It is said that the p value for a t-test can be calculated as one-tailed or two-tailed. This makes sense as Condition A scores can be higher, or lower than Condition B scores (so a two-directional hypothesis is often appropriate).
We can also analyse the same data with One-way ANOVA and get the exact same p value (for a two-tailed t-test). But this time it is said that the analysis is one-tailed (because the F distribution is one-tailed). But it is effectively being used to assess a two-directional hypotheses (as the F distribution doesn't care which condition scores are higher).
Consequently, if we were to test a one-directional hypothesis with an ANOVA, would we have to divide the p value by 2? Or should we just avoid using ANOVA for one-directional hypotheses?
When testing the differences in the mean values of two independent samples, identical statistical conclusions are obtained by applying the t-test and ANOVA (one factor and two modalities). Specifically, this can be proved if we start from the F-statistics of ANOVA (one factor two modalities) we get the value of t-statistics.
The difference between F-test (with two groups) and a two-sample t-test is that the t-test consideres the mean difference (µ1-µ2) whereas the F-test consideres the squared mean difference (µ1-µ2)². Taking the square will erase the sign of the mean differences (squared values are always positive). Since the F-test "sees" only x², it cannot decide what the sign of x is.
In fact, when t is t(n-1)-distributed, then F=t² is F(1,n-1) distributed.
I think one way ANOVA can be used but should be supplemented with a post hoc test of multiple pairwise comparison. The Fisher's LSD can be used to test the one tailed hypothesis
In principle, always try to avoid one-directional testing when formulating hypothesis tests because these tests could be misleading in terms of the results obtained.
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