For each of several subjects, I have mean reaction times for each of several stimuli. For each individual subject, I want to regress the RTs (as Y) against the stimuli (as X) and see if I get a slope that is significantly different from zero. For that, I used Matlab's fitlm function which gives me, for the X predictor, a coefficient estimate and a p-value. I then want to see if, at the group level, if those coefficients (slopes) are significantly different from zero, using a 1-sample t-test.
My questions: 1) For each subject, is it correct to look at the p-value as an indication of whether the slope is significantly different from zero, or should I look at a goodness-of-fit measure instead? I thought that, as in the case of correlation, the question of slope is more to do with the notion of effect size than that of statistical significance
2) Is it correct to say that those p-values represent within-subject variability while the p-value of the 1-sample t-test represents between-subjects variability? In other words, can the effect (significant linear dependence between Y and X) be present at the subject level but not necessarily at the group level?