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284 S. J. Luck
For the data shown in Fig. 22.1a, b, the SD was 5.73 μV and N was 20, so the
aSME is 5.73 20por 1.28 μV. The SME is an estimate of the expected error in
the score, so it is the inverse of the precision (i.e., a greater SME indicates poorer
data quality). To decide whether the SME for a given score is bad (large) or good
(small), you can compare it to the score itself. For example, the score in this case was
a time-window mean amplitude of 7.66 μV, and the estimated error of this score (the
SME) was 1.28 μV. An error of 1.28 μV for a score of 7.66 μV isn’t great, but it isn’t
terrible. I will have more to say about interpreting SME values later.
Note that the aSME will increase if there is more trial-to-trial variability in the
scores
obtained from the single-trial EEG epochs or if we have fewer trials in our
averaged ERP waveform (all else being equal). Both of those things make perfect
sense for a metric of data quality for averaged ERPs.
The aSME is automatically computed by ERPLAB Toolbox (version 8 and
higher
) for a set of default time windows when you create averaged ERP waveforms,
and you can also specify custom time windows. The aSME can also be computed by
the MNE-Python package (Gramfort et al.,
solution in BrainVision Analyzer (BrainVision Analyzer, Brain Products GmbH,
a
Gilching, Germany). And it is straightforward to use Eq. 22.1 to compute the aSME
in custom code; Matlab examples are provided at https://doi.org/10.18115/D58G91.
I hope that it will eventually be a standard part of all ERP analysis software, because
everyone should be concerned with data quality.
2013). It should also be available soon as
22.2.2 Exactly What the SME Means
Now that we’ve seen how the aSME is computed, let’s consider exactly what it
means. You may have noted that Eq. 22.1 is the same as the familiar equation for the
stand
ard error of the mean or SEM. As an example of the SEM, imagine that you
measured the height of 16 participants, and you found that the mean of these
16 single-participant heights was 180 cm with a SD of 32 cm. The standard error
of this mean would be calculated by dividing the SD by the square root of the
number of participants, which would be 32
bar graph showing the mean of 180 cm with error bars of 8 cm. You probably have
some intuitions about whether an SEM of 8 cm is large or small relative to a mean of
180 cm. You can use those same intuitions when thinking about whether an aSME is
large or small relative to an ERP amplitude score.
The aSME
the single-trial time-window mean amplitudes from a single participant. In other
words, if you score the time-window mean amplitude from each individual trial for a
participant, and take the mean of these values, the aSME is the standard error of this
mean. It turns out that the mean of the single-trial time-window mean amplitudes is
exactly equal to the time-window mean amplitude obtained from the averaged ERP
waveform. So, we can use the standard error of the single-trial mean amplitudes to
estimate the standard error of the time-window mean amplitude obtained from the
averaged ERP waveform.
is just like the SEM, except that it is the standard error of the mean of
16p¼ 8 cm. You might then create a
22 Quantifying EEG and ERP Data Quality 285
This is a key point, but it can be a little confusing, so it’s worth repeating in a
different way. If we obtain the time-window mean amplitude from 300 to 500 ms for
each of the 20 single-trial EEG epochs in Fig.
values, we will get a mean of 7.66 μV. This is exactly the same value I obtained
20
22.1b, and we take the mean of these
when I measured the time-window mean amplitude from 300 to 500 ms in the
averaged ERP waveform. This was not an accident: You will always get the same
value by scoring the time-window mean amplitude from the single-trial epochs and
then averaging these values together or by first averaging the single-trial waveforms
and then scoring the time-window mean amplitude from this averaged ERP waveform. If we take the SD of the 20 single-trial values (5.73 μV) and divide by the
square root of 20 (4.47), we will get an SEM of 1.28 μV. This is the SEM of the
20 single-trial values, but it is also the standard error of the time-window mean
amplitude obtained from the averaged ERP waveform, because this value obtained
from the averaged ERP waveform is necessarily the same as the mean of the singletrial values. In other words, the standard error of the mean of the single-trial values is
the standard error of estimate for the score obtained from the averaged ERP
waveform. When we use the standard error of the mean (SEM) in this way, we
call it the standardized measurement error (SME).
