# Within subjects regression

Hi Mike

Hope you’re doing well in these challenging times,
I was checking the chapter 34 about regression in the ANTS book,

I have a couple of questions regarding the implementation in the Matlab code,

1. I see a small difference in the treatment between total power and the independent variables: the RTs and alpha power. The IV are zscored, and the total power is ranked with tiedrank. These functions normalize data, so maybe there are no big differences between the two. But I wonder if there is any reason to use one or another for the data or for the regressors,

2. More theoretically, how would you deal with baseline-corrected data? I mean suppose I have found an change of alpha power between an incongruent and a congruent condition for an experiment X. Then I want to dig in this effect and see if I see a correlation (or a regression) between alpha power and some regressor such as reactions times and trial-level behavioral responses. For the classical analysis I usually run some t-tests or ANOVA on baseline-corrected data. How would you do for correlations or regression at the trial level?

José

Hi José.

1. Single-trial power can have large values, in part because outliers can only be positive, and in part because kindof large amplitudes will become huge power values due to the squaring. Z-scoring won’t affect those large divergences but rank-transforming will (for the same reason that Spearman correlations are robust to outliers compared to Pearson correlations). The interpretation then becomes monotonic changes in power correlate with RT (or whatever).

I don’t know if rank-transforming power data in within-subject regression is always necessary, but I’ve found it to be a good idea.

1. You don’t need to baseline normalize for within-subject regression. The 1/f will be absorbed into the intercept term in the model, and anyway, rank or z-scoring the power data will remove the 1/f. Furthermore, the regression will be sensitive to the variance across trials that can be explained by RT, and baselining won’t change that.

As for statistics, you can do a t-test on the regression coefficients across subjects.

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