Subject line of the year

It makes you feel better about all those stats classes -- but are you sure it needs the comma?

(Just another promotional email from a publisher, and apologies to Dr. Manly.)

Polling sins: No, no and don't

Sigh.  In order, more or less: 

1) Polls don't have "error rates." That figure isn't a rate, and it doesn't count errors. (Your fielding average actually does produce an error rate, if you subtract it from 1 and move the decimal point around.) 
2) You can describe the figure as "percentage points" if you want, but "4.9%" is simply wrong. Take some finding in any poll that reaches 50% -- "do you approve or disapprove of the job Rudolph is doing as lead reindeer?" -- and add 4.9% to it, and you'll get 52.5%. Should Rudolph poll at 10% approval, adding 4.9% would give you 10.5%. The "margin of error," on the other hand, applies equally to any point in the distribution. That's what the next sentence means, but ...
3) Adding and subtracting percentage points is not "statistically adjusting" a finding. It's "addition and subtraction." Third-graders can do it. It really is that simple.
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You've got to ask yourself one question

Two questions, actually. The first is "compared to what?" Am I 45% more likely to be murdered in de Blasio's Manhattan than in de Blasio's Brooklyn, or than in Bloomberg's Manhattan, or Duggan's Detroit, or La Guardia's Manhattan, or in the casbah by Colonel al-Mustard with a candlestick?

Murders are way up so far this year in Manhattan, The Post has learned.

Sixteen people were killed around the borough between the first of the year and Sunday. Over the same period last year, the figure was 11. That’s an increase of about 45 percent.

So given that we're comparing de Blasio's second year with his first, you're more likely to be murdered in de Blasio's Manhattan than in ... de Blasio's Manhattan. Your next question should be something like"No, not 'which borough.' Compared to what risk?" That takes a little more work.
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Negligent journalism

We do have sort of an obligation to report what candidates and their little friends say and do when they're out there urging you to make your comparative decisions in their favor. We don't have an obligation to help them lie:

Bush* said the dysfunction in Washington, D.C., with President Barack Obama and Sen. Majority leader Harry Reid has led to a recession where economic growth is only about 2%. He said under Republican leadership, the U.S. can grow at 3.5% to 4%.

"The dysfunction in Washington, D.C., with President Barack Obama and Senate Majority Leader** Harry Reid" is sort of random reporter-speak, but probably not too inaccurate a reflection of the speaker's opinion. Fine. "He said under Republican leadership, the U.S. can grow at 3.5% to 4%" -- well, even the AP would want a complementizing "that," and as opinions go, it's on the flying-unicorns side, but if that's his pitch, we need to let him make it.

The problem is in the middle: "A recession where economic growth is only about 2%." News flash for Jeb, and for the folks who wrote it and who waved it along into print: That's not a recession. The cheapest first-year-econ definition of a recession would be two straight quarters of GDP shrinkage. You don't have to like the way the economy is going, but if you say it's doing something it's not, you're in the same category as the poll unskewers and the goober at the New York Post who's going to come out any month now with definitive proof that the usurper's minions rigged the BLS employment data in fall 2012. That's not a good place for the press -- the honest press, at least -- to be.

* Jeb, if you're scoring along at home
** How do you hide a five-dollar bill from a reporter? Put it in the stylebook. "Sen." is short for Senator, not Senate, and "majority leader" should be capitalized before the name. Sheez.

The endless capacity for self-delusion

You'd think we would have learned in the 2012 election -- or, you know, maybe back when Iraq invaded Kuwait -- that the one thing the courtier press can't afford to do is give bad information to the party. When that happens, we get a condition called "bounded rationality": leaders make decisions that appear perfectly rational, as long as nobody minds that the information they're based on is clueless. And in that light, Bill Kristol is hard to distinguish from the advisers who told Saddam Hussein that invading Kuwait would be a nearly consequence-free way of settling his lingering interstate disputes over slant-drilling and those pesky loans from the earlier war:

The new Quinnipiac poll of the New Jersey Senate contest shows Jeff Bell only 11 points down to Cory Booker, 51 to 40 percent, among likely voters. It goes without saying that a race can move a dozen points in the final five weeks of a campaign—especially when a little known challenger (but one who's well-regarded by those who do know of him) is taking on a pro-Obama incumbent who's barely above 50 percent in an anti-Obama, anti-incumbent year.

