Example: I am measuring radioactivity with a Geiger counter. I have statistical error (with the 95% confidence interval), but I also have systematic error (e.g. the Geiger counter’s sensitivity is ‘guaranteed’ to be within 5% of a specified value). If I am reporting an unusual finding, I’d want the result not to be explainable by the sum of statistical error and the bound on the systematic error. Bottom line is, generally there’s no guarantee that “95% confidence” findings will go the other way 5% of the time. It is perfectly OK to do something that may inadvertently boost the confidence.
Example: I am measuring radioactivity with a Geiger counter. I have statistical error (with the 95% confidence interval), but I also have systematic error (e.g. the Geiger counter’s sensitivity is ‘guaranteed’ to be within 5% of a specified value). If I am reporting an unusual finding, I’d want the result not to be explainable by the sum of statistical error and the bound on the systematic error. Bottom line is, generally there’s no guarantee that “95% confidence” findings will go the other way 5% of the time. It is perfectly OK to do something that may inadvertently boost the confidence.