Wording in "Test summary" portion of HypothesisTests.jl output

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:

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

    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”?

It would have to be “at the 5% significance level” (because the confidence level is 1-alpha and the significance level is alpha), but otherwise this seems like a reasonable request. Please file an issue! :slightly_smiling_face: