andrew_gelman_stats andrew_gelman_stats-2012 andrew_gelman_stats-2012-1562 knowledge-graph by maker-knowledge-mining
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Introduction: I recently wrote about the difficulty people have with probabilities, in this case the probability that Obama wins the election. If the probability is reported as 70%, people think Obama is going to win. Actually, though, it just means that Obama is predicted to get about 50.8% of the two-party vote, with an uncertainty of something like 2 percentage points. So, as I wrote, the election really is too close to call in the sense that the predicted vote margin is less than its uncertainty. But . . . when people see a number such as 70%, they tend to attribute too much certainty to it. Especially when the estimated probability has increased from, say 60%. How to get the point across? Commenter HS had what seems like a good suggestion: Say that Obama will win, but there is 25% chance (or whatever) that this prediction is wrong? Same point, just slightly different framing, but somehow, this seems far less incendiary. I like that. Somehow a stated probability of 75% sounds a
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1 I recently wrote about the difficulty people have with probabilities, in this case the probability that Obama wins the election. [sent-1, score-0.781]
2 If the probability is reported as 70%, people think Obama is going to win. [sent-2, score-0.455]
3 Actually, though, it just means that Obama is predicted to get about 50. [sent-3, score-0.368]
4 8% of the two-party vote, with an uncertainty of something like 2 percentage points. [sent-4, score-0.36]
5 So, as I wrote, the election really is too close to call in the sense that the predicted vote margin is less than its uncertainty. [sent-5, score-0.94]
6 when people see a number such as 70%, they tend to attribute too much certainty to it. [sent-9, score-0.532]
7 Especially when the estimated probability has increased from, say 60%. [sent-10, score-0.561]
8 Commenter HS had what seems like a good suggestion: Say that Obama will win, but there is 25% chance (or whatever) that this prediction is wrong? [sent-12, score-0.57]
9 Same point, just slightly different framing, but somehow, this seems far less incendiary. [sent-13, score-0.418]
10 Somehow a stated probability of 75% sounds all too sure, whereas saying that there’s a 25% chance of being wrong seems to better convey the uncertainty in the prediction. [sent-15, score-1.409]
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same-blog 1 1.0 1562 andrew gelman stats-2012-11-05-Let’s try this: Instead of saying, “The probability is 75%,” say “There’s a 25% chance I’m wrong”
Introduction: I recently wrote about the difficulty people have with probabilities, in this case the probability that Obama wins the election. If the probability is reported as 70%, people think Obama is going to win. Actually, though, it just means that Obama is predicted to get about 50.8% of the two-party vote, with an uncertainty of something like 2 percentage points. So, as I wrote, the election really is too close to call in the sense that the predicted vote margin is less than its uncertainty. But . . . when people see a number such as 70%, they tend to attribute too much certainty to it. Especially when the estimated probability has increased from, say 60%. How to get the point across? Commenter HS had what seems like a good suggestion: Say that Obama will win, but there is 25% chance (or whatever) that this prediction is wrong? Same point, just slightly different framing, but somehow, this seems far less incendiary. I like that. Somehow a stated probability of 75% sounds a
Introduction: The other day we had a fun little discussion in the comments section of the sister blog about the appropriateness of stating forecast probabilities to the nearest tenth of a percentage point. It started when Josh Tucker posted this graph from Nate Silver : My first reaction was: this looks pretty but it’s hyper-precise. I’m a big fan of Nate’s work, but all those little wiggles on the graph can’t really mean anything. And what could it possibly mean to compute this probability to that level of precision? In the comments, people came at me from two directions. From one side, Jeffrey Friedman expressed a hard core attitude that it’s meaningless to give a probability forecast of a unique event: What could it possibly mean, period, given that this election will never be repeated? . . . I know there’s a vast literature on this, but I’m still curious, as a non-statistician, what it could mean for there to be a meaningful 65% probability (as opposed to a non-quantifiab
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Introduction: This post is by Phil Price. Bill Kristol notes that “Four presidents in the last century have won more than 51 percent of the vote twice: Roosevelt, Eisenhower, Reagan and Obama”. I’m not sure why Kristol, a conservative, is promoting the idea that Obama has a mandate, but that’s up to him. I’m more interested in the remarkable bit of cherry-picking that led to this “only four presidents” statistic. There was one way in which Obama’s victory was large: he won the electoral college 332-206. That’s a thrashing. But if you want to claim that Obama has a “popular mandate” — which people seem to interpret as an overwhelming preference of The People such that the opposition is morally obligated to give way — you can’t make that argument based on the electoral college, you have to look at the popular vote. That presents you with a challenge for the 2012 election, since Obama’s 2.7-point margin in the popular vote was the 12th-smallest out of the 57 elections we’ve had. There’s a nice sor