... But take a further look at the poll results. Booker leads Bell, 51-40. Seventy-six percent of Booker supporters and 84 percent of Bell supporters say their mind is made up. Do the math. Among those whose mind is made up, Booker leads Bell 39 to 34 percent.

So Booker's hard lead over Bell is a mere 5 points.

"Hard lead" is kind of a novel statistical concept, so maybe it's rude to point out that with a +/- 3-point maximum margin of sampling error* (at 95% confidence for the full sample of 1,058), this one's also pretty close to the traditional standard of statistical significance. But by all means continue:

He'll outspend Bell over the next month. But money can't buy you love. Sometimes, it can't even buy you votes. If New Jersey flips in November, we'll remember this Quinnipiac poll as Jeff Bell's fire bell in the night.

Or not. Two more recent polls (CBS/NYT, in the field Sept. 20-Oct. 1 with 2,011 likely voters, and Monmouth, in the field Oct. 2-5 with 477 likely voters) give Booker even larger leads. Without Quinnipiac's "is your mind made up, or do you think you might change your mind before the election?" question, we can't calculate "hard support" in those polls, but let's follow Kristol's suggestion and take a "deeper look" at the Quinnipiac results anyway. Since we're all making up our own stats, we can test the Uppity Black Guy Factor: How is support for one smooth-talking black dude related to opposition to another smooth-talking black dude?

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Today in framing

If a 3 percent change in quarterly GDP is a big deal at the Fair 'n' Balanced Network, just imagine what 4 percent might look like:

U.S. economic growth accelerated more than expected in the second quarter and the decline in output in the prior period was less steep than previously reported, bolstering views for a stronger performance in the last six months of the year.

Gross domestic product expanded at a 4.0 percent annual rate as activity picked up broadly after shrinking at a revised 2.1 percent pace in the first quarter, the Commerce Department said on Wednesday.

So given the play to the first-quarter revisions released last month, we should expect something like ... oh. (Right, that's the 12th bullet down there amid the "Latest News.")

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Actually, yes

You can see why this is a big deal for the cousins over at the Daily Caller:

After a year of seeing President Obama’s approval ratings plummet, the president’s pollster is offering a strikingly candid and pessimistic New Year’s resolution.

Reporters should go the next “year without reporting any public polling data,” Joel Benenson, president and CEO of Benenson Strategy Group, said.

Well, sort of. He was responding to a request for resolutions from Politico's Playboook, and that's a fragment of his suggestion "for Playbookers." So although it's not in any meaningful sense a resolution "for reporters," more than a few reporters might want to consider paying attention to it -- for example, Alex Pappas, or any other political authority who uses "Real Clear Politics" and "average" in the same sentence. In short, if you don't understand how surveys are done, or how public opinion works, it might be a really good idea to take a year off and -- you know, shut up.

On making stuff up

Return with us now to those thrilling days of yesteryear -- specifically, the late innings of the 2012 presidential campaign, when somehow it became all the rage in (ahem) some circles to declare that any quantitative data you found unpleasant had been baked. The polls were crooked, and long-established gubmint surveys were being fabricated at the order of the Kenyan usurper and his cabal of Chicago street thugs.

Let's look in on a slightly less spittle-flecked version of those claims: even if the numbers are valid, the craven librul media will spin them on command from Kenya Chicago the White House. We had some questions at the time about the assertions of directional bias made by Kevin Hassett, director of economic-policy* studies for the American Enterprise Institute (and, by some wild coincidence, a Romney adviser). Here, he's discussing the two main Bureau of Labor Statistics surveys on employment, reported the first Friday of each month: the "household" survey, which produces the percentage called the unemployment rate, and the "establishment" survey, which tracks nonfarm payroll employment (expressed as jobs added or lost):
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When I use a survey, said Humpty Dumpty ...

Hey, kids! Of the two Bureau of Labor Statistics surveys reported the first Friday of each month in the eagerly awaited* report on jobs and joblessness, which one should the right-thinking young person take more seriously? Is it ...

The Household Survey reaches deeper into the recesses of the economy than does the Establishment Survey. It also does not involve conjuring jobs out of thin air, a la the Establishment Survey's "birth/death model."

Well, that seems pretty clear. It's the household survey, which produces the unemployment rate, not the establishment survey, which produces the number of jobs added or lost. But what did it look like last October? Oh NOES!!!!!

