Does the margin of error have a falloff curve (i.e. the middle is more likely than the ends, like a normal distribution), or is it 'flat' range of uncertainty? I'm looking for a more clear understanding of "statistical tie". It's been difficult for me to research. Here is an example that hopefully clarifies:
Assume a normal, random survey, A vs B, with a margin of error of 6%. Option A polls at 48%. Option B polls at 52%.
Can Option A legitimately say they have a 'statistical tie', simply because their 6% range overlaps with B's range?
Is Option A just as likely to end up with 45% (or 51%) of the vote, as they are 48%?
First one: yes, we can say that there is no 'statistically significant difference .. but of course if you had to put your money and be forced to choose one of the options and were looking for the highest percentage, you would go for option B: just because we are not 95% confident (the value typically used for statistical significance) that option B would be preferred over option A, we might still be 60% confident.
Second one. No. If A polls at 48%, then the actual percentage is more likely around 48% than around 45% ... though with a margin of error of 6% the difference will be quite small. Please note my use of around 48% and around 45% .. you never want to put any kind of confidence in the claim that it is exactly some percentage .. if tou deal with whole numbers, that may simply be impossible (e.g. there is no exact 45% of 101), and if you deal with real numbers, the chance that it is exactly some percentage is infinitesemal.