illusion arises because our visual

system tends to focus on the distance between two curves along an axis that is approximately

perpendicular to the curves (e.g., the horizontal difference between the condition A and condition

B waveforms at the Cz site). However, the difference in amplitude at a given time point is the

vertical distance between the two waveforms at that time point. The steeper the slope of two

overlaid waveforms, the more our visual system focuses on the horizontal difference between

the waveforms rather than the vertical distance, and this leads us to underestimate the true

P1 P2

N170 Face Car

Figure 2.8 ERPs elicited over visual cortex by car and face stimuli, with the N170 effect highlighted by the shaded region. Adapted

A Closer Look at ERPs and ERP Components 65

difference in amplitude between the two conditions. Once you look at the difference waves in

figure 2.9 , you can see that the difference between conditions A and B is exactly the same at Fz

and Cz in this experiment. This is yet one more advantage of difference waves.

Although difference waves are an incredibly useful way to isolate the underlying components

from the mixture of components in the parent waveforms, they do have some limitations. First,

you are making implicit assumptions about the nature of the difference between conditions A

and B when you choose whether to compute A minus B or to compute B minus A. Consider,

for example, the simulated experiment shown in figure 2.7 . The difference waves in this experi-

ment make it look as if a frontal positive component is larger in condition B than in condition

A, but the effect was actually created (in my simulations) by decreasing the amplitude of a frontal

negative component. Thus, you need to be careful about the implicit assumptions you are making

about the direction of the effect when you subtract one waveform from another.

Another important issue is that the difference wave will always be noisier than the parent

waveforms. To understand why this is true, consider what happens when you add two waveforms

rather than subtract two waveforms. When you add two waveforms, A and B, some of the noise

in A cancels out noise in B, but mostly the noise increases rather than canceling, and the overall

noise in the summed waveform increases (although it doesn ’ t double). It turns out that exactly

the same thing happens when you subtract one waveform from the other instead of adding the

two waveforms. The reason for this is that the noise at a given point in the waveform can be

either positive-going or negative-going, so it doesn ’ t matter whether you add or subtract pure

noise (on average). The end result will be a noisier waveform. However, this is not usually a

problem in practice. If you do a statistical analysis on the difference waves, the p value may be exactly the same as if you did the analysis on the parent waveforms (this is true for linear mea-

sures, such as mean amplitude, as will be discussed in chapter 9). For example, if you have

Condition A

Condition B Minus Condition A Condition B

300150 450 750600

Fz Cz

300150 450 750600

Figure 2.9 Visual illusion in which the effect of an experimental manipulation appears to be smaller when it is superimposed on a

steeply sloped ERP wave. In this example, the difference between conditions A and B is exactly the same size at the Fz

and Cz scalp sites (as shown by the difference waves). However, because this difference is superimposed on a steeply

sloped P3 wave at the Cz site, but not at the Fz site, the effect looks smaller at Cz than at Fz when judged by looking

at the parent waveforms rather than by looking at the difference waves.

66 Chapter 2

waveforms for conditions A and B in two groups of subjects, you could do a two-way analysis

of variance (ANOVA) on the mean amplitude from 400 to 600 ms with factors of condition and

group. Alternatively, you could measure the mean amplitude from 400 to 600 ms in difference

waves formed by subtracting the condition B waveforms from the condition A waveforms and

then do a t test comparing these values for the two groups. The p value from this t test will be identical to the p value from the group × condition interaction in the ANOVA.

What Is an ERP Component?

A Conceptual Definition We are now ready to provide a formal definition of ERP component . In the early days of ERP research, a component was defined primarily on the basis of its polarity, latency, and general

scalp distribution. For example, the P3a and P3b components were differentiated on the basis

of the earlier peak latency and more frontal distribution of the P3a component relative to the