The professional economists and the press usually emphasize the establishment survey because it is viewed as less volatile. ... Back when President Bush presided over a jobless recovery, the household survey tended to show better news. At the time, every media organization carefully emphasized the establishment numbers, and warned that the household numbers are suspect. That, of course, is what happens when a Republican is in office. For President Obama, you can expect a household survey lovefest.

So, to sum things up, if the household survey makes the Kenyan Muslim commie look worser, it's better, but if it makes him look gooder, it's badder. Got it? This could be on the final.

* Not quite an "important psychological barrier," but close.

One born every minute

Further evidence that cluelessness afflicts the newsroom as well as the public at large:

Lottery players at Tuzzo's Circle News in Hollywood think today's their day. So do those at a Pembroke Pines Publix and others at Government Discount in Miami.

At least, the numbers are on their side. Those South Florida retailers rank high among venues that have sold tickets awarding $600 or more, according to a Sun Sentinel analysis of Florida Lottery winnings since 1993.

(Visit SunSentinel.com/lotterydata to see where lottery tickets with payouts of $600 or more have been sold since 1993.)

Sigh. Yes, it's generally true that many lottery players, wherever they are, "think today's their day." Whether players at these three venues are more likely to hold that view than others isn't the sort of question you can answer with a feature story. Whether "the numbers are on their side" is a bit simpler: No. They aren't.

It's a free country, and Congress shall make no law abridging, &c &c &c, so you're perfectly entitled to do whatever you want with your "analysis" time and your frontpage space. In some cosmic sense, sharing popular delusions about the lottery isn't any worse than publishing the horoscopes. But if you'd like to be taken seriously when you proclaim "study says" or "poll reveals," you need to run a disclaimer with your "want to hit the lottery" tales:

On the other hand, you might as well go ahead and play your mom's birthday. It has the same predictive value as this analysis: None.

There's a reason it's called the stupidity tax, you know.

Real numbers and made-up differences

Here's the offending lede from which the Freep's deck is taken (the main hed, stripped across the biz front,* is "U.S. job growth slumps in April"):

U.S. job growth slumped in April for a second straight month. It suggested an economy that is growing steadily but still sluggishly, which could tighten the presidential race.**
 
The AP is either stating a testable proposition about measurable stuff or it's just tossing words around at random because it thinks it needs to say something about the relationship between the business cycle and campaign politics. We can't rule out the latter, but let's be charitable and assume the former. That would mean, among other things, that there's a current state of tightness in the presidential race that could become tighter -- in a way attributable to real movement in the population, rather than chance -- owing to the rate at which the economy is growing. Is there?

One way to find out is to look a roundup of surveys about the presidential race. Let's use the index at Real Clear Politics (not the "RCP average," which can neither tighten nor loosen because it's a meaningless number). Of the four most recent as of this writing, we find two tracking polls -- Rasmussen, with 1,500 likely voters for a standard error of .013,*** and Gallup, with 2,200 registered voters (SE .011) -- in which the candidates are separated by a point and two polls in which they're tied. For the race to get any tighter, the campaigns would basically have to start executing their own supporters whenever things start looking up, and that's not going to be good for contributions in the long term.

What the AP probably means is something like: Mediocre expansion that manifests itself in nonspectacular ways tends to be a drag on the incumbent. That's an accurate if not especially interesting observation; the AP may have declined to make it out of concern that it would be pilloried as a lapdog of the Maoists. But it's a different sort of claim than suggesting that the race -- I'm trying to avoid excessive scare quotes here, but the election is still six months away -- is going to "tighten." Should the Rasmussen tracking poll show Romney up by 2 points on Sunday, it doesn't mean he's going to take on ballast until the race is even again.

Lesson for editors? When a story makes a bogus claim, don't amplify it in the headline. Ask for evidence, and if the evidence isn't forthcoming, get rid of the claim.  

* Yes, the Web site uses a comma to coordinate the clauses. Yes Web editing is every bit as important as print editing. Yes, people really do think less of products that don't care.
** There may be a few die-hards at the AP flagellating themselves over the relative clause, on grounds that it doesn't modify anything tangible, but that's not a real grammar concern and it's not particularly a sensemaking concern.
*** Meaning the "margin of error" at 95% confidence is ...?

Why we (used to) have editors

Dear CNN:

No, it isn't. It's nowhere near that. I hardly know where to start with this one, but you have to start* somewhere, so -- no.

