Making stuff up with numbers

Nothing wrong with the headline, as long as you don't expect headlines to be true or anything. The race might indeed be "tightening," but none of the evidence here supports such a conclusion -- mostly because the "polls" don't show anyone "tied" with anyone else. Fox isn't the only cable network to get this point wrong, but it appears to be the most consistent in lying about numbers for partisan gain, so let's have a look:

Two polls released Sunday show Democratic presidential front-runner Hillary Clinton tied with presumptive Republican nominee Donald Trump in a likely general election race, after having a double-digit lead just months ago.
  
Clinton leads Trump 46-to-43 percent in a NBC News/Wall Street Journal poll, compared to a similar one in April in which Clinton had an 11-point lead.

Odd. A 3-point lead wasn't a "tie" last week, when Fox reported on its own poll:

Donald Trump tops Hillary Clinton in a hypothetical head-to-head matchup, according to a new Fox News Poll that also finds majorities of voters feel both frontrunners lack strong moral values and will say anything to get elected.

Trump has a 45-42 percent edge over Clinton, if the presidential election were held today.  That’s within the poll’s margin of sampling error.  Last month, Clinton was up by 48-41 percent (April 2016).

Hmm. Let's return to Sunday's story for a moment:

Earlier Sunday morning, a Washington Post/ABC News poll showed voters favored Trump over Clinton 46-to-44 percent. The numbers also show Clinton losing an identical 11-point lead since earlier this spring.

Both polls were within the statistical margin of error, which means Clinton and Trump are essentially tied.

Well, no. It doesn't mean that. Not that the misperception isn't widely shared -- for example, by NBC itself (here, in its MSNBC guise):

Hillary Clinton’s advantage over Donald Trump has narrowed to just three points — resulting in a dead-heat general-election contest with more than five months to go until November, according to a new national NBC News/Wall Street Journal poll.

Clinton, who remains a heavy favorite to win the Democrat nomination, leads the presumptive GOP nominee 46 percent to 43 percent among registered voters, a difference that is within the poll’s margin of error of plus-or-minus 3.1 percentage points.

NBC isn't done with the stupidz:

In a more hypothetical matchup, Democrat Bernie Sanders leads Trump by 15 points, 54 percent to 39 percent.

No. Sanders-Trump is an equally hypothetical matchup to Clinton-Trump. It's about what respondents say they would do if a contest between two people who haven't been nominated yet was held today, rather than in November. The writer might think Sanders-Trump is less likely, but that doesn't make it more "hypothetical*." The bigger question for people interested in campaign coverage is whether one kind of cluelessness is more or less honest than another. That's going to require a brief detour into what polls do and what "margin of error" means. If you want a refund because this is the same stuff posted here eight years ago, feel free to email the management.

OK. If you want to know what voters think, you can ask all the voters in the country what they think, which would take years and cost millions of lives, or you can ask a sample of voters what they think. A competently chosen random sample of voters can answer a question, hypothetical or not, with a striking degree of accuracy; "margin of error," or confidence interval, describes how closely the sample can be expected to resemble the population on that question. Somewhere, among all the voters in this favored land, is an actual, settled, four-decimal-points value for the hypothetical Trump vs. Clinton question. How good is our guess?

Short answer, better than you think (almost certainly better than you think if your main concern is whether you agree with the politics of the outfit that sponsored the poll). If 48% of the population thinks X, and you ask (or Fox, or NBC, or Satan himself asks) 1,000-odd representatives of that population whether they think X, your result will almost certainly be between 45% and 51%.

Your result will also probably be between 46.5% and 49,5%, which gets to the number Fox and NBC leave out: the confidence level. The margin of error that they report (NBC says 3.1 points; Fox says 3, but that's because Fox doesn't round 3.06 upward) is at a confidence level of 95%, meaning that 19 times out of 20, a random sample will be that close to the real value in the population.

What does it mean to be "within the margin of error"? Well, not "statistical dead heat" (there is no such thing). If you poll 1,000 voters in the hotly contested Crook vs. Liar campaign and get a result of 48% for Crook and 45% for Liar, the odds are that Crook is ahead. You have about one chance in three of being wrong, rather than one chance in 20, but if you think that's an even bet, you shouldn't go to the county fair by yourself.

That's a quick and oversimplified** way of approaching the question of how we tell cluelessness from dishonesty. Cluelessness, after all, is the human condition; you don't have to watch "House of Cards" very long before somebody says something stupid about the margin of error. Fox is distinctive because it makes its mistakes in a consistent direction: "within the margin of error" means a tie when the bad guys are ahead but a lead when the good guys are ahead. That's not just lying, it's lying to the paymaster; if Satan himself is funding the poll, you should do yourself the favor of assuming he wants a cold-eyed interpretation of the results, rather than one that says "remain calm, all is well."

Professional courtesy disclaimer: Fox is generally a model in reporting its own polling results; it tends to go into the crazy weeds when it plays with other people's data. That says a lot about news routines at Fox, but it's also a reminder that survey procedures should be judged by how well they are done, rather than who did them.

* Compare, say, "Do you approve or disapprove of the job the president is doing?" -- which doesn't ask you to hypothesize about anything.
** For one thing, it assumes a maximum margin of sampling error, calculated as if every proportion was split 50-50. That's an imperfect assumption that's more relevant in some cases than others, but it does save a lot of work.