P3b component (Squires, Squires, & Hillyard, 1975). However, polarity, latency, and scalp dis-

tribution are superficial features that don ’ t really capture the essence of a component. For

example, the peak latency of the P3b component may vary by hundreds of milliseconds depend-

ing on the difficulty of the target – nontarget discrimination (Johnson, 1986), and the scalp dis-

tribution of the auditory N1 wave depends on the pitch of the eliciting stimulus in a manner that

corresponds with the tonotopic map of auditory cortex (Bertrand, Perrin, & Pernier, 1991). Even

polarity may vary: the C1 wave, which is generated in primary visual cortex, is negative for

upper-field stimuli and positive for lower-field stimuli due to the folding pattern of this cortical

area (Clark, Fan, & Hillyard, 1995). The difficulty of using latency, scalp distribution, and polar-

ity to identify components becomes even greater when multiple components are mixed together

at a given electrode site. For example, the N2 elicited by an oddball is superimposed on top of

P2 and P3 waves, so the overall voltage during the N2 time range is often positive.

I do not mean to imply that you should not use latency, scalp distribution, and polarity to help

identify ERP components. In fact, these factors are extremely useful in determining whether a

given experimental effect reflects, for example, a P3a or P3b component. However, these factors

do not define an ERP component; they are merely superficial consequences of the nature of the component. Instead, a component should be defined by the factors that are intrinsic to the com-

ponent. For example, an influential discussion of ERP components by Manny Donchin, Walter

Ritter, and Cheyne McCallum noted that, “ an ERP component is a subsegment of the ERP whose

activity represents a functionally distinct neuronal aggregate ” (Donchin, Ritter, & McCallum,

1978, p. 353). My own, very similar definition is this:

Conceptually, an ERP component is a scalp-recorded neural signal that is generated in a specific

neuroanatomical module when a specific computational operation is performed.

By this definition, a component may occur at different times under different conditions, as

long as it arises from the same module and represents the same computational operation (e.g.,

A Closer Look at ERPs and ERP Components 67

the encoding of an item into working memory in a given brain area may occur at different delays

after the onset of a stimulus because of differences in the amount of time required to identify

the stimulus and decide that it is worth storing in working memory). The scalp distribution and

polarity of a component may also vary according to this definition, because the same cognitive

function may occur in different parts of a cortical module under different conditions (e.g., when

a visual stimulus occurs at different locations and therefore stimulates different portions of a

topographically mapped area of visual cortex). It is logically possible for two different cortical

areas to accomplish exactly the same cognitive process, but this probably occurs only rarely and

would lead to a very different pattern of voltages, and so this would not usually be considered

a single ERP component (except in the case of mirror-image regions in the left and right

hemispheres).

Although this definition captures the essence of an ERP component, it is completely useless

as an operational definition. That is, because we are recording the mixed signals from multiple

generators at every electrode site, we have no way of directly determining the contribution of

each neuroanatomical module to the observed waveform. And we don ’ t ordinarily know the

computational operation reflected by a scalp voltage. So we cannot use this definition to deter-

mine which component is being influenced by a given experimental manipulation or to determine

whether the same component is active in multiple experiments. However, this definition is useful

insofar as it helps to formalize what we believe is going on under the skull.

You should also keep in mind that many well-known ERP components (e.g., N400, mismatch

negativity, P3b) are probably not individual components according to this definition. That is,

multiple brain areas that are carrying out similar but somewhat different computations likely

contribute to these scalp-recorded voltage deflections (see, e.g., the chapters on these compo-

nents in Luck & Kappenman, 2012b). As research progresses, we gain the ability to subdivide

these multicomponent conglomerations into their parts. In some cases, this leads to new names

for the individual components. For example, the “ N2 component ” that was identified in early

ERP studies turned out to consist of a set of many different individual components that can be

separated by means of various experimental manipulations, and these individual components

(sometimes called subcomponents ) were given new names (e.g., anterior N2 , N2c , N2pc ). In some cases, these subcomponents have been divided even further (see, e.g., Luck, 2012b). In

other cases, we still use a single name to refer to something that likely consists of multiple

similar components, especially when we don ’ t yet have good methods for isolating the individual

subcomponents (e.g., N400 is still used even though there are probably at least two neurally distinct subcomponents that contribute to it).

An Operational Definition Manny Donchin provided an alternative definition that is more like an operational definition: “ A

component is a set of potential changes that can be shown to be functionally related to an

experimental variable or to a combination of experimental variables ” (Donchin et al., 1978, p.

