[jhgb]

> which was lower but not in a significant way

But if "result [was] lower but not in a significant way" means "result was not proven to be lower", how does saying "lower but not really lower" make ever any sense? It seems to me that such nonsensical formulation ought not to be ever used by anyone.

[jjcon]

Because significance thresholds can vary pretty dramatically. Plenty of experiments done in physics for instance have reported results even though they didn't yet reach a 5 sigma threshold (3x10e-7). In physics something can be highly highly likely but still not 'significant' enough to warrant a discovery. They simply couch it as, hey this was the result and even though it isn't 'significant' the high likelihood may warrant additional research here. Reporting a binary significant/not significant is far less useful.