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Introduction: An interview with me from 2012 : You’re a statistician and wrote a book, Red State, Blue State, Rich State, Poor State , looking at why Americans vote the way they do. In an election year I think it would be a good time to revisit that question, not just for people in the US, but anyone around the world who wants to understand the realities – rather than the stereotypes – of how Americans vote. I regret the title I gave my book. I was too greedy. I wanted it to be an airport bestseller because I figured there were millions of people who are interested in politics and some subset of them are always looking at the statistics. It’s got a very grabby title and as a result people underestimated the content. They thought it was a popularisation of my work, or, at best, an expansion of an article we’d written. But it had tons of original material. If I’d given it a more serious, political science-y title, then all sorts of people would have wanted to read it, because they would
5 0.19644256 1569 andrew gelman stats-2012-11-08-30-30-40 Nation
Introduction: Barack Obama’s win has a potentially huge effect on policy. The current budget negotiations will affect the level and direction of government spending and on the mix of taxes paid by different groups of Americans. We can guess that a President Romney would have fought hard against upper-income tax increases. Other areas of long-term impact include the government’s stance on global warming, foreign policy, and the likelihood that Obama will nominate new Supreme Court justices who will uphold the right to abortion announced in Roe v. Wade. When it comes to public opinion, the story is different. The Democrats may well benefit in 2014 and 2016 from the anticipated slow but steady recovery of the economy over the next few years—but, as of November 6, 2012, the parties are essentially tied, with Barack Obama receiving 51% of the two-party vote, compared to Mitt Romney’s 49%, a split comparable to Al Gore’s narrow victory in 2000, Richard Nixon’s in 1968, and John Kennedy’s in 1960.
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same-blog 1 0.96394396 1562 andrew gelman stats-2012-11-05-Let’s try this: Instead of saying, “The probability is 75%,” say “There’s a 25% chance I’m wrong”
Introduction: I recently wrote about the difficulty people have with probabilities, in this case the probability that Obama wins the election. If the probability is reported as 70%, people think Obama is going to win. Actually, though, it just means that Obama is predicted to get about 50.8% of the two-party vote, with an uncertainty of something like 2 percentage points. So, as I wrote, the election really is too close to call in the sense that the predicted vote margin is less than its uncertainty. But . . . when people see a number such as 70%, they tend to attribute too much certainty to it. Especially when the estimated probability has increased from, say 60%. How to get the point across? Commenter HS had what seems like a good suggestion: Say that Obama will win, but there is 25% chance (or whatever) that this prediction is wrong? Same point, just slightly different framing, but somehow, this seems far less incendiary. I like that. Somehow a stated probability of 75% sounds a
Introduction: The other day we had a fun little discussion in the comments section of the sister blog about the appropriateness of stating forecast probabilities to the nearest tenth of a percentage point. It started when Josh Tucker posted this graph from Nate Silver : My first reaction was: this looks pretty but it’s hyper-precise. I’m a big fan of Nate’s work, but all those little wiggles on the graph can’t really mean anything. And what could it possibly mean to compute this probability to that level of precision? In the comments, people came at me from two directions. From one side, Jeffrey Friedman expressed a hard core attitude that it’s meaningless to give a probability forecast of a unique event: What could it possibly mean, period, given that this election will never be repeated? . . . I know there’s a vast literature on this, but I’m still curious, as a non-statistician, what it could mean for there to be a meaningful 65% probability (as opposed to a non-quantifiab
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Introduction: Gregg Easterbrook : Gingrich is a wild card. He probably would end up a flaming wreckage in electoral terms, but there’s a chance he could become seen as the man unafraid to bring sweeping change to an ossified Washington, D.C. There’s perhaps a 90 percent likelihood Obama would wipe the floor with Gingrich, versus a 10 percent likelihood Gingrich would stage an historic upset. This is the dumbest thing I’ve seen since . . . ummm, I dunno, how bout this ? It actually gets worse because Easterbrook then invokes game theory. What next? Catastrophe theory? Intelligent design? P.S. Maybe I should explain for readers without an education in probability theory. Let’s suppose “wipe the floor” means that Obama gets 55%+ of the two-party vote, and let’s suppose that “an historic upset” means that Obama gets less than 50% of the vote. Now try to draw a forecast distribution that has 90% of its probability above 0.55 and 10% of it’s probability below 0.50. It’s a pretty weird-loo
4 0.87384957 1574 andrew gelman stats-2012-11-12-How to Lie With Statistics example number 12,498,122