353). They summarized this idea more compactly by saying that, “ an ERP component is a source

68 Chapter 2

of controlled , observable variability ” (Donchin et al., 1978, p. 354). This is very similar to the idea, illustrated in figures 2.5 and 2.7 , that difference waves can be used to isolate ERP compo-

nents. Donchin et al. noted that electrode site is one key source of variability, which corresponds

to the idea that changes in the scalp distribution of a difference wave between the early and late

parts of the effect mean that different components are active in the early and late parts of the

effect. Thus, by this definition, any consistent difference between the waveforms in different

experimental conditions is an ERP component. This is a clear and easily applied operational

definition of ERP component . However, there are two shortcomings of this operational definition. First, it ignores the key

idea that an ERP component is generated by a specific neuroanatomical module (or “ neural

aggregate ” to use the terminology of Donchin et al., 1978). That is, even if the scalp distribution

of an experimental effect did not vary over time or over the conditions of a particular experiment,

the scalp distribution might clearly indicate that more than one dipole was active (e.g., if

the scalp distribution did not follow a simple dipolar pattern). In such a case, we would want

to conclude that multiple components were active, but tightly interlinked. And we could reason-

ably assume that these components could be shown to be functionally distinct in future

experiments.

Second, Donchin ’ s operational definition focuses exclusively on experimental (controlled) manipulations, completely ignoring variations that are spontaneous or correlational in nature.

To take an obvious example of why this is an unnecessary limitation, consider a case in which

a patient group and a control group differ in terms of the voltage between 150 and 250 ms over

lateral frontal electrode sites. In this case, there must be at least one ERP component (according

to my conceptual definition) that varies between these groups. This is just as convincing as an

experimentally controlled within-subject difference in the voltage between 150 and 250 ms over

lateral frontal electrode sites. Subtler examples are also important to consider. For example, if

you look at the distribution of voltage over the scalp from moment to moment as the EEG

spontaneously varies, it is possible to used advanced statistical techniques (e.g., principal com-

ponent analysis, independent component analysis) to isolate systematic patterns of covariation

across electrode sites that reflect spontaneous fluctuations in the amplitude of underlying ERP

components.

When taking these factors into consideration, we can update Donchin ’ s operational definition

as follows:

An ERP component can be operationally defined as a set of voltage changes that are consistent

with a single neural generator site and that systematically vary in amplitude across conditions,

time, individuals, and so forth. That is, an ERP component is a source of systematic and reliable

variability in an ERP data set.

This should not be taken to imply that we cannot isolate a component until we have determined

its generator. If the scalp distribution of a putative component has a complex structure that is

inconsistent with a single dipole, then this should not be considered a single component. But if

A Closer Look at ERPs and ERP Components 69

it has a simple structure that is consistent with a single dipole (or with a pair of mirror-symmetric

dipoles in the left and right hemispheres), then we can provisionally accept it as a single

component.

How Can We Identify Specific ERP Components?

Now that we have both a conceptual definition and an operational definition for ERP compo-

nents, we can consider in more detail a question that has come up many times in this chapter:

when we see differences in the ERPs between different conditions or different groups in a

given study, how can we determine which underlying components are responsible for these

differences?

This is still not an easy question to answer, because our operational definition applies to a

single data set and cannot be used to determine if the components (sources of consistent vari-

ability) that we see in one experiment are the same as the components that were observed in

another experiment. Scalp distributions can be helpful, especially when derived from difference

waves to eliminate the contribution of other overlapping components. If the scalp distribution

of the effect in the new experiment is the same as the scalp distribution observed in previous

experiments, then this is one piece of evidence in favor of it being the same component; if the

scalp distribution is different, then this is evidence against the hypothesis. In practice, this can

provide strong evidence against the hypothesis that two effects reflect the same component, but it cannot provide strong evidence in favor of the hypothesis. First, it is often impossible to provide direct quantitative comparisons of scalp distributions across experiments (e.g., when you

are comparing your data with published data from another lab), and this will make it difficult

to rule out the possibility that the scalp distribution in the new experiment is subtly but signifi-

cantly different from the scalp distribution in a previous experiment. Second, concluding that

two scalp distributions are the same requires accepting the null hypothesis, and conclusions of

this sort are almost always weak. Source localization techniques can also provide evidence about

whether generator sources are the same for ERP effects observed in different experiments, but

this is essentially equivalent to asking whether the scalp distributions are the same and therefore

has the same limitations.

