MORNING LINE: POLLS NOT AS BAD AS THEY SEEM
UPDATED
[With the help of new information from Survey USA and other sources we have updated this story. The main change is the effect of two additional GOP polls on Nevada that were badly off and which we had not counted. If included, this changes the overall error average from 5 - as we originally reported - to 9. Similarly, if you remove these three bad Nevada polls, the Progressive Review's rolling average goes from 9 to a highly respectable 5. We have also included several one shot polls that we had missed]
ALTHOUGH we can't recall seeing so many double digit errors in polling since we began tracking the trade in 2000, the pollsters are not doing as badly as it may seem. Our study of 31 pollsters – including the Review's rolling average - finds an overall average error of 5 points so far this year, about a point above the standard margin of error - provided you don't count 3 badly wrong polls on the Nevada GOP results. If these are included, however, the average error is 9. By comparison, state projections for the aforementioned surveys were in the 3-4 error range in 2000.
Fifty of the 91 polls came within a 4 point margin of error, but there were 27 polls with double-digit errors
Thirteen of these errors occurred in New Hampshire, with 9 in the Democratic contest. Five occurred in the Michigan GOP race and three in the Nevada GOP caucus.
So far, the best pollsters to take on a large number of races are Zogby and Strategic Vision with an average error of 6. Mason-Dixon had an average error of 7 and Rasmussen has an average error of 8.
If you remove the three Nevada GOP polls with their big errors, Research 2000 comes out on top with an average of 3, and the American Research Group comes in at 8 points.
Other pollsters that only surveyed one or two races did well:
One point error: McClatchy, Selzer, Des Moines Register, MIT and Survey USA.
Two point error: Concord Monitor
Three point error: ABC, Mitchell
Four point error: Fox, Insider Advantage
Five point error: Franklin Pierce, Public Policy Polling
The overall worst results were in New Hampshire Democratic race with an average error of 9 and Nevada GOP with an average error of 34. The best results were in the Nevada Democratic caucus with an average error of 2.
It is interesting to note that the poll errors are dramatically less for second and third place. In the first three primaries these averaged 2-3 percent.
Clearly the polls are being affected by factors hard to catch in a survey such as unexpected surges in turnout, late changes of mind, and tardy decisiveness among the undecided.
One gets the sense from all of this of a uncertain, uncomfortable and unhappy electorate, reflected in feelings not just about the course of the nation but about the choices they have been given. The days of deep loyalty to a party, cause or candidate would seem to be waning.
11 Comments:
It would be good if the Review could give its readers a "quick and dirty" but somehow accurate, definition of what technical terms like "rolling average" mean. This could be done with a glossary - a glossary easily accessible from the Review's main page -- or with a simple parenthetical aside. Some readers who don't even have much training in statistics can guess the meaning - as a woman named Pam did on the first page I found upon googling "rolling average." But some won't. Thanks anyway for a stimulating essay.
It has nothing to do with degrees in statistics.
Issues about nomenclature, in this instance, most likely reflect an unfamiliarity with the Review, and Sam, in general.
With time and a little patience the idiosyncratic definitions become clear enough.
Isn't that the case with any more or less established group of individuals sharing a common pursuit?
Would you demand a written glossary from musicians involved in a forum discussing Great 7th chords and symmetric scales, for example?
Seems to me that in such instances the burden resides elsewhere.
Fortunate enough to be exposed to some amazing individuals in my life, it early on became clear that to glean the most from such situations, one's best course of action was to listen & watch, rather than have answers handed out.
That gleaned through the extrapolative process is just so much richer.
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To Anonymous at 12:03a.m. - It appears that you would support wholeheartedly the educational precept of John Amos Comenius (1592 to 1670) who is supposed to have been the first educator in the West to state clearly the (dubious, so far as I am concerned )precept, "The more the teacher teaches, the less the student learns."
But I believe that said pedagogical guideline is the reason I never completely grasped the essential mathematical concept of "limit" during my high school years. (Sad fate! From there on in, a comprehensive understanding of the calculus was rendered impossible for the undersigned!)
But never mind: from context and by dint of my Google search, I was able to get the meaning (I think) of a "rolling average."
Of course, the Review is providing an essential service by being the only place I know of on the web to do such a readily accessible compilation of polls during such an critical election year.
Comenius had a good point. The best teachers are those who lead a student into making the discovery themselves. That results in deeper understanding and a greater probability of remembering.
Your high school math teacher apparently wasn't very good at this process, but that doesn't mean it doesn't work.
