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Suppose I have a 2 by 2 table and I am trying to conduct a Fisher's Exact Test. I am wondering when the two-sided test is used versus a one-sided test. In programs like R, they have greater, less, and two-sided. In most cases, I would only use either greater or less depending on the direction. However, when is the two-sided version ever used? Thanks.

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If you have a very strong assumption before exploring your data that the values of one group will be either lower or equal to the other group (alternative="less") or that the values of one group will be either higher or equal to the other group (alternative="greater") you can use a one-sided test to increase the power of this test:

A two-sided test:

If you are using a significance level of 0.05, [...] .025 is in each tail of the distribution of your test statistic [...] you are testing for the possibility of the relationship in both directions. [...] The mean is considered significantly different from x if the test statistic is in the top 2.5% or bottom 2.5% of its probability distribution, resulting in a p-value less than 0.05.

A one-tailed test:

When using a one-tailed test, you are testing for the possibility of the relationship in one direction and completely disregarding the possibility of a relationship in the other direction. [...] A one-tailed test will test either if the mean is significantly greater than x or if the mean is significantly less than x, but not both. [...] The one-tailed test provides more power to detect an effect in one direction by not testing the effect in the other direction. A discussion of when this is an appropriate option follows.

https://stats.idre.ucla.edu/other/mult-pkg/faq/general/faq-what-are-the-differences-between-one-tailed-and-two-tailed-tests/

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