The significance of 'significant' I am writing up a paper where I report the results of a set of analyses using Bayesian parameter estimating but am really struggling to come up with synonyms for significant. 
Take this sentence.
"The analysis presented above allowed us to estimate whether people given decaffeinated coffee and told truthfully that it was decaffeinated still experienced a significant reduction in caffeine withdrawal."
All my training in stats has been using NHST and the language that goes along with it. The problem is that 'significant' is a perfect word to capture effects that are noteworthy without sensationalising them with adjectives like 'pronounced' or 'large'.
So in co-opting the word 'significant' and giving it a specific meaning frequentism has also prevented its use by other statistical traditions as a neutral descriptor of noteworthy effects 
Does anyone have some suggestions?
p.s. 'noteworthy' does not seem to work to my ears. 
 A: I would recommend leaving words like "significance" out of such descriptions. Be specific instead. For your example sentence (evidently intended for a Discussion section), try something like:

"People given decaffeinated coffee and told truthfully that it was decaffeinated experienced a reduction of X (95% credible interval, Y-Z) in caffeine withdrawal versus those who were not so informed."

The magnitude of the reduction will speak for itself (provided that your measure of caffeine withdrawal is standard) and having 0 outside the credible interval will provide assurance that there is likely to be a true difference.
For the Introduction, again emphasize the magnitude with something like:

We thus designed a study to estimate the magnitude of the difference in caffeine withdrawal symptoms when participants were truthfully told that their beverages would be decaffeinated.

I'm not sure what boilerplate language should be used in the Methods to replace the usual "statistical significance was accepted at p < 0.05 in two-sided tests." Maybe something like "We report 95% credible intervals for our analyses" will do.

I disagree with your premise that "'significant' is a perfect word to capture effects that are noteworthy." Sometimes it just means that you had a large enough study to make a (statistically significant) mountain out of a (practically meaningless) mole-hill. Saying something specific is almost always better than using a generic descriptor.
