Tuesday, July 29, 2008

Dueling Gallup polls can both be true

One Gallup poll shows an 8 point Obama lead

Another Gallup poll shows a 4 point McCain lead

The pundits and internet bloggers all yell "they both can't be true"!

but of course they can.

First of all people always seem to forget that the margin of error is based on each result.

For example for the:

Obama 48
McCain 40

+/ 2 percentage points in a 95% confidence

That means, 5 times out of a hundred you would expect the results to be wildly inaccurate.

The other 95 times the sample would yield a result for:

Obama between 46 and 50
McCain between 38 and 42

So the race could be Obama +4 or Obama +12

In the other with:
McCain 49
Obama 45
+/- 4 percentage m.o.e.

it could be:

McCain between 45 and 53
Obama between 41 and 49

So Obama could be up 4 or McCain could be up 12

First of all there is overlap in these polls within the 95% confidence level at:

Obama up 4, up 3, up2, up 1, tied, mccain up 1 - 4

The other possibilities don't overlap.

Since there are thousands of polls each year, more of them than used to be the case will wind up in the 5% no confidence.

But even so, there is an overlap here that says, the race is probably close.

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