I have participants who were measured two times. First, without any intervention. And second, with an intervention. Thus, I should use paired t-test as both measurements are normally distributed (controlled with Kolmogorov-Smirnov test and eyeballing(plotting)).
But how to replace this test with a linear regression? The following approach isn't correct as both groups include the same participants? Any other modelling options (multilevel etc)?
y ~ group
A paired t-test is a test of whether the mean difference between conditions among individuals is different from 0. (It doesn't require normal distributions of the individual measurements among participants in either condition individually, so your K-S test and plots weren't really needed.) A normal distribution of the differences among individuals is assumed for standard significance tests, but other tests can be performed if that assumption is untenable.
So if you have single pre- and post-intervention measurements on all individuals, you can simply model
(postValue - preValue) ~ 1
to put this in a linear regression context. That will, however, just give you the same result as the standard paired t-test.
