· September 11, 2012 at 7:49am

Since a fair number of folks seem to be scared by recent polls, here's an interesting poll from CNN today.  It has Obama leading Romney 52% to 46% (yikes!).  But (see page 21) Romney leads among independents 54% to 40%.    If you assume that each respondent is either D or I or R, you can use these numbers to back out, for each level of I, the percentages of D and R in the poll.  (It's two linear equations in two unknowns, once you specify I.)

If I = 20%, you compute D = 44.63% and R = 35.37% (using the equation .52 = .97D + .4I + .02R), or a 9.26% D over R.

If I = 40% instead, you compute D = 36.63% and R = 23.37%, or an 13.26% difference.

For I between 20% and 40%, the difference is between 9.26% and 13.26%---the larger is I, the larger is the computed value of D minus R.

Of course, we don't know I.  (CNN doesn't supply the sample statistics.)  But we can compute for each I the level of support for Romney given the computed D and R, and the closest we come to 46% is when I = 20%, for a "lean-Romney" number of 45.7%.   (If we went lower with I, we could come closer.   At I = 40%, the computed "lean-Romney" is 44.3%.)

So, the best guess I can make is that CNN's sample is I = 20%, D = 45% (or so), and R = 35%.

Conclusion #1:   CNN has some very interesting sampling procedures.  This strikes me as propaganda and not a serious exercise in polling.

Conclusion #2:   Chill out.  The polls for public consumption can't be taken seriously this far away from the real polling day.

Joined
Aug '12

### Re: A New Poll by CNN

Sir, thank you for the mathematical analysis as it is music to this engineer's ears.

Digging through the data I wish there was a third equation so that you could solve for D, R, or I and then solve for all the others, but unfortunately the two equations you came up with seem to be it (and then interpolate to the I/R/D breakdown).  Either way I agree, the CNN poll seems to be sensationalized.

### Re: A New Poll by CNN

So you're saying that if the sample size matched the most recent estimation of registered voters by party affiliation —Gallup has 40% I, 31% D, and 27% R— then Romney would be ahead by a couple of percentage points instead of behind by 6 points.

But CNN's poll is of likely voters and Gallup's survey is of registered voters.  Aren't independents less likely to vote?  I haven't been able to find a recent survey that breaks down likely voters by party affiliation.

Joined
Jun '12

### Re: A New Poll by CNN

Actually, we have a good indication of their partisan split on the top of page 5 of the .pdf.

BASED ON 441 REGISTERED DEMOCRATS -- (SAMPLING ERROR: +/- 4.5% PTS.);
BASED ON 397 REGISTERED REPUBLICANS -- (SAMPLING ERROR: +/- 5% PTS.)

Stanford University

### Re: A New Poll by CNN

 ConservativeWanderer: Actually, we have a good indication of their partisan split on the top of page 5 of the .pdf. BASED ON 441 REGISTERED DEMOCRATS -- (SAMPLING ERROR: +/- 4.5% PTS.);BASED ON 397 REGISTERED REPUBLICANS -- (SAMPLING ERROR: +/- 5% PTS.) 59 minutes ago

That's registered voters, not likely.   But let's go with those figures.   The total sample size of registered voters is 875.   If 441 are democrats and 397 are republicans, that leaves 37 independents.  So their sample of registered voters was 50.4% democrat, 45.4% republican, and 4.2% independent.  Really?   Compare this with the figures quoted in Diane Ellis' post above.

And if I apply the conditionals from page 20 to this percentage breakdown, I get 51.4% for Obama and 47% for Romney.   Back on page 2, they say that the registered voter preference is 53% for Obama and 45% for Romney.   It's possible, I guess, that the conditionals among registered voters is that different from the conditionals for likely voters, but this whole poll...gives off an odor.

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Jun '12

### Re: A New Poll by CNN

 David KrepsThat's registered voters, not likely.   But let's go with those figures.   The total sample size of registered voters is 875.   If 441 are democrats and 397 are republicans, that leaves 37 independents.  So their sample of registered voters was 50.4% democrat, 45.4% republican, and 4.2% independent.  Really?   Compare this with the figures quoted in Diane Ellis' post above.And if I apply the conditionals from page 20 to this percentage breakdown, I get 51.4% for Obama and 47% for Romney.   Back on page 2, they say that the registered voter preference is 53% for Obama and 45% for Romney.   It's possible, I guess, that the conditionals among registered voters is that different from the conditionals for likely voters, but this whole poll...gives off an odor. · 3 minutes ago

Not only that, but that's a small sample size for this sort of polling. Rasmussen, for example, does a sample of 1,500 for their Presidential tracking polls.

Edited on September 11, 2012 at 4:15am

Joined
Aug '10

### Re: A New Poll by CNN

The fact that CNN won't publish the sampling data tells you all you need to know about this poll.

Obama and his official media organs are banking that your average voter won't read beyond the headlines, whether it's polls that oversample Dems or a horrible jobs report that is trumpeted as "Lower unemployment rate!"

If they are right this country is cooked - if they are wrong their re-election campaign is cooked...

Joined
Jul '12

### Re: A New Poll by CNN

We need to put this in a system ala row reduced echelon form. But that was 20 years ago for me. I can no longer calculate a determinate in a matrix.

### Re: A New Poll by CNN

David, thanks for the quantitative analysis.  I guess I need to add fact-checking public opinion polls to my personal list of voter responsibilities

Joined
Sep '11

### Re: A New Poll by CNN

 George Savage: David, thanks for the quantitative analysis.  I guess I need to add fact-checking public opinion polls to my personal list of voter responsibilities · 1 hour ago

The fact that you are correct, Mr. Savage, is a sad commentary on the integrity of the information we get on a daily basis.

