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Often times, in python's scipy library's statistical tests(e.g. Fisher Exact Test), there is an option for two-tailed or single tailed. But for single-tailed it says "less" or "greater." I don't quite understand what it means when it states:

Use a one-sided alternative hypothesis (also known as a directional hypothesis) to determine whether the population parameter differs from the hypothesized value in a specific direction. You can specify the direction to be either greater than or less than the hypothesized value. Source

Can someone please clarify this? What do they mean by direction? If I have a one tailed distribution with the mean close to 0 and no negative values, then what exactly would "less" do and "greater" do?

Here's an example of my frequency dist. enter image description here

The x-axis is # of samples and y-axis is number of components of interest and each sample is an image.

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  • $\begingroup$ Mean zero and no negative values would imply your distribution has all mass at 0. $\endgroup$ – Michael M Oct 12 '17 at 20:34
  • $\begingroup$ I've edited the OP. It's close to 0. In other words, my data might fifteen 0s and four or five values between 1-3. @MichaelM $\endgroup$ – Christian Oct 12 '17 at 20:51
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Fisher Exact Tests consider all possible permutations of $2 \times 2$ contingency tables. Each table permutation can be ranked in terms of its degree of association by considering the odds ratio. An odds ratio which is greater than 1 shows a positive association between an exposure and an outcome whereas an OR less than 1 shows a negative association.

$$ \begin{array}{c|cc|c} & D & \bar{D} & \text{Total} \\ \hline E & a & b& a+b\\ \bar{E} & c& d& c+d\\ \text{Total} & a+c& b+d& n=a+b+c+d\\ \end{array} \qquad OR = (ad)/(bc) $$

The null hypothesis of a two sided Fisher's Exact Test is that the odds ratio of outcome and an exposure is 1 whereas the alternative is that it is not 1. A single sided test has a null hypothesis that the odds ratio is either less than 1 or greater than 1.

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  • $\begingroup$ So how should I know what to set for the null hypothesis: less or greater? In other words, is it possible for you to please state how to make the decision to set the null hypothesis with regards to less/greater than in layman terms without bringing in odds ratio? $\endgroup$ – Christian Oct 12 '17 at 21:04
  • $\begingroup$ @Christian if you do not know, you probably want to run a two tailed test. $\endgroup$ – AdamO Oct 12 '17 at 21:07
  • $\begingroup$ Hmm, I see. But my frequency distributions are clearly one-tailed. As in the OP, it is averaged close to 0, no positive values, and a few positive values. $\endgroup$ – Christian Oct 12 '17 at 21:14
  • $\begingroup$ I've added a graph to show what I mean. Any ideas? @AdamO $\endgroup$ – Christian Oct 12 '17 at 21:38
  • $\begingroup$ @Christian your graph makes no sense. Label the axes and describe a "sample". $\endgroup$ – AdamO Oct 13 '17 at 14:27

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