"Probability of Being Ahead by a Certain Amount" Question

[DSchles]

Thanks Don.

I am in no way trying to make this political, but we are constantly bombarded with public opinion polls in the media where they act so sure of the results of polls based on "1000 registered voters", or "1000 likely voters", +/- 3% margin of error, blah, blah, blah...so if I'm interpreting your response correctly, these types of polls are basically worthless?

No, didn't say that! With 1,000 people polled, the typical margin of error is, indeed, a bit higher than 3%. So, it might say that candidate A leads B by 55 to 45, give or take 3 percentage points. That means the vote could actually be as close as 52-48 or as far apart as 58-42 ... or more (see below). And that's a big difference (as Hillary might tell you!)!! So, the values simply aren't very reliable.

For 5,000 observations, standard error drops to 1.4%, and so, if I tell you that your SCORE in a game is, say 50, you now can feel reasonably confident that it probably is somewhere between 50.71 and 49.29. For most, that might be acceptable, but for researchers, and those of us who obsess over every decimal point, it isn't nearly accurate enough. And, the true result will lie outside of these upper and lower limits almost one-third of the time, so, again, the results can leave much to be desired.

Don

[Wave]

No, didn't say that! With 1,000 people polled, the typical margin of error is, indeed, a bit higher than 3%. So, it might say that candidate A leads B by 55 to 45, give or take 3 percentage points. That means the vote could actually be as close as 52-48 or as far apart as 58-42 ... or more (see below). And that's a big difference (as Hillary might tell you!)!! So, the values simply aren't very reliable.

For 5,000 observations, standard error drops to 1.4%, and so, if I tell you that your SCORE in a game is, say 50, you now can feel reasonably confident that it probably is somewhere between 50.71 and 49.29. For most, that might be acceptable, but for researchers, and those of us who obsess over every decimal point, it isn't nearly accurate enough. And, the true result will lie outside of these upper and lower limits almost one-third of the time, so, again, the results can leave much to be desired.

Don

Ahhh...now I think I get it, so then it is simply a matter of acceptable degrees of accuracy.