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I have an experimental setup with 2 factors, site and disturbance treatment. I have reason to suspect that plots at site A will be more affected by treatment than plots at site B. My response variable is change in the % of the plot covered by a species over time. Site A has about half the starting species cover as site B. At regular intervals, a portion of the plot is haphazardly removed through disturbance (at 3 different levels).

The response variable is created by using repeated cover measures on each plot to draw a linear regression through the points, to eliminate temporal auto-correlation and generate an independent set of response variables. The slope of this regression is the response variable, which is change in percentage of plot covered by the species per annum.

I have generally been suffering from low power. I am interested in testing the interaction of site and treatment, but am interested in using a 1 tailed test, testing if Site A is more heavily affected by treatments than site B (in other words, if sites with lower initial species cover are more affected by disturbance treatments). I can't think of a biological reason to test the other way around (that higher initial species cover would yield higher vulnerability to disturbance).

Another reason I want to use a 1 tailed test is because when I looked at the slopes of the treatments at each site, it became apparent that Site A was losing cover while Site B was remaining fairly stable.

My questions are: 1) Is it appropriate to use a one-tailed distribution to increase power in this situation? 2) Is it tautological (or logically unsound) to look at the means of each site and decide a 1-tailed test is appropriate? 3) At this point (not having yet used a 1-tailed F table but wanting to), is this decision still considered a priori? Or am i now in the post-hoc zone since the data have already been collected?

Thank you in advance for your assistance.

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My rule of thumb for a one tailed test is to ask "If the result was in the opposite direction to that which I expect (or hypothesize) will my conclusions be the same as if there is no difference?" If that isn't true, then you shouldn't be doing a one tailed test. For example, if you are seeing if some doctors have more patients die than would be expected, because you suspect the doctors are murdering their pateints, a one tailed test should be used. If a doctor has exactly the expected number of patients die, or fewer than the expected number of patients die, your conclusions are the same - there is no evidence they're murdering the patients.

The only time I've seen one tailed used is if the p-value is marginally significant. No one ever says they're using a one-tailed test if their p-value is 0.001 or 0.800, because there's no need. So the use of one-tailed tests immediately makes me believe that someone is trying to deceive me.

Yes, it's very unsound to look at the data and decide that a one-tailed test is appropriate. You could just make up a p-value if you want to, and this would also be unsound. What you're suggesting isn't that bad, but it's getting closer.

Finally, there's no such thing as a one-tailed F-table.

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    $\begingroup$ Thank you for the rapid, helpful and honest response. I misspoke on the F-table, I was referring to the 0.95 quantile table as opposed to the 0.975 table. $\endgroup$ – MANOVAboard Dec 4 '14 at 14:37

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