We can also ask whether the component that we isolate in one experiment shows the same

pattern of interaction with other factors as the component that was isolated in prior experiments.

For example, if we believe we are seeing a P3b effect, we can ask whether it interacts with the

probability of the stimulus category (see Luck et al., 2009; and see Experiment 4 in Vogel, Luck,

& Shapiro, 1998). This can be a useful adjunct to comparisons of scalp distribution, but it

requires a very solid theory of the interactions that should occur. Some of the clearest cases

involve combinations of experimental factors and scalp distribution; as will be described in

chapter 3, the N2pc, contralateral delay activity (CDA), and LRP components are isolated by

computing a difference wave in which the waveforms recorded over the ipsilateral hemisphere

(relative to an attended location or a response hand) are subtracted from the waveforms recorded

70 Chapter 2

over the contralateral hemisphere. These components can be very easily isolated from other ERP

components, and they have been particularly useful for testing precise hypotheses about atten-

tion, working memory, and response selection.

In general, the difficult problem of identifying ERP components is solved in the same way

that every other difficult problem in cognitive neuroscience is solved: with converging evidence.

If you make a slight change in an experimental paradigm and you find the same effects as before

(in terms of latency and scalp distribution), it is very likely that you have isolated the same

underlying ERP components. If you then make a very large change in the paradigm, and now

you find a very different latency or a somewhat different scalp distribution, you have to do some

further research to determine whether you are still looking at the same component. If the latency

is quite different, you can look for other evidence that the timing of the relevant process has

changed. If the scalp distribution is a little different, you can look at whether the scalp distribu-

tion changes over the time course of the effect, suggesting that you now have two components

contributing to the effect. If the scalp distribution is approximately the same as in your prior

research, you can run additional experiments to see if the effect interacts with other manipula-

tions in a way that is predicted by your hypothesis about the nature of the underlying component.

You could also ask whether subject-to-subject differences in the scalp distribution of your new

experimental effect are correlated with subject-to-subject differences in your previous effect.

The bottom line is that it is more difficult to isolate and identify specific ERP components

than people typically realize, but this challenge can be overcome if you think carefully about

the problem and come up with clever ways to test your hypotheses. Chapter 4 will describe a

variety of strategies for overcoming this challenge, including circumventing the problem entirely

by designing experiments that do not depend on identifying a specific ERP component.

Suggestions for Further Reading

Donchin, E. (1981). Surprise! … Surprise? Psychophysiology , 18 , 493 – 513.

Donchin, E., Ritter, W., & McCallum, W. C. (1978). Cognitive psychophysiology: The endogenous components of the

ERP. In E. Callaway, P. Tueting, & S. H. Koslow (Eds.), Event-Related Brain Potentials in Man (pp. 349 – 441). New York: Academic Press.

Kappenman, E. S., & Luck, S. J. (2012). ERP components: The ups and downs of brainwave recordings. In S. J. Luck

& E. S. Kappenman (Eds.), The Oxford Handbook of ERP Components (pp. 3 – 30). New York: Oxford University Press.

Makeig, S., & Onton, J. (2012). ERP features and EEG dynamics: An ICA perspective. In S. J. Luck & E. S. Kappen-

man (Eds.), The Oxford Handbook of ERP Components (pp. 51 – 86). New York: Oxford University Press.

N ä ä t ä nen, R., & Picton, T. (1987). The N1 wave of the human electric and magnetic response to sound: A review and

an analysis of the component structure. Psychophysiology , 24 , 375 – 425.

Picton, T. W., & Stuss, D. T. (1980). The component structure of the human event-related potentials. In H. H. Kornhuber

& L. Deecke (Eds.), Motivation, Motor and Sensory Processes of the Brain, Progress in Brain Research (pp. 17 – 49). North-Holland: Elsevier.