F Stat vs. T Stat relationship

[confused]

I have a question about the F Stat vs. T stat relationship. I know that for ANOVA, the F stat = t^2, thus the p value of the (non-directional) F stat can be cut in half for a directional test (which is equivalent to a 1 tailed t test). Is the same true for an ANCOVA? What I am trying to do is test whether 1 group scores higher on a measure than another group, but my design uses covariates (thus the ANCOVA instead of a regular ANOVA). My impression is that since I'm talking about a relationship between the F and t distributions, that using the F stat from the ANCOVA and cutting the corresponding P-value in half would be equivalent to the p value of a one-tailed t test with the same degrees of freedom, and thus allow me to do a directional ANCOVA as I desire. (This uses the relationship of F=t^2 to find t, and the p value of the one tailed t-test with the same degrees of freedom would be ½ the p value of the two tailed t test, or the non-directional F test). I would like to make sure that this is accurate from a statistical standpoint. If not, is there an alternative way to do a directional ANCOVA test?

Can anyone shed some light on this and/or give me a good reference for some reading on the subject.

thanks!