Is there a way to "block" a t-test in R?

Question

I'm looking for a way to "block" a t-test that will allow me to use three measurements per subject, instead of just averaging them.

The problem is this: My way of measuring has (intrinsically) big errors, so I measured the same subject three times to account for that error (technical triplicates). I typically block my ANOVAs or consider subject and technical repetition as a Random Effects in a Linear Mixed Effect model, in order to take the nature of my measurements in consideration.

However, in this case I only have treatment (5 subjects, 3 measurements per subject = 15) and control (7*3 = 21) in my set, so a t-test would be more adequate, but I cannot find a way to "block" a t-test. A paired t-test is not applicable since the treatment is not applied to the same subjects (would be impossible) and a normal t-test does not take in consideration the error within repetitions. Is there a function in R to do this?

Answer 1

A t-test is just a special case of ANOVA. Take data that you would regularly do a t-test for and instead do ANOVA (2 groups, oneway) and you will notice that the p-value is exactly the same (if the t-test was 2 tailed) and the F statistic from the ANOVA is the square of the t statistic from the t-test (exactly equal if doing a pooled t-test, approximately if using the approximate t test).

So "blocking" a t-test is really just doing an ANOVA with blocking as well.

If you don't want to assume equal variances (the pooled t-test) then you can still do a mixed effects model instead of the ANOVA and just allow for unequal variances in the mixed effects model.