Sometimes in popular science books and articles, even ones written by scientists, I see phrases like the one in the title. For example, they’d be comparing the effect of independent variables A and B and say something like (1) “B had a greater effect than A, but the difference wasn’t statistically significant.”
As far as I understand the idea of statistical significance, its whole point is to help us figure out whether two quantities, as far as we know, really ARE different or only seem different because of random variation. Which would then mean that the quote above means pretty much the same thing as (2) “As far as they could tell, the effects of A and B were the same.” But saying it the first way kind of insinuates, especially for people who aren’t well-versed in statistics, that the effects really ARE different, and the whole “not statistically significant” part just gets ignored.
Am I right that (1) means the same as (2) but is misleading? Or is there a difference between (1) and (2)?