Even if the hed hadn't overstated our household April gasoline cost by a factor of five or more, that's not the "monthly" bill. The point of the story, to the extent that it has one, is that rising prices produced a certain national average for April. The monthly bill for 2011 would be lower, and the monthly bill for academic year 2010-2011 would be lower still. If you have some reason to think April was typical, you sort of ought to tell us. But that points to a different issue, so let's look at the prose itself:

NEW YORK (CNNMoney) -- Round-trip airfare from New York to Los Angeles. More than a dozen dinners for two at Applebee's. Two 16 GB iPod nanos.

These are just a few of the things you could have bought if you weren't spending $368.09 a month on gasoline.

See above: I'm not, and the amount I spent in April 2011 isn't an accurate reflection of my spending "a month" anyway. But there's a larger and stupider assumption in play. I'm happy to stipulate that it's possible to buy a ticket for a round-trip cross-country flight for $368, but I was buying gasoline in March too -- and in February and January and December. So it isn't as if I'm giving away two iPods a month that I wasn't giving away before. The April-to-April difference in dinners for two at Applebee's is less than four.
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Peeve alert

What follows is totally and complete- ly a peeve. I don't know if anyone shares it, it has no empirical or theoretical foundation, the world is unlikely (p>.05) to become a better place if everyone pays attention, and you're under no obligation to agree anyway.

That said: Will you people please stop saying "do you want to become a statistic?" That's exactly what you want to be. I get up every morning with the intent of being a statistic -- several of them, actually. I want to cover my couple dozen passenger-miles without being hit by a gravel hauler. I don't expect to be shot during a faculty meeting. I'd like to make dinner and not come down with a great honking case of food poisoning. (OK, we screwed that one up a few weeks ago, but that doesn't change the broader fact that you're just as much a "statistic" when you don't get sick as when you do.)

I can't make a serious case that "don't be a statistic" actually makes people dumber, but anything we can do to take the fright out of numbers ought to help at least a little bit. A statistic isn't a bad thing to be. What we ought to be doing is encouraging people to take steps that make them more likely to be in the right column when the "calculate" button is pushed.

End peeve. But while you're at it, if you have to overlay the hed on the art (and you don't), never put red and pink over red. That's just dumb.

'Individuals and statistics'

This seems like a partic- ularly Escher- esque bit of news judgment: People don't understand that a number doesn't necessarily mean anything just because it looks big, so it becomes a frontpage story* because editors don't understand that a number doesn't necessarily mean anything just because it looks big, so people see a frontpage story confirming their suspicions and refuse to believe that the next big number doesn't ... I am he and you are he and you are me and we are all together.

Anyway! These stories** showed up on front pages just in time -- coincidence, or what? -- for the first Bad Science column of the year by the stellar Ben Goldacre:

'Six hundred pregnancies despite contraceptive implant," said the BBC. "500 fall pregnant after having contraceptive implant," said the Express. "Contraceptive implant alert," said the Daily Mail: "Hundreds of women fall pregnant after birth control fails."
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Break out the clue bat

Is it polling season again already? All right, let's let Motown's Oldest Daily show us how to get almost everything wrong, on the off chance some of us want to get it right before the next round.

First question: Is the hed true? (this is the 2A hed; a truncated version of the story is also the 1A lede.) For several reasons, probably not. First, the survey measures intent, not cause. We have no way of knowing whether "conservative endorsements" made a difference because we didn't ask about it. That may make intuitive sense, since the poll followed the endorsements, and it may be what the pollster claims, but it's still a post hoc error, and asserting it as a fact is sloppy practice.

Question 1A, though: Is Cox (Mike Cox, the state AG) actually "on top"? That's less of a yes-or-no question than a "how likely" question, and the way you answer it sets a precedent that can affect your credibility. Cox is ahead by 2 points* in a sample of 400 Republican likely voters. Let's see what the paper thinks about that:

Cox's 2-percentage-point advantage over U.S. Rep. Pete Hoekstra of Holland was within the poll's margin of error but still statistically significant, especially since he overcame a 12-percentage-point lead Hoekstra had in late May.

Um, no. You can't be "within the margin of error" and "statistically significant" at the same time, any more than a basketball player can be 5-foot-6 and 6-foot-5 at the same time. (And a change in Candidate A's support from Time 1 to Time 2 has nothing to do with the significance of the A-B gap at time 2, but that's dogpiling.) So let's recap those terms briefly.

