More fun with percentages of percentages

      4 Comments on More fun with percentages of percentages

An off-hand comment by a reader of the Rhetorica led me to PIPA’s survey of Misperceptions, The Media and The Iraq War, which I had glanced at a year ago. The comment, though, led me to one of the things that bugs me about such surveys, and the way people think of them.

It seems that a large number of people in this country were misinformed about the attitudes of people outside the country concerning our invasion in Iraq:

In March 2003, shortly after the war started, PIPA/KN asked respondents “How all of the people in the world feel about the US going to war with Iraq.” Respondents perceived greater support for the war than existed at the time, or has since. Only 35% perceived correctly that the majority of people opposed the decision. Thirty-one percent expressed the mistaken assumption that views were evenly balanced on the issue, and another 31% expressed the egregious misperception that the majority favored it.

The misperceptions correlated well with support for the war:

In the PIPA/KN poll conducted in late March, shortly after the onset of the war, among those who wrongly believed that the majority of the people in the world favored the US going to war with Iraq, an overwhelming 81% said they agreed with the President’s decision to go to war with Iraq, despite his failure to garner UN Security Council approval. Among those who, also incorrectly, believed that views were evenly balanced on this question, 58% said they agreed. Among those who correctly believed that the majority of people opposed it, only 28% said they agreed with the President’s decision

In other words, anti-invasion people were well-informed, and pro-invasion people were ill-informed, right? Now, the problem is that once you start dealing with percentages of percentages, it’s hard to keep in your head what they actually mean. The famous example is the rare-disease diagnosis test with far more false positives than true, simply because there are so few true positives. So in cases like this, I try to do the hundred-people breakdown. In this case, out of a hundred people:

  • 35 respond that the invasion is unpopular outside the US, breaking down into 25 anti-invasion respondents and ten who support the war anyway
  • 31 respond that opinion is evenly mixed, breaking down into 13 anti-invasion respondents and 18 supporters
  • 31 respond that world opinion is in favor of invasion, breaking down into 6 antis and 25 pros

Now, let’s assume that people largely come to their decisions independently, that is, world opinion is likely to strengthen, rather than persuade. So it seems that of the 53 people who support invasion, 47% claim the support of the world (given that there is no reward for a correct answer, I would guess that at least three or four people out of that 25 know very well that the world is against them, and say otherwise). Of the 44 who are against the invasion, only 57% correctly claim the support of the world (to be fair, I should admit that at least three or four of those would claim world opinion if it were against them, all the same as the other side). So the antis have an edge, but not a huge one. It’s nothing to brag about.

More important, the number of people whose opposition to invasion correlates in this instance with being well-informed is around 25 out of a hundred, and the ill-informed support is around 25 out of a hundred, with fully half the population in the muddle in the middle. If you add in the likelihood of bullshit, I’m not convinced by the claim that the pro-invasion were ill-informed while the well-informed were anti-invasion. Put another way, if you pick randomly one person in the sample and ascertain whether that person is pro-invasion or anti-invasion, I don’t think you can predict with terrific accuracy whether that person is well-informed or ill-informed (on this issue).

I first noticed this sort of thing in the 2000 primary campaign, when Mr. Zogby made a big deal out of the people who, in the New Hampshire primaries, expressed that John McCain was their first choice and Bill Bradley their second, or vice versa. This was, in fact, a surprisingly high minority of supporters of Mssrs. McCain and Bradley, but since the two candidates didn’t have that much support themselves, the total number of these cross-party mavericks was, if I remember correctly, about 5% of the voters. Had Mr. Zogby suggested that this 5% was a small but key core of mavericks who actually vote, I would have agreed, I think, but he suggested that this group indicated the mood of the populace. I think not.

I don’t really have a point about the war, or about the Senators, just that when pollsters start talking about percentages of percentages, reach for your calculator. Alternately, remember Dogbert’s advice about market research: any really competent market research for a new product will reveal that 40% of people can’t afford your product, 40% wouldn’t accept your product for free, 10% will buy any damn thing that’s put on a shelf, and 10% are just completely insane.

