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I measured electrophysiological signals at two different conditions, baseline and effect. At each condition I sampled 10 signals, because there is a variance in amplitude due to uncontrolable factors (temperature fluctuation, flow variation, interference, local charge shifts ...).

I repeated this experiment with different subjects and now wonder wether there is a test that can capture the fact that I have 10 measurements for one subject at one condition or wether I just should use a paired t-test with the means.

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This sounds like a mixed model would fit the experimental design very well. The relevant test would be a comparison between nested models where a null model would only include the random component of subject compared against a model that included a fixed component for your baseline/effect along with the random subject component. Typically, this is a Chi-square test for nested models.

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