But what does this standard error actually mean? Roughly speaking, the standard
error
of a score tells you how consistent the score would be if you could repeat the
same experiment many times in a given participant (without any learning or fatigue)
and obtain the score for each repetition of the experiment. For example, imagine that
we took the participant whose data are shown in Fig.
oddbal
l experiment 10,000 times (without any learning or fatigue, but with different
22.1a, b and repeated the same
random noise in each repetition). Each time, we would get 20 oddball trials, create an
averaged ERP waveform from these 20 trials, and obtain the time-window mean
amplitude from 300 to 500 ms in this averaged ERP waveform. We might get a score
of 8.2 μV for the first repetition of the experiment, 6.9 μV for the second repetition,
6.3 μV for the third repetition, etc. This is illustrated in Fig.
22.1d.
We would end up with 10,000 P3 amplitude scores for this participant (one for
each of the 10,000 repetitions of the experiment). We could then quantify the
variability of these 10,000 scores. If the scores are very consistent, this means that
our score has high precision (i.e., that we have good data quality). But if the scores
vary widely from repetition to repetition, this means that our score has low precision
(i.e., that we have poor data quality). Figure
22.1d shows a simulation of this
imaginary procedure in which the true score was 7.5 μV. You can see that the
score obtained from most experiments was within
1.5 μV of the true value of
7.5 μV, but sometimes the score was quite a bit lower or higher.
We could
score across repetitions of the experiment. The SD of the scores in Fig.
μV, which means that 68% of the single-experiment scores were within 1.3 μV of
1.3
use the SD of these 10,000 scores as a measure of the consistency of the
22.1d was
the mean across the 10,000 scores (because 68% of values will fall within 1 SD of
the mean given a normal distribution). The SD of these 10,000 scores seems like a
very good way of quantifying the precision of the time-window mean amplitude
score from this participant, because it tells us how close to the true value we can
286 S. J. Luck
expect the score from a single experiment to be (on average). However, this
approach is impractical in reality, because it requires repeating the experiment
10,000 times, and it assumes no learning or fatigue.
The magic of Eq. 22.1 is that it allows us to take the single-trial values from a
single experiment and use them to estimate the SD of the scores we would obtain
from the averaged ERP waveform if we repeat ed the experiment an infinite number
of times (with no learning or fatigue). In other words, the SME we compute by
applying Eq. 22.1 to the data from the one experiment shown in Fig. 22.1a, b is an
e of the SD of the frequency distribution of scores shown in Fig. 22.1d. In
estimat
techni
cal terms, Fig. 22.1d shows the sampling distribution of the time-window
mean amplitude score, the standard error of this score is the SD of the sampling
distribution, and Eq. 22.1 allows us to estimate this standard error. Equation 22.1 is
only an estimate, but you can see that the estimated value of 1.28 μV is quite close to
the value of 1.3 μV obtained by simulating 10,000 repetitions of the experiment.
To summarize: the SME quantifies the variability (lack of consistency) that we
expect to see in our score if we repeated the experiment for a given participant
would
an infinite number of times (expressed as the SD of the distribution of scores across
repetitions). A large SME value indicates low consistency, which means that we
cannot be confident that the score we obtain in a single experiment is close to the true
value. When our score is a time-window mean amplitude, we can estimat e the SME
using the data from a single experiment by measuring this score from the single-trial
EEG epochs and applying Eq. 22.1 to these single-trial scores. In other words, when
we quantify the amplitude of an ERP component by scoring the time-window mean
amplitude from the averaged ERP waveform, the SME is the same as the SEM.
22.2.3 SME for Other Types of Scores and for Transformed
Waveforms
Unfortunately, Eq. 22.1 is valid only for time-window mean amplitude scores. It is
not valid for peak amplitude scores, for peak latency scores, or for any other kind of
amplitude or latency score that I have ever seen. However, there is a procedure called
bootstrapping that you can use to estimate the SME for virtually any amplitude or
latency score that can be obtained from an averaged ERP waveform. We call this the
bootstrapped SME or bSME, and it is described in detail in Luck et al. (
t, it cannot be automatically computed by any software package, but it can be
presen
computed by means of a relatively simple script in Matlab or another high-level
programming language; several example Matlab scripts are available at
org/10.18115/D58G91.