To Anonymous at 1:35 pm - Thanks for the reply. I'm taking the chance of making a drawn-out dispute over what might be a trivial issue- but the theory that learning must be "drawn out of" a student - which, upon further reflection, I realize also has the support of the Platonic Socrates, Rousseau, William James and, in the 20th century, John Dewey, is in large part responsible for the inadequate educational levels in our country today.
For the most part, the teacher I mentioned was very good at exemplifying math concepts, but not those of physics. (He doubled as both a math and basic physics instructor at the high school I attended.) And the best teacher I had in the sciences -- a chemistry teacher - did not abide by Commenius' precept. He was merely a very enthusiastic and very verbally skillful instructor.
The notion that pupils can somehow learn "on their own" (without being taught to do so explicitly by means of teaching methods which themselves do not involve self-instruction) is based upon a fiction of human "initiating self-causation" which is a founding myth of the West. It is a powerful myth, which will, if we do not in our Western cultures, find our way past it toward a more accurate account of basic human nature, destroy our way of life in the long run.
Certainly, it is good to equip every student with the very powerful ability of learning without having to be formally taught. But (1) while one day a genius may devise a pedigogical technique of doing so (even though every teacher knows that there are such students who crop up now and again), it doesn't follow that said students, when they have learned to learned without formal instruction, have acquired that ability "on their own" . And (2) frequently, the skilled teacher only furnishes the student with an illusion that they have "done it themselves."
Such a theory of education, of course, by leaving the student to learn "by themselves" (in truth, nothing ever really happens in the real, physical universe "by itself" - on this see my second paragraph in this post on our Western myth of "initiating self causation," as applied to us humans) enables the teacher to instruct with the burden of success or failure falling onto the student, not the teacher or that teacher's educational system.
The pedagogical methods you mention have been in use in America's public schools for the last 50 years at least. In my part of the world, children who come from culturally impoverished homes (in comparison to their mostly white classmates) are blamed as not being bright enough because they do not learn efficiently "on their own." More and more, in the process of exculpating itself from the accusation of inadequate performance, the teaching profession is finding fault with students in a way which suggests a racial deficit - not a pedagogical one on the part of the teaching profession or the public schools.
The problem we have in America is not that our students aren't bright enought to learn as Comenius - a 16th century "expert" - would have them learn and it is not that we have too many inept teachers. The fundmental problem is that our schools are not teaching- in large part because our backward educational establishments have the "intellectual authority" of Comenius, of Rousseau, or William James, or John Dewey - for their failure to teach.
What is more important to a genuinely democratic polity ("political culture") than a very high level of education among a citizenry? (The connection between effective education and democracy used to be a commonplace well into the 20th century - but not today.) Consider how well the model polities of Sweden or Finland (for example) would work if their citizenry were as well-educated as ours in the U.S. has become in just the last 30 years. Yet it is liberal educators, not conservatives, who are the stauchest defenders of our present ineffiicient system, which relies on outdated, pre-scientific theorizing along Comenius's lines, on how to educate people.
Correction to my post above - Because of multiple distractions while writing that lengthy post, I got it bass-ackwards in regard to my high school physics-math instructor.
I wrote, incorrectly and confusingly: "For the most part, the teacher I mentioned was very good at exemplifying math concepts, but not those of physics,"
when I should have written the exact reverse: "For the most part, the teacher I mentioned was very good at exemplifying physics concepts, but not those of math." (The course I spoke of where I did not learn - or, by my own interpretation, "was not efficiently instructed in"- the concept of "limit" was pre-calculus course.
I can't agree that the severe shortcomings of the US education system are the fault of the Socratic method. Our schools suffer from operational, legal, and economic problems, and an absurd obsession with poorly designed tests, that are the primary causes of the general stupidity of our population. Dead philosophers have nothing to do with it. (I speak as one with experience in the trenches as a high school teacher.)
If there are teachers claiming to use these methods who then blame a lack of learning on their students, then they don't deserve the title of teacher. Whatever the methods, the teacher is still responsible for the result.
Clearly your personal experience as a student tells you something different, but my experience as a teacher and as a theater director have shown me that, although you can sometimes get good short-term results by spoon-feeding some rote material to people, the only way to get them to remember things, apply reasoning to them, and thoroughly incorporate them into their world view is to lead them (a very active process in which you constantly adjust the questions you ask based on the kind of answers you get) to discovering the relationships between facts themselves. I don't claim it's easy and I agree with you that it's a method that can't be taught in some by-the-numbers way, but I still know, from having tried both approaches, that this one has better results in the long run.
To Anonymous at 3:29 pm Jan 21:
I shall have to defer to your worldly-wiser experience as a teacher and a theater director.
