Simple pair-wise t-tests as sophisticated fixed-effects methods

Post date: Mar 31, 2014 11:58:34 PM

I have been studying the book "fixed effects regression methods for longitudinal data using SAS" by Paul Allison. I love this guy, and I guess if I want to be a teacher I should gain an attitude very similar to his teaching attitude, though it's all in the book. I imagine it would have been wonderful if I could be his student in statistics. 

Well anyway, the ordinary pairwise t-test where there are two measurements or say observation from the same unit -can be a person, a tree, a roadway segment, etc.- can be considered or in fact is actually following a fixed-effects method. Why is it called pair-wise? Because we are conducting the test on the same unit before and after some experiment, -say sometime passed from the first measurement- but it's always been the same guy we are measuring. Whatever related to the unit, let's say its race if it's a person, is not changing over the time. It’s fixed. Or the person's sex has not changed. Therefore, whatever the result of the treatment is between the first and the second measurement (or observation) does not have anything to do with the fixed characteristics of the experimental unit. In other words, we can say if we have found a change from the first to the second observation, we are sure that it is not related to the stable characteristics of the given unit. However, all these are conducted on an average basis, meaning several units are considered and then finally the average is examined, but anyhow, those units remain the same. Whatever is causing the change between the two observations is either as a result of our treatment, or something we have not measured.

So far, I wrote about the typical t-test. Let's switch to the fixed-effects methods. In a model using this method, the outcome (dependent or response value) of a unit is presented as the summation of: overall average outcome of the distribution to which the unit belongs, the stable effects of each unit, the effect of the changes that have occurred since the last measurement, and random variations. 

In every experiment, we can say, since we cannot measure all the prevailing variables that might or might not affect the value of a the variable of interest, by using the fixed effects method, we can at least be sure that we are accounting for those stable characteristics of any experimental unit; and this reduces the bias of the model estimates.