### Illinois Governor's Race: Misreading the polls.

http://www.dailykos.com/story/2006/7/14/12642/2045

## IL-Gov: Is Blago pulling away?

### by kos

## Fri Jul 14, 2006 at 09:06:42 AM PDT

Rasmussen. 7/6. Likely voters. MoE 4.5% (4/8 results)

Blagojevich(D) 45 (38)Topinka(R) 34 (44)

Huge turnaround. While Blago may be unliked and corrupt, even that might not be enough to hand the governor's seat to Republicans, not matter how much voters might flirt with Topinka (the only statewide elected Republican in the state). That's how far in the dumps Illinois Republicans are in.

The Blagojevich campaign has run an advertising campaign raising the question "What is She Thinking?" about Topinka and touching on issues ranging from the state budget to Iraq. The Blagojevich campaign has also raised complaints about lease payments by Topinka to a developer who is also a contributor. A better job performance in the state may also have something to do with the turnabout.

So, is this a huge turn-around? Well, maybe, maybe not.

Let's go to the poll itself:

http://www.rasmussenreports.com/2006/State%20Polls/July%202006/ilGovernor.htm

Survey of 500 Likely VotersJuly 6, 2006

Election 2006: Illinois Governor | |
---|---|

Rod Blagojevich (D) | 45% |

Judy Baar Topinka (R) | 34% |

July 13, 2006 After trailing earlier in the campaign season, Illinois Governor Rod

Blagojevich (D) now leads Republican State Treasurer Judy

Baar Topinka by 11-points in his bid for re-election. The latest Rasmussen

Reports poll shows Blagojevich with 45% of the vote to 34% for Topinka.

The Blagojevich campaign has run an advertising campaign raising the

question "What is She Thinking?" about Topinka and touching on issues

ranging from the state budget to Iraq. The Blagojevich campaign has also

raised complaints about lease payments by Topinka to a developer who is

also a contributor. A better job performance in the state may also have

something to do with the turnabout.

The governor, too, has had to contend with charges of impropriety, but

that's old news and he has more money to spend on campaign ads. Many

Republicans in the state concede that he has managed to put Topinka on the

defensive lately.

What is the key? The key is this: the poll was of 500 likely voters. This type of poll is what is known as a proportion. The theory is something like this: when you poll 500 voters, you are interested in, say, the number that say that they will vote for Blagojevich. That number (out of 500) is denoted by the letter "p" and the appropriate distribution is the binomial distribution. Typically, one then divides by the number polled to get a proportion.

The standard deviation is the square root of the variance, so here we have "sd" = (.5*.5/500)^.5 = .0224. Since we are 95% confident that the true proportion will be within 2 standard deviations of the one that we actually measured, we have that Blagojevich's support is between .45 +- 2*(.0224) = (.4052, .4948).

In the previous poll, it was .38 +-2*(.0224) = (.3352, .4248). Note that these two confidence intervals overlap.

Now that doesn't mean that we can say that there is no change but it does point out that the change might not be as dramatic as it seems at first.

If we now measure the difference between the two proportions, and use the fact that the new variance is the sum of the absolute values of the two variances:

"variance" = 2*.5*5./500, so the standard deviation is: .0316, and so the difference in Blagojevich's support is (.45-.38) +- 2*.0316 = (.007, .133), which means that this difference in support for Blagojevich (between polls) might be less than 1%.

We can say, with confidence, that Blagojevich did not lose support.

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