However, I stand pat on my contention (do you think I'd be producing all this extra verbiage if in order to show how much I agree with you, Anonymous!?) that those many individuals processed through our schools could be more effectively educated with more lucid textual and (by teachers) verbal explanations of the materials to be taught, and even with more carefully programmed introduction of those materials. I don't think that we have reached the ultimate in quality in our learning and teaching in America's schools - the entire process of teaching and learning could be made more efficient and rewarding to both teachers and students - that is to say, it could be improved, even though the year is 2008.
Just to annoy myself further (- and Gol-dang It [ :-) ] if I'm gonna get annoyed over something so trivial, then I hope this annoys you too! [but not by too much]), I looked up "limit" in the current Encyclopedia Britannica (2005 edition, which I have on DVD ROM) and found this:
Limit
mathematical concept based on the idea of closeness, used primarily to assign values to certain functions at points where no values are defined, in such a way as to be consistent with nearby values. For example, the function (x2 ["x squared"] - 1)/(x - 1) is not defined when x is 1, because division by zero is not a valid mathematical operation. For any other value of x, the numerator can be factored and divided by the (x - 1), giving x + 1. This is equivalent to the quotient for all values of x except 1, in which it is equal to 2, in contrast to the quotient that has no value. This value of 2 is then assigned to the function (x2 ["x squared'] - 1)/(x - 1) not as its value when x equals 1, but as its limit when x approaches 1.
(The Britannica exposition of "limit; mathematics" continues:)
One way of defining the limit of a function f (x) at a point x0 ["subscript 0"), written as
(An equation is then given in the Britannica text, as part of the explanation. which would not paste here)
is by the following: if there is a continuous (unbroken) function g(x) such that g(x) = f (x) in some interval around x0 ["subscript 0"], except possibly at x0 ["subscript 0") itself, then
(Another equation is then given as part of the continuing Britannica explanation, which extends for another paragraph.)
_____________
Aside from the fact that the entry as I've given it is as clear as mud to someone not educated in mathematics up to the level of pre-calculus math (and the rest of this short Britannica textual definition of "limit" isn't much clearer), kindly note how the expression "continuous (unbroken)" as given in the Britannica sentence which begins "One way of defining the limit of a function...." is not itself defined, even though, it must be admitted, the definition of "continuous (unbroken)" might , after several re-readings, be inferred from one or more of the propositions in the first paragraph of this Britannica explanation of what the concept of "limit" means in mathematics.
To me that failure to clarify with a few carefully chosen words is a defect in the exposition of this topic - that expression ("continuous" [unbroken]) should not have to be the occasion for a conceptual "easter egg hunt" in which a partly-mathematically educated reader works his or her bacward - a needless distrating digression, in my experience - through the text in order for said intelligent reader to grasp the concept of "limit."
My simple point about teaching methods --or about technical or near-technical discussions or references to - "rolling averages" - is that it adds nothing to the learning experience of a Britannica reader/student for that reader/student to have to "winkle out" the meaning of "continuous(unbroken)" by devling backward even such a short text as this one I've given as an example.
To put a fine point on it: it adds nothing to the learning experience, in this Britannica example, for "continuous[unbroken]" not to be clearly defined in relation to what has been said already (even if so doing might mean some repetition of the content of "what has already been said" about "limit" in the first paragraph). And another point I would make is that it is disorientating for most students, coming upon such an encyclopedia entry, not to have the mathematical concept of "limit" clearly placed within its appropriate various branch of mathematics, (e.g. - "analytic geometry") and into its ordered relation to other mathematical concepts and operations.
Hey, director guy, bear in mind that if somebody doesn't have hardware capable of running the calculus program, the method they use to download it is irrelevant.
Woa...! This conversation begins with a query about "technical terms like 'rolling average'" and it mushrooms into a discussion of Comenius, the US educational system, and the definition of continuity! To return to Louis's starting comment, I have often encountered this on blogsites: there will be a term or an acronym I'm not familiar with; if I query it, someone will post a reply like, "XYZ is so constantly mentioned by posters on this site that giving its full name (or definition) in each thread would be too tedious." What many don't seem to realize is that not all comers will be regular readers of a site; some will be shopping around looking for different viewpoints, or just googling for a specific answer. (The surfing metaphor should be self-explanatory.) For those readers-by-chance who get attracted by a particular thread or linked page, the lack of definitions or full names can be very annoying and may spoil the site's chance of acquiring a new regular. So in the case of "rolling average" a little pop-up definition would be nice. But nothing is perfect; as it is, I don't know how Sam gets everything done.
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