Trump Approval Rating At Highest Point Since August, Despite Unpopular Foreign Interventions

[AZJonnie]

22. I only took issue due to the specific phrasing of "is explained" rather than "could be explained"

And you're essentially saying the same thing here, no offense

Same point here. The observed data may turn out to be statistically insignificant once you test the difference, but you can’t conclude that solely because the margins of error overlap

As an example, say you do two polls completely identically, same sample sizes, same methodology. With two 1,000‑person polls, a move from 60% to 65% is roughly a 2.4‑sigma shift. Under standard assumptions, if there were truly no change, seeing a swing that big in the positive direction would happen less than 1% of the time. So it is highly likely that the true change is positive; the main uncertainty is how big the increase really is.

A key point is that if the sample mean is 60% with a 3% margin of error, that does not mean the true approval rate is equally plausible anywhere from 57% to 63%. Under the usual polling assumptions, values closer to 60% are more plausible than values at the edges like 57% or 63%