A randomly drawn sample gives you a picture of the population you're trying to generalize about. How good a picture depends on a lot of things, but for today's purposes, it's primarily the size of the sample. (That's why you should always use "margin of sampling error" on first reference; that's a statistical function, and it has nothing to do with error introduced by, say, faulty question design.**) If you draw a lot of these samples, they'll eventually form a normal distribution around the "population value," or the result you'd get if you asked all Republican likely voters in Michigan. The margin of error describes the width of that curve at its base. Nineteen times out of 20, a sample of 400 will fall within 4.9 points on either side of the population value. There's a 5 percent chance (the 20th case) that it won't.***

Where does statistical significance come in? A "significant" difference means that at a predetermined level of confidence (traditionally**** 95%), your sample difference represents a real difference in the population. In a case like ours, a 50-44 difference between A and B wouldn't be significant: draw the curves yourself and you'll see the overlap.

That doesn't mean there's no difference. If we turn down the confidence level to about two-thirds, the overlap goes away (draw the same curves with a base of 2.5 points on either side of the sample, rather than 4.9 points). A is probably leading B, but we're a lot less confident than we used to be. And when the gap gets down to 2 points, the best thing you can say is that there's an uncomfortably high likelihood that the difference came about by accident.

Not only is the difference in today's story nonsignificant, but we need to be careful about those changes from last month too. Given same-size samples, neither change (Cox's 8-point increase and Hoekstra's 6-point decline) would be significant. Both are more likely to be real than not, but you can't proclaim one set of rules and play by another.

Is it appropriate to compare the May and June samples? Well, sorta. This month's poll has 800 likely voters, 400 from each party, yielding a margin of sampling error of 4.9 points at 95% confidence for the two party subsamples. May's poll reports an N of 600, with a margin of 4 points, but it doesn't give subsample sizes. Not necessarily apples and oranges, but at the least two different varieties of apple.

Couple of lessons to take away. One, there's not a lot of news value in this poll. Phrase it as "holder of statewide office looks more like being about even with congressman in non-incumbent race for governor than a month ago" and you get a better picture. Two, the standards you set now are the ones you're likely to be held to later. Readers won't be able to tell statistical ineptitude from partisan bias, and if you're this careless about what gets a poll story to the top of the front, you can expect them to infer the worst whenever they disagree with a result.

* Hi, Fish!
** "If the election were held today, would you vote for A or do you hate America?"
*** If you want proof, go to seminary.
**** There's still no excuse for not reporting it.

My soul unexpectedly rose

Eds: Emergency adverb deletion notice follows text.

Strayhorn notes the predictable reappearance of Satan's Adverb in the AP's jobs lede of Thursday:

The number of people filing new claims for unemployment benefits unexpectedly rose last week by the largest amount in three months.

... and, recalling the old ban on "died unexpectedly" in obits,* wonders if it's time to impose a similar ban on AP ledes about economic statistics.

I'm inclined to agree, and not because I dislike adverbs (I don't) or because the one at issue is charmingly misplaced*** (are people filing unexpectedly, or is the rise unexpected?). I think the bigger problem is that journalists appear -- again -- to be genuflecting to some form of statistical inference they don't understand, and thus taking the collective eye off the ball. We're making this a story about how well the bookies did, rather than how well the horses ran.

Here are some recent examples of AP treatment of the same statistic, with the supporting evidence (when supplied; it's usually a graf or two away) in parens:

Feb. 25: Initial claims for U.S. unemployment benefits unexpectedly rose last week while measures of economic sentiment in Europe and business investment in Britain declined.

Feb. 18: The number of newly laid-off workers filing applications for unemployment benefits unexpectedly surged last week after having fallen sharply in the previous week. (Economists surveyed by Thomson Reuters had expected new claims to fall modestly.)

Feb. 4: The number of newly laid-off workers filing initial claims for jobless benefits rose unexpectedly last week, evidence that layoffs are continuing and jobs remain scarce. (The Labor Department said Thursday that new claims for unemployment insurance rose by 8,000 to a seasonally adjusted 480,000. Wall Street economists had expected a drop to 460,000, according to Thomson Reuters.)