Thank you,
-Vardibidian.

4 thoughts on “More fun with percentages of percentages

  1. david

    however it was the general trends of this poll, over the two years that they’ve been doing it, that convinced me in the spring that in a tight election, bush would win, because there were simply too many people who believed in a hussein-9/11 connection for it not to affect the results. you’re concerned with exactly how much water is coming out of each spigot; however, in this situation, it’s the amount of water that splashes from the bucket that matters, not the volume of water properly contained. if it doesn’t overload the metaphor, all the water that doesn’t go in a bucket, rolls downhill toward the incumbent.

    Reply
  2. Chaos

    Now, let’s assume that people largely come to their decisions independently, that is, world opinion is likely to strengthen, rather than persuade. So it seems that of the 53 people who support invasion, 47% claim the support of the world (given that there is no reward for a correct answer, I would guess that at least three or four people out of that 25 know very well that the world is against them, and say otherwise). Of the 44 who are against the invasion, only 57% correctly claim the support of the world (to be fair, I should admit that at least three or four of those would claim world opinion if it were against them, all the same as the other side). So the antis have an edge, but not a huge one. It’s nothing to brag about.

    Bah? I am confused about the comparison you are making here. It seems that you are saying that the number of antis who are right is not very much greater than the number of pros who are dead wrong. That doesn’t help.

    I know i’m a biased anti here, but it seems to me that, since we know (well, to the extent that we know anything we read on TV, anyway) world opinion was anti, we can say that (as you note) 57% of the antis correctly claim world opinion, but 10/53, or 19%, of the pros correctly disclaim world opinion. (Note that “correct” != “1 – dead wrong”, because of the large number who believe opinion is split, who are also wrong.) Now, as you note, you can close that gap 10% at least on the basis of people lying, but it’s still a big gap.

    Reply
  3. Vardibidan

    Chaos,
    I am, in fact, saying that the percentage of antis who were right isn’t much greater than the percentage of pros who were dead wrong. Think of it like the false positive: people think that the person who tests positive is more likely to have the rare disease than not to have it, that, in fact, testing positive means that the person has the disease. In this case, people think that the numbers mean that being in opposition to the invasion means that a person is well-informed, that is, right, and that supporting it means that a person is wrong. Those are the ideas that I’m comparing, and they are not, um, what’s the word, complementary? Anyway, they do in fact measure different things, but I compare them because people do compare them. In a two-minute NPR piece on the numbers, I wouldn’t be surprised to hear that opposers ‘knew’ that world opinion was on their side, while supporters ‘wrongly believed’ that it was on theirs. Would that surprise you? Do you think the evidence supports that statement?
    Now, it’s true that I’m shifting the ‘evenly balanced’ people from one side to the other in this, leaving them out of either well-informed or ill-informed, as the case may be (PIPA does this as well, only more openly). I’m doing that in imitation of how I think people think. People don’t think that the ill-informed supporter believes that world opinion was evenly balanced. That may well be an error, but it is the sort of error people make and will make in talking about things like this, which is what I’m on about.
    On re-reading my post, I think I implied criticism of PIPA, and I think that PIPA actually did a fairly good job explaining what the numbers were and what they meant, in speaking to numerate people. We are not, on the whole, numerate people, though (and still wouldn’t be were numerate a real word). I don’t know how PIPA ought to deal with that, but when the incorrect stereotype predictably flowers from their numbers, it bugs the heck out of me. And, of course, David is quite correct that they are quite right about their bigger point, which is that Our Only President’s support came in large measure from ill-informed people, that Our Only President and his cabal of cronies wanted as many people as possible to be ill-informed, and that the success of that campaign of secrecy and lies had a substantial effect. That seems to imply a mental image, or stereotype, of the well-informed Democrat and the ill-informed Republican; I wouldn’t be surprised to discover that less than half of the votes came from either of those camps. Similarly, the PIPA report seems to imply a mental image of a few knowledgeable doves and a lot of deluded hawks, and in fact only half the population were either, and within that half it was pretty evenly split.
    Thanks
    -V.

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