Does the "Sig." column in the SPSS output for ANOVA The "Sig." column in SPSS output for t-test is a two-tailed p-value, i.e. if one want to decide whether to reject a null hypothesis, they need to compare the predetermined significant level with the "Sig." value divided by 2 instead of the value itself.
What about the SPSS output for F-test? It seems that it is a one-tailed p-value (i.e. one can directly compare it with the significance level of a one-tailed test). It would also not make sense if it was two-tailed as F-distribution is not symmetric. But I am still unable to find the confirmation.
 A: Conceptually, this is a two-tailed $p$-value. The right tail of the $F$ distribution reflects more variability than expectation and the left tail less variability than expectation. If we consider the restricted case with 1 degree of freedom in the numerator we have an $F$ that is simply $t^2$. The two-tailed $p$-value for this $t$ will be the same as $p$-value reported in the SPSS ANOVA table for the right tail of the $F$ distribution. Once you have 2 or 3 degrees-of-freedom in the numerator (i.e., when you are comparing 3 or more means), the directionality of the mean differences is no longer meaningful. Hence, the right tail (one-tailed) is for larger differences in either direction between the means then you would expect given the standard errors.
A: It is one tailed. In the ANOVA context, the statistic is calculated as between groups variance / within groups variance. Formulated as such, you only care if the ratio is positive; values <= 1.0 can never be significant, and so it is pointless to consider. Thus, you by definition have a directional hypothesis, and a one-tailed test. 
You could reformulate the question nondirectionally, as in the context of a variance ratio test, but this is less common, and often times one simply puts the larger variance in the numerator anyway, leading again to a one-tailed test. 