See where this might be going? Here's the AP of March 4:

The Labor Department also said that initial jobless claims dipped last week after two straight weeks of unexpected increases. New claims fell to 469,000, better than the 470,000 economists had forecast.

At this point -- the difference between a prediction of 470,000 and a result of 469,000 -- it's probably pertinent to note that there are (broadly) two ways to make predictions of this sort. You can look at sheep entrails, the flight of birds or the Magic 8-Ball, or you can put some stuff into an equation and hit a button. Extispicy is for the Sunday morning talk shows, but if you're actually crunching numbers, there ought to be some sort of interval within which I, as a lay reader, can tell whether missing by a fraction of 1 percent makes you a tyro or a pretty good "expert."

For the second time in a week, I'm complaining about a procedure I don't know, but having survived a couple of fairly scary classes in which baby whales were sacrificed to the gods of multiple regression, I don't think it's an unfair question. How does the forecast that "economists" offer to Thomson Reuters come about, how can I judge the relationship between the prediction and the result, and if the gap is alarming, should I blame the economy or the economists?

I will point out further that the prediction/reality gap in the statistics of unemployment claims isn't just a parlor game before we bring out the gin. At some news outlets, routine economic stats that used to be categorized as "business" stories are now "politics" stories. (The curious reader might want to hazard a guess at the point in early 2009 where this phenomenon occurred.) It's hard to wage a campaign against stupidity when media reporting itself makes "stupid" the default option.

Thus ordered: AP economy ledes will henceforth be stripped of adverbs relating performance to predictions. That relationship may be set out in subsequent grafs only if the reporter appears capable of explaining how it is derived and the rough confidence interval in which it operates. That means the horse likes mud.

* On the sensible grounds that if you don't expect to die, you aren't paying attention. Now that I have grown old and descriptivist, I no longer insist** that my obit say "died expectedly." I will settle for "died unsurprisingly but was really annoyed at the timing of it."
** Though Language Czarina still has the list of people who are to be whacked upside the head with a stick if they are assigned to write the said obit.**** Do not be misled by her classroom evals. She will hurt you.
*** One good reason for opposing the split-verb superstition is that putting the adverb between the auxiliary and the main verb is often a good way to reduce this sort of ambiguity. Imagine what might happen if we taught students to diagram sentences, rather than looking rules up in journalism textbooks. Just make it "rose unexpectedly."
**** Nobody out there in readerland, as far as I know.

Today's do-it-yourself tip

Suppose you get an irate phone call or eighty over the next few days from readers demanding to know why you and your Marxist colleagues are suppressing the bombshell story in which the chief Climategate perp confesses that global warming is a hoax. (It has to be true; after all, Rush said it, and there it is at the Fair 'n' Balanced Network!)

Well, sorta. Here's how Fox puts it:

The embattled ex-head of the research center at the heart of the Climate-gate scandal dropped a bombshell over the weekend, admitting in an interview with the BBC that there has been no global warming over the past 15 years.

Wanna know what he really told the BBC?

Do you agree that from 1995 to the present there has been no statistically-significant global warming?

Yes, but only just. I also calculated the trend for the period 1995 to 2009. This trend (0.12C per decade) is positive, but not significant at the 95% significance level. The positive trend is quite close to the significance level. Achieving statistical significance in scientific terms is much more likely for longer periods, and much less likely for shorter periods.

See why we keep on complaining about people who ignore confidence levels? He's not saying there isn't a trend; he's saying it's a trend that's close to significant at conventional levels (95%) but not quite there.

So what do you tell the reading public? OK, imagine you have some dread disease -- infectious palinitis or something, usually fatal within a year of diagnosis. There is no cure. But there's a new miracle drug we've been testing, and people seem to be symptom-free two years later. Want some?

Dunno. How good is the study? It's very good, but as with any such study, there's a chance we got our result by accident; it could be a false positive, meaning we got a good result by some accident unrelated to the treatment. There's about a 7 percent chance that it won't help if you take it. Still want some?

I would, even though we're hovering around 93% confidence rather than the arbitrary 95% level that the story mentions. That's the difference between "approaching significance" and "significant," or the difference between "no global warming" and "no statistically significant global warming" if you get your news from Planet Fox.

Your callers aren't necessarily stupid (though you shouldn't rule that out). But they've demonstrably been lied to -- by Limbaugh, which isn't a surprise, but also by a purported news outlet, which should be. Who knows? They might appreciate finding out what they're missing.