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Good Morning, I Have two main questions about r^2:

1. If I am doing a P300 experiment with two subjects, and I found that one has a bigger value of r^2 than the other one, what this exactly means? That one can evoked stronger the P300?

2. In the dissertation that is posted here to find more information about coefficient of determination, I found that the equation describes the correlation coefficient and no the coeficcient of determination, according to Wonnacott and Wonnacott (r^2=Sxy/SxSy). I know how you calculate this in the software but I would like to have more clarity of this concept, the latter because I tried to do it by myself and I don't know how to calculate the covariance (SxSy) between two vectors of different lenghts (at least this is no possible in Excel).

Thank you so much,
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Eliana

Eliana,

The r^2 is a metric that shows how different two sets of signals are, e.g., the signals (at a particular time/channel) corresponding to target vs. non-target stimuli. In other words, it is similar to just calculating the difference between two signals, except it is sort of normalizing the variance to see how big of a difference one can expect in single trials. Thus, if you see higher r^2 values, you see bigger differences, meaning stronger P300 differences in single trials. (There may be a P300 with a big amplitude, but the noise and thus single-trial variance also very large, which would result in a small r^2 but a big amplitude difference.)

You do not calculate the covariance between the two vectors (target/non-target). You calculate the covariance between the signal and the task. The signal is a vector of amplitudes (one number in each trial). The task is a vector of values that indicate whether it's a target-trial or a non-target trial (e.g., you can use 0 for non-target and 1 for target). Thus, these two vectors are always the same length.

Gerv