The bSME
from difference waves or other transformations of the ERP waveform. For example,
imagine that you ran an N170 experiment in which you presented participants with
pictures of faces and pictures of cars. You would find a larger N170 for the faces, and
also allows you to quantify the data quality for scores that are obtained
2021). At
https://doi.
22 Quantifying EEG and ERP Data Quality 287
you could create a face-minus-car difference wave to isolate the face-specific
processing from all of the nonspecific brain activity that is equal in the face-elicited
and car-elicited ERP waveforms. You could use the onset time of this difference to
quantify the speed at which the brain differentiated between faces and cars, and you
could compare the onset times in a patient group and a control group. In other words,
your score is the onset time measured from the difference w
bSME value for this score for each participant to determine whether you are
obtaining a good estimate of that participant’s true onset time (i.e., the score you
would obtain if you had an infinite number of trials).
No matter whether you are using aSME or bSME, it is an estimate of the standard
error of the score. That is, it’s an estimate of what would happen if you repeated the
experiment an infinite number of times in a given participant (assuming no fatigue or
learning), obtained the score for each repetition, and took the SD of these scores. It
therefore provides a metric of the precision of the score you obtain from a given
participant in one experiment.
ave. You could obtain a
22.2.4 Combining Scores Across Participants, Channels,
and Conditions
You will get a separate SME value for each score you obtain. For example, you will
get separate SME values for each participant. If you obtain the score from multiple
channels, you will get a separate SME value for each channel for each participant
(but if you average across a cluster of channels prior to obtaining the score, you will
get a single SME value for the cluster). You will typically get separate values for
each experimental condit ion (separately for each participant and channel), unless
you average across conditions or make a difference wave across conditions prior to
obtaining the scores. The fact that you get an SME value for each score can be very
valuable, because you can determine whether some participants, channels, or conditions are particularly noisy.
Sometimes,
with a single number. In these cases, you can simply average the SME values across
participants. You can also average the SME scores across channels and/or conditions, although you might consider averaging across the channels prior to scoring
and/or obtaining scores from difference waves (see Luck & Gaspelin,
ssion of the statistical advantages of averaging across channels or making
discu
difference waves between conditions prior to scoring). You can also combine the
single-participant SME values using the root mean square instead of the mean,
which has some advantages but is not usually necessary to obtain an overall metric of
data quality for a given study (see Luck et al.,
however, you want to summarize the data quality for an entire study
2017 for a
2021 for
details).
288 S. J. Luck
22.2.5 Why the Scoring Method Matters
You might be wondering why I have been putting so much emphasis on the scores
we obtain from averaged ERPs rather than the data quality of the EEG itself. One
reason for this, as I mentioned earlier, is that the scores are what we put into our
statistical analyses and use to test our scientific hypotheses. I don’t care how clean or
noisy my EEG is except insofar as the noise impacts the scores I will use to test my
hypotheses. In this section, we will discuss a second reason for focusing on scores,
namely the fact that a given type of noise may make one scoring method very
imprecise without having much impact on a different scoring method. In other
words, data quality depends on how the scoring method interacts with the noise in
the data.
This is illustrated in Fig. 22.2, which shows a noise-free simulated ERP wave-
with a P3 component peaking at 400 ms (Fig. 22.2a) and the same waveform
form
with the addition of unrelated high-frequency noise (analogous to muscle noise;
Fig. 22.2b). If we score the amplitude of the P3 component as the peak voltage
between
the score (i.e., the score is very different when obtained from the original waveform
versus the contaminated waveform). However, if we score the P3 amplitude as the
time-window mean amplitude between 300 and 500 ms, the high-frequency contamination has only a small impact (i.e., the score is nearly identical for the original
and contaminated waveforms). This is because the rapid upward and downward
deflections largely cancel out when we average across the 300–500 ms period. For
the noisy data in panel B, the SME would be very large for the peak amplitude score
but very small for the time-window mean amplitude score.
much
important thing that I have learned from my efforts to quantify ERP data quality is
that my eyes are not a good judge of how noisy an ERP waveform is. My eyes are
drawn to high-frequency variations in the signal, but these high-frequency variations
300 and 500 ms, the high-frequency contamination has a large impact on
The waveform in panel B “looks noisy ,” but that noise doesn’t actually have
impact if we are using time-window mean amplitude scores. Perhaps the most
Fig. 22.2 Example of how the effect of noise on a score depends on the scoring method. (a) ERP
waveform with no noise. (b) Same waveform as A, but with high-frequency contamination added.
