Question time (some of the specifics that follow have been changed slightly, but hopefully not enough that it affects the answqers): suppose that you've reported results of an RCT with HR=0.82 and p-value=0.08 for one of the trial's secondary outcomes.
You used the phrases "tended to ____ less" / "modest reduction in ____" / and "there was a small ____ benefit" to describe these results.
Not just one, but several of the manuscript reviewers say things along the lines of "The ____ results are not statistically different" and "The reported benefit of ____ has been overstated. There is no statistical significance"
I do not believe the phrasing used was unreasonable. The incidence of ____ was lower in one of the treatment arms. It was not "significantly lower" at the 0.05 threshold but it was, you know, lower. It's a descriptive word, folks.
Authors should be permitted to state something like "The incidence of ____ was lower in XXX versus YYY" - they are reporting a fact about the results that occurred in the trial. Whether this constitutes strong evidence that the apparent difference is reflective of a true benefit
...is admittedly another question. But saying that all findings with p>0.05 must be called "no difference" is clearly absurd. If the incidence of an endpoint was 15% in one arm and 20% in the other, there's NOTHING wrong with saying that it was lower in one arm than the other..
...as long as your phrasing is correct. You're reporting the results that occurred in the trial. 15 percent is lower than 20 percent. The statistical hypothesis test that accompanies this is meant to address whether the observed data are sufficient to conclude that...
...these data would be unlikely to occur under the null / are incompatible with the null hypothesis of no difference.