Joined
Sep '12

### Re: A New Poll by CNN

David,  According to Mike Flynn at Breitbart , http://www.breitbart.com/Big-Government/2012/09/10/Did-CNN-Rig-Its-Own-Poll , the sample only included 5% independents. Also, ho points out another anomaly:

There is another, more serious concern, however, The second question of the poll asks Obama and Romney voters whether their vote is "for" their candidate or "against" the other candidate. The sample size for this question is reported to be (top of page 3):

BASED ON 351 LIKELY VOTERS WHO PLAN TO VOTE FOR OBAMA -- SAMPLING ERROR: +/- 5 PERCENTAGE PT

And,

BASED ON 340 LIKELY VOTERS WHO PLAN TO VOTE FOR ROMNEY -- SAMPLING ERROR: +/- 5.5 PERCENTAGE PTS

Those numbers didn't look right to me, considering the headline number reported in the poll. There were 709 Likely Voters in the sample. The 351 votes for Obama is 49.5%. The 340 votes for Romney is 47.9%. In other words, a 50-48 match-up. That's a lot different than the 52-46 reported in the headlines. " . Something is fishy about their numbers.

Joined
Sep '12

### Re: A New Poll by CNN

Drudge is also reporting other polls that are very tight. The bounce is gone, I think.

Stanford University

### Re: A New Poll by CNN

 Carol: David,  According to Mike Flynn at Breitbart , http://www.breitbart.com/Big-Government/2012/09/10/Did-CNN-Rig-Its-Own-Poll , the sample only included 5% independents. Also, ho points out another anomaly:

The first point, about 5% independents, is consistent with the calculation above of 4.2% independents among registered voters.  Whether it is 4% or 5%, it is a ridiculous sample with this as the percentage of independents.

But the second catch from Flynn is really a killer.   If there are 875 registered voters and they broke 53% for Obama and 45% for Romney, that gives 463 or so Obama voters and 393 Romneys, not the 441/409 numbers reported on page 3.

And 709 breaking 52% for O and 46% for R would be 368 for O and 326 for R, not (as Flynn points out) the 351 and 340 numbers reported on page 3.

So added to the charge of stacking the sample, to get the results they wanted, we can add a charge of doing some very strange arithmetic, once they got their stacked sample.

Maybe someone should ask them to try again?

Joined
Nov '10

### Re: A New Poll by CNN

Thank you for the very interesting quantitative analysis.

But Obama's reelection hinges on  just a few minor percent changes, up or down, in the rate of unemployment. Does anyone doubt that if unemployment were at 7% Romney would stand a chance? This is demonstrative of  the fundamental absurdity of our situation. Take a step back and look at it. It's absurd.

What I said re. the change in the very soul of the body politic...

Stanford University

### Re: A New Poll by CNN

I can't resist, so let me add one more:   Back on page 21, they give
"sampling error" figures for each column.  In particular, for the column of folks who identified as Democrat, the sampling error is plus/minus 6, while for Independents and Repubs, it is plus/minus 6.5.

If they have a sample of 700 or so, with something on the order of 5% independents and more than 40% Republicans, and if the Repub sample has over 95% going one way while the independents is a lot closer to 50-50, there is no way that "sampling errors" for the two are the same.   My back of the envelope calculation suggests that the standard error of the percentage estimate for the I's should be around eight times that for the R's.   My back-of-the-envelope may be wrong (it's been a while since I did any statistics).   But they can't be equal or anywhere close.

So (1) ridiculous sample, (2) crazy arithmetic, and now (3) wacky statistics.

But it is CNN.

Joined
Feb '12

### Re: A New Poll by CNN

So, let me see if I have a grip on this...we still don't know...does that about cover it?

Joined
Jun '12

### Re: A New Poll by CNN

 Natalie: So, let me see if I have a grip on this...we still don't know...does that about cover it? · 4 hours ago

And CNN is still biased.

Joined
Aug '10

### Re: A New Poll by CNN

I agree that this poll is way off. The only comment I'd like to make is that we can't make much of the supposed double digit lead by Romnry with independents. With the numbestood indie responses so low (37), we just can't know with any certainty where they stand. We'd have to find another poll.  Big fail, CNN!

Joined
Nov '10

### Re: A New Poll by CNN

ConservativeWanderer

 Natalie: So, let me see if I have a grip on this...we still don't know...does that about cover it? · 4 hours ago

And CNN is still biased. · 2 hours ago

Biased to the point where they apparently make gross arithmetic errors in favor of the result they want to find.

Joined
Jul '12

### Re: A New Poll by CNN

Dr. Kreps. I knew your name was familiar. I was exposed to your research on game theory in grad school. You meet the most interesting people here. :)

Joined
Jun '12

### Re: A New Poll by CNN

The sample population of registered D and R (for registered voters) can be computed directly (as Dr K does in thread post #4 above).  You don't need to go through the estimation procedure he describes in the OP.  Futhermore, there's a world of difference between "self identifying" as an I, being registered D/R/no affiliation and responding to a poll as an I and planning to vote for Romney.  Until Dr K can square the circle on all those variables and explain exactly how he solved for I, I'm skepitcal of his skepticism.

And regarding the p values (post #14 above), those can be computed directly as well using:

For the table referenced in 14 above, for I (the std error Dr K questions):  p = .4, 1-p = 1-.4=.6, n= 710.  Plug that into your calculator and you get about 1.7 basis points.  D and R work out to .64 and .52 points respectively.  CNN *over* stated its margin of error.  In other words, they were too conservative.

I'm all for taking interim polls worth a grain of salt but nothing here convinces me CNN deliberately cooked the books on this poll.

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