We often see a news piece on a poll showing that Frip is ahead of Frap, 48% to 46%, followed by a declaration that Frip and Frap are "statistically tied."
This phrase is nonsense. If the poll above was conducted properly, the odds are pretty good that Frip really is ahead, just perhaps not with "95% confidence."
And the 95% confidence level is itself arbitrary: there is no real reason to prefer it to 93% confidence, or 97% confidence. And the magical power granted to passing the 95% threshold is completely unwarranted: if a poll one week shows Frip ahead with 94.9% confidence, it will be reported that Frip and Frap are in a "statistical tie," but if, the next week, Frip is ahead with 95.1% confidence, it will be reported that he has a "decisive lead." But if we applied statistical reasoning to the difference between the two polls themselves, we would surely find that their predictions were "statistically tied," and far more "tied" than were Frip and Frap in the poll that put Frip ahead with 94.9% confidence!