You flip a coin, I guess heads because I know it's a 50-50 probability.
But I'm not "guessing" when a pollster says that candidate A is leading candidate B by 3% with a 4% margin of error. My model, and my equation that fits the model, tells me that a 3% lead with a 4% MOE is equivalent to the leader winning 80.4% of the time.
Perhaps that is the part that you are not understanding.
-PJ
I’ll just let Wikipedia argue with you,
“When a study involves multiple statistical tests, some laymen assume that the confidence associated with individual tests is the confidence one should have in the results of the study itself. In fact, the results of all the statistical tests conducted during a study must be judged as a whole in determining what confidence one may place in the positive links it produces. For example, say a study is conducted which involves 40 statistical tests at 95% confidence, and which produces 3 positive results. Each test has a 5% chance of producing a false positive, so such a study will produce 3 false positives about two times in three. Thus the confidence one can have that any of the study’s positive conclusions are correct is only about 32%, well below the 95% the researchers have set as their standard of acceptance.”
When Wiki says, “some laymen assume”, they are talking about you. So aside from you, the only people I know that put faith in ensemble averages of data they don’t understand is the Intergovernmental Panel on Climate Change.