Why can’t the Washington Post report on the Washington Post’s poll ?

The Washington Post had two articles on their latest poll. The first focused on the Presidential horse race. The second noted that US adults disapprove of congress and then went on to discuss other results. At the very end of the the second article this follows:

Obama’s proposal to raise taxes on millionaires to help close the deficit enjoys wide public support — three-quarters of adults, including majorities of independents, moderates, conservatives and Republicans, back it.

Among the few groups that don’t favor such tax increases are Republicans who strongly support the tea party movement; they oppose the proposal by more than two to one.

This isn’t news to anyone who pays attention to polls anymore, but it is more newsworthy than the observation that most US adults have noticed that Congress is not functioning. Importantly, opinion leaders don’t pay any attention to polls even when discussing public opinion.

It is widely argued that Obama has decided to fire up the base with populist proposals which will increase turnout of Democrats and liberals but reduce his support among moderates and independents. In fact, his populist proposal is supported by a majority of self identified Republicans and conservatives. Obama is moving towards the center of public opinion. He is also firing up the base*.

Also and less importantly:

Paul Kane’s and Scott Clement’s understanding of statistics is essentially as low as possible.

They wrote

Only 3 percent of Americans said they “strongly approve” of the performance of lawmakers on Capitol Hill — essentially as low as possible, given the poll’s margin of error of four percentage points.

That is they said that mathematical statistics proves that we can’t agree on anything. They definitely asserted that it is “essentially” impossible for 100% to agree on somethnig.

The problem is that pollsters have reported nonsense standard errors for so long that journalists have been convinced of something absurd.

In fact, the variance of the mean of a sample from a binomial distribution depends on the true probability — in this case the fraction of the population which strongly approve of the performance of Congress. To be modest, pollsters always present the highest possible standard error corresponding to an evenly divided population. To be honest, I think they report the largest plausible standard errors due to sampling alone to hide the fact that poll responses deviate from actual voting for reasons other than sampling error.

In any case the standard error corresponding to 3% is 100% times the square root of (0.03*0.97/(smple size) or roughly 0.55%. The convention is to report a number plus or minus 2 standard errors so 3% plus or minus 1.1%. This would be a 95% interval if the distribution were normal. Using the normal approximation, one can reject the null that the true fraction of strong approvers of Congress is zero at the 95% level.

Of course if one has any sense at all, one rejects that nul at the 100% level not the 5% level, since some people said they strongly approve of Congress. The normal approximation works very well even for fairly small samples so long as the true probability is close to 0.5. Obviously it doesn’t work whenever it gives an x% level which includes the hypothesis that no one in the population would say something which someone in the sample said.

But that is an advanced topic.

Next topic English. An obviously false statement is not made true by adding the qualifier “essentially.” The fact is that some US adults strongly approve of our Congress. This is appalling, but they really exist. The word “essentially” was used to assert that this mere fact is negligible. This contempt for mere facticity reminds me of Hegel (them’s fighting words where I come from).

Hegel did have a point. A historical movement can turn into its opposite. So the theory of statistics has become a way for some people to dismiss inconvenient data as “essentially” non-existent.

* More on taxes (my usual rant)

*I have long complained that the MSM failed to report the strong majority support for a more progressive tax code (revealed by dozens of polls on the question dating back to the early 90s). They are now reporting it — at the very end of articles. I think that under reporting of the strength of left populism is a systematic error partly caused by the self interest of opinion leaders.

Even now, many people (including the usually reasonable Charlie Cook) consider a proposal with majority support among conservatives the result of a decision to give up on winning the support of moderates. This is crazy.

I think part of what is going on is that people naturally approximate the infinite dimensions of opinion with one dimension left vs right. If you average over issues and people, the average US adult is to the right of Obama (he believes in evolution and global warming and is skeptical about the death penalty. It bothers him when he violates due process right. Etc). Even two dimensions are enough to find one where Obama is to the right of the average American. The average American is eager to soak the rich. Obama prefers soaking the rich to the alternative, but he’d really rather reform health care and regulate greenhouse gas emissions.

Another part of what is going on is that political reporters lose touch with the USA outside the beltway. In official Washington raising taxes on the rich above Clinton era levels was (until yesterday) an extreme left wing position. In the general population it is a centrist position. On this issue, the median voter is far to the left of the median congressman,the median political operative, and the median pundit.

Finally there is the “opinions on optimal re-election strategy differ — both sides have a point” problem. There are people who call themselves Democratic strategists who argue that running on a soak the rich platform is bad strategy (Penn-Schoen no not the PR firm the … yes the PR firm and the P stands for politicians). This approach would clearly cause increased turnout of liberals and Democrats. If one assumes they must have a point, one must assume that it will cause moderates and independents to vote Republican or make Republcians more likely to vote. Therefore one must conclude that moderates and independents will vote against a proposal supported by a majority of moderates and independents or that Republicans and conservatives will be outraged by a proposal supported by a majority of Republicans and conservatives. This is crazy. But there is the methodological a priori that both sides must have a point, so it must be true.