The high-frequency noise distorts the peak amplitude between 300 and 500 ms but has relatively
little effect on the mean voltage during this measurement window
22 Quantifying EEG and ERP Data Quality 289
have minimal impact in most studies using time-window mean amplitude as the
dependent variable. Low-frequency noise is not as visually distinctive but is a bigger
problem than high-frequency noise in many ERP studies, especially those examining
relatively long-latency components such as P3 and N400.
22.2.6 Example SME Values for 7 Common ERP
Components
Now let’s see what SME values look like in some actual experiments, using the data
from the ERP CORE (Kappenman et al., 2021). This online resource (freely
available at https://doi.org/10.18115/D5JW4R) contains data from 40 neurotypical
young
adults, each of whom was tested in optimized versions of 6 standard ERP
paradigms that were designed to isolate 7 common ERP components. Each paradigm
took about 10 min. Figure 22.3 shows the SME values, averaged across participants,
each component. Note that these compo nents are described in more detail in
for
Chap. 19.
Difference waves were used to isolate the component of interest from all of the
other
overlapping components. The P3b component was isolated from an oddballminus-standard difference wave in an active visual oddball paradigm. The N170
component was isolated from a faces-minus-cars difference wave in a visual categorization paradigm. The mismatch negativity (MMN) was isolated from an
oddball-minus-standard difference wave in a passive auditory oddball paradigm.
The N400 component was isolated from an unrelated-minus-related difference wave
in a visual word priming paradigm. The lateralized readiness potential (LRP) was
isolated from a contralateral-minus-ipsilateral difference wave (relative to the
response hand) in a flankers paradigm. The error-related negativity (ERN) was
isolated from an incorrect-minus-correct difference wave in the same flankers
paradigm used for the LRP (but from a different part of the scalp, averaged across
contralateral and ipsilateral). The N2pc component was isolated from a contralateralminus-ipsilateral difference wave (relative to the target side) in a simple visual
search paradigm.
The amplitude of each component was scored as either the time-window mean
amplit
ude or the peak amplitude from these difference waves. The latency was
scored as either the 50% area latency (the latency that evenly divided the area
under the curve into two equal-sized areas) or the peak latency from these same
difference waves. A separate, optimized time window and electrode site was chosen
for each component.
The resul
SME depends on the scoring method. For the amplitude of a component (Fig. 22.3a),
the
SME was about 20% worse (i.e., 20% larger) for peak amplitude scores than for
time-window mean amplitude scores. For the latency of a component (Fig. 22.3b),
SME was up to 400% worse for peak latency scores than for 50% area latency
the
ts shown in Fig. 22.3 (from Zhang & Luck, 2023) demonstrate that the
290 S. J. Luck
3
A SME for Amplitude Scores
Time-Window Mean Amplitude
Peak Amplitude
2
1
Standardized Measurement Error (µV)
0
P3b
40 oddballs
160 standards
60
B SME for Latency Scores
N170
80 faces
80 cars
MMN
200 oddballs
800 standards
N400
60 unrelated
60 related
LRP
200 left
200 right
ERN
~50 incorrect
~350 correct
N2pc
160 left
160 right
50
50% Area Latency
Peak Latency
40
30
20
10
Standardized Measurement Error (ms)
0
P3b
40 oddballs
160 standards
N170
80 faces
80 cars
MMN
200 oddballs
800 standards
N400
60 unrelated
60 related
LRP
200 left
200 right
ERN
~50 incorrect
~350 correct
N2pc
160 left
160 right
Fig. 22.3 Bootstrapped standardized measurement error (SME) values from the seven ERP
components in the ERP CORE dataset (Kappenman et al., 2021), as derived by Zhang and Luck
(2023). The number of trials per condition is given for each component. The SME values were
obtained
via bootstrapping from the difference wave used to isolate a given component (e.g.,
oddball minus standard for P3b). Separate SME values were obtained from each participant at the
optimal electrode site for each component, and these SME values were then averaged across
participants, with error bars indicating the standard error of the mean SME value across participants.
