More on polls real quick... A response to Sasha's post.

So here's how i boil down what's going on. With 95% confidence we can say the following two things:

1) Bush's numbers changed by something between +.3% and -8.3%

2) Bush's numbers changed by something more negative than -.4%


I'm not claiming that the latter is preferable because the odds of a drop of 8 percentage points is a priori unlikely (the reason given in the text book for using method 2), but only because the question we are trying to answer is "did bush's numbers drop?" not "are bush's numbers within a certain band around the mean?"

Stated otherwise, you are right that the result of the two polls is that Bush's approval rating changed by -4% with margin of error of +/- 4.3%. However, you can't simply say that because 4.3% > 4% we can't be confident that his approval ratings dropped.

This is true of any poll. Suppose we needed 50% or more to pass a measure, and a poll gave a "yes" estimate of 54% +/- 4.3%. You could still say with the required 95% confidence level that the measure was going to pass even though at first glance it seems that 50% is within the margin of error.