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I'm looking at the association between two categorical variables in a genus of birds. The variables are 'Conservation Concern' (Yes/No) and another binary variable (Yes/No) and I have these for every species in the genus. I know there may be issues with the variables (i.e. have they been adequately described) but they are what they are. I've calculated odds ratios but I'm not sure if I'm supposed to do a statistical test to show they are different.

When I run a statistical test (e.g. a Fisher's exact test) I get an odds ratio of 6 (agreeing with my hand calculation) and a p-value of 0.11. This means I can't say there is a significant difference in conservation status between the two groups. But the point of tests like Fisher's exact test is to tell you whether the odds ratio is different from 1, because they are usually used to infer things about a greater population, but I'm not trying to estimate a value as I know what it is, and it's 6. However, I suspect I should instead just be interpreting this as "I can't say this difference isn't due to chance".

I've looked at this question but am still unsure, mainly because that example involves a changing population.

I am wary of reporting results without supporting them with statistical analyses. But I also think it is weird to discount a known true value. I therefore don't know whether or not it's appropriate to use a statistical test in this case to make inferences about my data.

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    $\begingroup$ As described in the linked thread, if the values are known, there is no uncertainty and no statistics. Unless you want to extrapolate your results outside your sample, but this is not what you are saying. $\endgroup$
    – Tim ♦
    May 9 at 12:07
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    $\begingroup$ Sometimes there is uncertainty and a use for statistical analyses even in such situations. It depends on what you want to know and how you frame it. For instance, would it be of interest to know how often odds ratios this extreme would arise if one of the categorical variables were (hypothetically) assigned randomly to the species? If so, Fisher's Test answers that question (according to a specific model of random assignment). If the random assignment scenario has no meaning or interest in the application (even hypothetically), then hypothesis testing is meaningless, too. $\endgroup$
    – whuber ♦
    May 9 at 18:52

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Hypothesis testing is only appropriate if we estimate a population parameter, i.e., if there is a "true" population parameter (e.g., a group mean, or a coefficient in a linear relationship), which we don't know, but can estimate based on a random sample of data and a hypothesized relationship. The null hypothesis then is that the true parameter is equal to some specific value, or less than/greater than a particular value. The test tells us whether the estimate is consistent with the null hypothesis or not.

In your case, you know the true value, so you don't need to hypothesize about it. If you want to analyze whether it differs from some other value, all you have to do is look at whether there is mathematical equality or not.

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