Separate SME values are shown for two different amplitude scoring methods (a: time-window mean
amplitude and peak amplitude) and for two different latency scoring methods (b: 50% area latency
and peak latency)
22 Quantifying EEG and ERP Data Quality 291
scores. A lower SME value translates directly into larger effect sizes and greater
statistical power (Luck et al.,
more
likely to yield a significant p value for a scoring method that produces lower
SME values. This is a very direct way in which the SME can help you with your
research: It can help you figure out which methods lead to the best data quality and
therefore the largest effect sizes and greatest statistical power. Note that timewindow mean amplitude and 50% area latency also have many other advantages
over peak amplitude and peak latenc
Figure 22.3 also shows that the SME values differ greatly among the different
ERP components. For the amplitude scores, this can be explained primarily by
differences in the number of trials used in each of the paradigms. For the latency
scores, however, the SME values are not simply a function of the number of trials.
They also vary with the shape of the waveform being measured, with lower SME
values for narrow, “sharp” components like N170.
Note that the units of SME are the same as the units of the score. For amplitude
, the SME quantifies your uncertainty about the true amplitude, and both the
scores
score and the SME of that score are in units of microvolts. For latency scores, the
SME quantifies your uncertainty about the true latency, and both the score and the
SME of that score are in units of milliseconds.
If you have recently set up a new ERP lab, and you would like to know if you are
getting
paradigms and compare your SME values to those shown in Fig. 22.3. If you are
collecti
recording environment (e.g., a hospital room), or with a noisier EEG recording
system (e.g., a dry electrode system), you can run one or more of the ERP CORE
paradigms and see how much worse your SME values are compared to those in
Fig.
ronment with a high-quality EEG system). With some simple math, you can figure
out how much your effect sizes and statistical power will be reduced by the greater
SME values, and you can estimate how many more trials you would need to collect
to make up for the noisier data (see Luck et al.,
compa
research!
reasonable data quality, you can run one or more of the ERP CORE
ng data from a more challenging population (e.g., children), or in a noisier
22.3 (which come from neurotypical young adults tested in a low-noise envi-
re my data quality with a set of values like these when I first started doing ERP
2021), which means that a real effect in your data is
y (
see Chapter 9 in Luck,
2021). I wish I had been able to
2014).
22.2.7 Using SME to Determine Optimal Processing
and Analysis Procedures
One of the most valuable aspects of the SME is that it gives you the ability to
determine which data processing methods and parameters will yield the best data
quality in your own research. That is, you can try several different methods and/or
parameters with your own data and see which ones yield the smallest SME values.
You can then apply those methods and parameters to future studies. As an example, I
292 S. J. Luck
will explain how SME can be used to deter mine the optimal filtering settings for a
given study, but must be combined with other factors to avoid problems. But make
sure to keep in mind that the SME quanti fies only the precision, and you’ll need to
make sure you don’t choose methods that are biased and create bogus differences
between groups or conditions.
You might think that the best filter would be the one that produces the best
(smallest) SME. However, there are two other important factors to consider. One is
that filters reduce the size of the signal as well as the size of the noise. This is
illustrated in Fig. 22.4a, which shows a single-participant averaged ERP waveform
and without the application of a 5 Hz low-pass filter. This filter passes low
with
frequencies and attenuates high frequencies, and you can see that it reduces the highfrequency fluctuations and “smooths” the waveform. However , it also dramatically
reduces the amplitude of the P1 and N1 peaks. A filter that decreases the signal more
than it decreases the noise would do more harm than good.
Figure 22.4b shows what happens
when the same filter is applied to an artificial
ERP waveform designed to simulate the N170 waveform from the ERP CORE
dataset (Kappenman et al., 2021). You can again see that the filter reduces the
ude of the N170, and you can also see that it “smears out” the waveform,
amplit
making it appear to onset earlier and offset later.
