The ERP Boot Camp! Averaging!

Transcription

1 The! Averaging! All slides S. J. Luck, except as indicated in the notes sections of individual slides! Slides may be used for nonprofit educational purposes if this copyright notice is included, except as noted! Permission must be obtained from the copyright holder(s) for any other use! Averaging and S/N Ratio! S/N ratio = (signal size) (noise size)! µv effect, 10 µv noise -> 0.5:10 = 0.05:1! - Acceptable S/N ratio depends on number of subjects! Averaging increases S/N according to sqrt(n)! - Doubling N multiplies S/N by a factor of 1.41! - Quadrupling N doubles S/N (because sqrt(4) = 2)! - If S/N is.05:1 on a single trial, 1024 trials gives us a S/N ratio of 1.6:1! Because sqrt(1024) = 32 and.05 x 32 = 1.6! - Ouch!!!! So, how many trials to you actually need?! - Two-word answer (begins with it and ends with depends )! - On what does it depend?! 1

2 # of s and Statistical Power! Goal: Determine # of subjects and # of trials needed to achieve a given likelihood of being able to detect a significant difference between conditions/groups! Power depends on:! - Size of difference in means between conditions! - Variance across subjects (plus within-subject correlation)! - Number of subjects! Variance across subjects depends on:! - Residual noise that remains after averaging! - True variance (e.g., some people just have bigger P3s)! Residual noise after averaging depends on:! - Amount of noise on single trials ( noise + ERP variability)! - # of trials averaged together! # of s and Statistical Power!!"#$%&'$()$*+,&-+("..&/012,+#.& '#" '!" &#" &!" %#" %!" $#" $!" #" Put resources into more trials when the single-trial noise is large relative to other sources of variance!!" $" '" $(" ('" %#(" 3041,(&"5&!()$%.&67"8&/+$%,9& ))*"+,-./0$!1" 234/" /0&!" ))*"+,-./0&!1" 234/" /0$!" ))*"+,-./0$!1" 234/" /0$!" Put resources into more subjects when the single-trial noise is small relative to other sources of variance! 2

3 # of s and Statistical Power! For my lab s basic science research, we usually run subjects with the following number of trials:! - P1: trials/condition! - N2pc: trials/condition! - P3/N400: trials/condition! We try to double this for studies of schizophrenia! Individual s! Averaged Data! 1 s s s s s s 1-6 s 1-7 Look at prestimulus baseline to see noise level! 8 +15µV s µV µV µV 3

4 Individual Differences! Subject 1 Subject 4 Illusion! Subject 2 Subject 5 Subject 3 Subject 61 Contralateral Target Ipsilateral Target +5µV µV Time Poststimulus (ms) Slope Illusion! 6! 5.5! 5! 5! 4! 3! 2.5! 2! 1.5! 2! 1! 0! 1! 4

5 Individual Differences! Subject 6 Session 1 Subject 6 Session 2 Subject 6 Session 3 +5µV Contralateral Target Ipsilateral Target µV Time Poststimulus (ms) Good reproducibility across sessions (assuming adequate # of trials)! Explaining Individual Differences! How could a component be negative for one subject?! P2! +5µV µV

6 Individual Differences! Grand average of any 10 subjects usually looks much like the grand average of any other 10 subjects! Assumptions of Averaging! Assumption 1: All sources of voltage are random with respect to time-locking event except the ERP! - This should be true for a well-designed experiment with no time-locked artifacts! Assumption 2: The amplitude of the ERP signal is the same on each trial! - Violations of this don t matter very much! - We don t usually care if a component varies in amplitude from trial to trial! - However, two components in the average might never occur together on a single trial! - Techniques such as PCA & ICA can take advantage of lessthan-perfect correlations between components! 6

7 Assumptions of Averaging! Assumption 3: The timing of the ERP signal is the same on each trial! - Violations of this matter a lot! - The stimulus might elicit oscillations that vary in phase or onset time from trial to trial! These will disappear from the average! - The timing of a component may vary from trial to trial! This is called latency jitter! The average will contain a smeared out version of the component with a reduced peak amplitude! The average will be equal to the convolution of the single-trial waveform with the distribution of latencies! - The Woody Filter technique attempts to solve this problem! - Response-locked averaging can sometimes solve this problem! Latency Jitter! Average Average Average Note: For monophasic waveforms, area amplitude does not change when the degree of latency jitter changes! 7

8 Latency Jitter & Convolution! ERP Amplitude! P3 when RT = 400 ms! P3 when RT = 500 ms! (Assumes P3 peaks at RT)! Time! Latency Jitter & Convolution! Probability of Reaction Time! If P3 is time-locked to the response, then we need to see the probability distribution of RT! 17% of RTs at 350 ms! 7% of RTs at 300 ms! 25% of RTs at 400 ms! Time! 8

9 Latency Jitter & Convolution! Probability of Reaction Time! If X% of the trials have a particular P3 latency, then the P3 at that latency contributes X% to the averaged waveform! 17% of P3s peak at 350 ms! 7% of P3s peak at 300 ms! 25% of P3s peak at 400 ms! Time! Latency Jitter & Convolution! ERP Amplitude! Averaged P3 waveform across trials = Sum of scaled and shifted P3s! We are replacing each point in the RT distribution (function A) with a scaled and shifted P3 waveform (function B)! This is called convolving function A and function B! ( A * B )! Time! 9

10 Example of Latency Variability! Parallel Search Serial Search Target = Target = Luck & Hillyard (1990)! Example of Latency Variability! Parallel Search! Serial Search! Stimulus Stimulus Stimulus Locked Averages +3µV -3µV 500 ms Response Locked Averages Response Set Size = 4 Set Size = 8 Set Size = 12 Response Luck & Hillyard (1990)! 10

11 The Overlap Problem! A: Original Waveform B: Overlap at -300, -400, -500 C: Overlap at -300 to -500 D: Overlap at 300, 400, 500 E: Overlap at 300 to 500 F: Waveform plus Overlap ( ) G: Waveform plus Overlap ( ) +5µV µV Time Poststimulus (ms) Overlap! Woldorff (1993)! Overlap for current event is equal to the ERP waveform shifted in time and scaled by the frequency of occurrence of each SOA (convolution of ERP waveform and distribution of SOAs)! 11

12 Steady-State ERPs! Stimuli (clicks)!! SOA is constant, so the overlap is not temporally smeared! Battista Azzena et al. (1995)! Galambos et al. (1981)! Transient ERP! 12

13 Time-Frequency Analysis! Single-! Waveforms! Conventional! Average! Average 10 Hz! Tallon-Baudry & Bertrand (1999)! 13