A Reality Check on Chris Bowers' "Reality Check" about Obama's Approval Among Liberals

Chris Bowers, over at Open Left, is getting a bit uncomfortable with the upcoming Public Policy Polling numbers showing Obama's approval rating at an astounding and steady 85% among liberals.  It doesn't come as a surprise to anyone except professional agitators like Bowers whose mantra - that liberals are abandoning Obama - goes ca-put with that poll.  A Gallup poll shows the president's approval among liberals at a lower 76%, according to Ezra Klein.

So he rained on the parade:

However, there is a serious flaw in citing these numbers: they are only based on a subsample of between 125-130, which gives them a margin of error of plus or minus 8.9%. That is, they are only based on a subsample of 125-130 registered voters if PPP's new national survey is anything like their national survey from last month, when 19% of their overall sample of 667 voters self-identified as liberal.

By way of comparison, across the last four Gallup weekly approval polls, which have a combined sample of 14,346 respondents, President Obama's job performance among self-identified liberals has only averaged 74%. With Gallup identifying 20% of the electorate as liberal so far in 2010, that would mean a liberal subsample of 2,869, that would mean a margin of error of only 1.8%. That makes the Gallup numbers far, far more reliable than the PPP numbers.
Sounds smart, doesn't it?  It is, if you don't know much about statistics. But he does not show his math, he just asserts the margins of error.  I am willing to bet he used some online calculator to crunch these numbers, like this one, putting in the sample sizes.  But unfortunately for Bowers, it doesn't always work that way.  For sample sizes over 40 with a significant population, the sample size matters less and less in a survey to determine the MOE.  Bowers' numbers also don't make any sense, since a subsample's margin of error cannot be smaller than the larger sample's (for Gallup it's +/- 3.0 percentage points).

In addition, Bowers quite amateurishly compares apples to oranges - he takes an aggregated sample (adds samples from many surveys together) and compares that to one survey from PPP.  You can't compare cumulative numbers to one standing survey.

Survey to survey, the sample size for Gallup is 1500, to PPP's 667 (for the whole population, and they roughly find the same percentage of liberals). But that's not even the whole story. Gallup surveys "national adults", whereas PPP surveys registered voters.  According to the US Census, only 65% of the US adult population is registered to vote.  So the Gallup sample of registered voters, assuming these percentages hold, is about 975.  Not that big a difference.

So I suppose Chris Bowers had a nice try.  But that's all it was: nice try.