Figure 22.4c shows the effects of a 2 Hz high- pass filter on an averaged ERP
wave
form. This filter dramatically reduces the SME for the P3 component in this
waveform by reducing slow drifts in the single-trial EEG epochs (which is not easily
appreciated when viewing the averaged ERPs). However, it also cuts the P3 amplitude by more than half. Figure 22.4d shows the impact of this filter on the artificial
waveform. The filter has only a small impact on the N170 amplitude, but it
N170
creates artifactual positive-going peaks right before and right after the N170 wave. If
you used this filter, you might write a paper saying that you had discovered new
positive-going face-related ERP components, and you might be very embarrassed
when someone else publishes a follow-up paper showing that your new components
were actually filter artifacts. This has actually happened to researchers, and it was
very embarrassing. It almost happened to me when I was in graduate school, but I
realized that the effects were filter artifacts before I wrote the paper.
The point
here is that, although filters may improve the SME by reducing
low-frequency or high-frequency noise, they may also reduce the amplitude of the
signal and distort the time course of the waveform. Consequently, the filter that
produces the best SME may actually reduce your effect sizes and create bogus
effects in your waveforms. My lab has therefore created an approach for determining
the optimal filter that takes into account the impact of filtering on the size of the
signal, the amount of noise, and the waveform distortion (Zhang et al.,
ude scores, this approach involves estimating the impact of a given filter on
amplit
2024a). For
the signal-to-noise ratio, defined as the magnitude of the signal (as determined from
an artificial waveform) divided by the magnitude of the noise (quantified as the SME
in a real dataset). It also involves quantifying the magnitude of the waveform
distortion using tools available in ERPLAB Toolbox (see details in Zhang et al.,
2024a). We then systematically assess the signal-to-noise ratio and waveform
22 Quantifying EEG and ERP Data Quality 293
A Real data, low-pass filter C Real data, high-pass filter
P3
Unfiltered
Amplitude (μV)Amplitude (μV)
N1
P1
5 Hz low-pass filter
P1
N1
P3
2 Hz high-pass filter
Unfiltered
B Artificial N170, low-pass filter D Artificial N170, high-pass filter
Artifactual peaks
5 Hz low-pass filter
Unfiltered
Fig. 22.4 Effects of low-pass and high-pass filters on real and artificial ERP waveforms. (a)
Averaged ERP waveform from an actual research participant, with and without the application of
a noncausal Butterworth low-pass filter with a 5 Hz half-amplitude cutoff and a slope of 48 dB/
octave. (b) Artificial ERP waveform, with and without the same low-pass filter as in (a). (c)
Averaged ERP waveform, with and without the application of a noncausal Butterworth high-pass
filter with a 2 Hz half-amplitude cutoff and a slope of 12 dB/octave. (d) Artificial ERP waveform,
with and without the same low-pass filter as in panel C. Note that both the low-pass and high-pass
filters reduce the size of the signal as well as reducing the noise. Note also that the high-pass filter
produces artifactual peaks (highlighted with blue circles) that are more easily observed in the
artificial waveforms
2 Hz high-pass filter
Unfiltered
071N071N
)sm( ycnetaL)sm( ycnetaL
distortion across a broad range of filter parameters. From the tested filters, we select
the filter that yields the best signal-to-noise ratio without exceeding a threshold for
the maximum allowable waveform distortion. The same approach can be used to
select the optimal filter for latency scores, except that most filters do not reduce the
size of the latency “signal, ” so the optimal filter is the one that produces the lowest
old f
noise (the smallest SME) without exceeding the thresh
or waveform distortion.
The optimal filter varies depending on what component you are measuring, how
you are measuring it, and the types of noise that are present in your data. As an
example, consider low-frequency noise, which mainly arises from skin potentials
and movement artifacts. This type of noise causes the signal to drift randomly away
from the prestimulus baseline voltage, with more drift at longer latencies, and this
can really reduce the precision of amplitude scores obtained from long-latency
components such as P3 and N400. This noise has much less impact on shorterlatency components, such as N170 and MMN, because the EEG has not had much
time to drift away from the baseline voltage prior to the measurement window.