I am a bit confused about the wording in the output of the hypothesis tests implemented in Hypothesistests.jl, and think that they might be improved. Take this instance of Fisher’s exact test:
FisherExactTest(4,3,2,4) Fisher's exact test ------------------- Population details: parameter of interest: Odds ratio value under h_0: 1.0 point estimate: 2.46629 95% confidence interval: (0.1815, 46.59) Test summary: outcome with 95% confidence: fail to reject h_0 two-sided p-value: 0.7669 Details: contingency table: 4 3 2 4
What I find confusing is the “outcome with 95% confidence” part. This may be okay when the test result is to reject h_0, but when failing to do so (as in this example), we do not do this with 95% confidence.
Is there any reason why this could not be phrased as “outcome at 95% significance level”?