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I am new to neuroscience (coming from a data science background), and I'm a little bit confused about the terminology used in many of the resources I have come across. Many studies mention "single-trial" analysis, "single-trial" EEG data and so on and I'm not sure what it means. My guess would be that "single-trial" refers to splitting EEG (or other) data into sub-series and treating each of them as separate trial, where trial means sample. But I don't understand why is it called "single" trial even if we use many of them in final analysis.

Example usage of 'single-trial" I don't understand:

Single-trial analyses refer to methods that consider the variance within subjects. Two broad families of methods can be distinguished: univariate methods extract information among trials in space, time, or both; multivariate methods extract information across space, time, or both, in individual trials. Single-trial analyses may thus be used for behavioral experiments (e.g., Etchells et al., 2011) and neuroimaging experiments (e.g., Cohen and Cavanagh, 2011; Macdonald et al., 2011; Milne, 2011; Rousselet et al., 2011; Touryan et al., 2011; Wutte et al., 2011). Single-trial analyses of neuroimaging data have seen their use increase since the late 1960s, starting with Donchin (1969). Despite this long tradition and several advantages over group analyses, single-trial analyses remain nevertheless marginal.

(source)

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EEG measures very, very small voltages.

Therefore, traditionally a very common EEG technique is to do something repeatable, like present the same sound, record EEG relative to that event, and average over several trials with the same event. This helps improve signal to noise, because any time-locked EEG responses are in every trial, whereas noise from outside sources averages out.

Single-trial analyses are those that avoid this traditional averaging step. Though I've also seen it misused where someone claims they are doing single-trial analysis when they definitely are not, so be wary and look at the actual methodology.

"Consider the variance within subjects" is certainly true, I just wouldn't consider it the primary organizing feature. But, indeed, it should be clear to you with a data science background that if you've averaged all the trials for a given state in a given subject, you don't have a measurable variance within that subject, so that's what they're referring to there.

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