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I have an experiment with 3 within-subject conditions: A, B and C. My dependent variable is reaction time. I am interested in comparing A to B and A to C. Using aov() on R I run an one way ANOVA with the two contrasts built in the model. Condition was a factor (in the sense of factor() ).

model1 = aov(reaction_time ~ condition + Error(subject/condition),
              data = My_data)
summary(model1, split=list(type = list("A vs  B"=1, "A vs  C" = 2)))

The summary function revealed that the overall model was significant. The contrast comparing A to B was significant (.012). The pvalue of the second contrast (A to C) was .0509. Since I have strong theoretical background for my comparisons, I divided the pvalue by 2.

One reviewer did not accept that. He claimed that since I reported a F test for the contrast (which is what aov() reports), I cannot conduct a one tailed test. I claimed that a F test comparing two groups is equivalent to a t-test comparing the same two groups. The obtained F value would the square of the t value, but the pvalue should be the same. Therefore, if I could divide the pvalue fo the t-test, I could similarly divide the pvalue of the F test.

What is wrong with my logic?

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