Introduction: This post is by Phil Price. Bill Kristol notes that “Four presidents in the last century have won more than 51 percent of the vote twice: Roosevelt, Eisenhower, Reagan and Obama”. I’m not sure why Kristol, a conservative, is promoting the idea that Obama has a mandate, but that’s up to him. I’m more interested in the remarkable bit of cherry-picking that led to this “only four presidents” statistic. There was one way in which Obama’s victory was large: he won the electoral college 332-206. That’s a thrashing. But if you want to claim that Obama has a “popular mandate” — which people seem to interpret as an overwhelming preference of The People such that the opposition is morally obligated to give way — you can’t make that argument based on the electoral college, you have to look at the popular vote. That presents you with a challenge for the 2012 election, since Obama’s 2.7-point margin in the popular vote was the 12th-smallest out of the 57 elections we’ve had. There’s a nice sor
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Introduction: 1. I can simultaneously (a) accept that Obama has a 72 percent chance of winning and (b) say the election is too close to call 2. Michael’s a Republican, Susan’s a Democrat 3. The narcissism of the narcissism of small differences 4. Obamanomics: A Counter-counterhistory 5. Not a gaffe 6. Categories influence predictions about individual consistency
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same-blog 1 0.98640043 1562 andrew gelman stats-2012-11-05-Let’s try this: Instead of saying, “The probability is 75%,” say “There’s a 25% chance I’m wrong”
Introduction: I recently wrote about the difficulty people have with probabilities, in this case the probability that Obama wins the election. If the probability is reported as 70%, people think Obama is going to win. Actually, though, it just means that Obama is predicted to get about 50.8% of the two-party vote, with an uncertainty of something like 2 percentage points. So, as I wrote, the election really is too close to call in the sense that the predicted vote margin is less than its uncertainty. But . . . when people see a number such as 70%, they tend to attribute too much certainty to it. Especially when the estimated probability has increased from, say 60%. How to get the point across? Commenter HS had what seems like a good suggestion: Say that Obama will win, but there is 25% chance (or whatever) that this prediction is wrong? Same point, just slightly different framing, but somehow, this seems far less incendiary. I like that. Somehow a stated probability of 75% sounds a
Introduction: Yu Xie thought I’d have something to say about this recent paper , “Evidence on the impact of sustained exposure to air pollution on life expectancy from China’s Huai River policy,” by Yuyu Chen, Avraham Ebenstein, Michael Greenstone, and Hongbin Li, which begins: This paper’s findings suggest that an arbitrary Chinese policy that greatly increases total suspended particulates (TSPs) air pollution is causing the 500 million residents of Northern China to lose more than 2.5 billion life years of life expectancy. The quasi-experimental empirical approach is based on China’s Huai River policy, which provided free winter heating via the provision of coal for boilers in cities north of the Huai River but denied heat to the south. Using a regression discontinuity design based on distance from the Huai River, we find that ambient concentrations of TSPs are about 184 μg/m3 [95% confidence interval (CI): 61, 307] or 55% higher in the north. Further, the results indicate that life expectanci
3 0.98128468 897 andrew gelman stats-2011-09-09-The difference between significant and not significant…
Introduction: E. J. Wagenmakers writes: You may be interested in a recent article [by Nieuwenhuis, Forstmann, and Wagenmakers] showing how often researchers draw conclusions by comparing p-values. As you and Hal Stern have pointed out, this is potentially misleading because the difference between significant and not significant is not necessarily significant. We were really suprised to see how often researchers in the neurosciences make this mistake. In the paper we speculate a little bit on the cause of the error. From their paper: In theory, a comparison of two experimental effects requires a statistical test on their difference. In practice, this comparison is often based on an incorrect procedure involving two separate tests in which researchers conclude that effects differ when one effect is significant (P < 0.05) but the other is not (P > 0.05). We reviewed 513 behavioral, systems and cognitive neuroscience articles in five top-ranking journals (Science, Nature, Nature Neuroscien
Introduction: This material should be familiar to many of you but could be helpful to newcomers. Pearl writes: ALL causal conclusions in nonexperimental settings must be based on untested, judgmental assumptions that investigators are prepared to defend on scientific grounds. . . . To understand what the world should be like for a given procedure to work is of no lesser scientific value than seeking evidence for how the world works . . . Assumptions are self-destructive in their honesty. The more explicit the assumption, the more criticism it invites . . . causal diagrams invite the harshest criticism because they make assumptions more explicit and more transparent than other representation schemes. As regular readers know (for example, search this blog for “Pearl”), I have not got much out of the causal-diagrams approach myself, but in general I think that when there are multiple, mathematically equivalent methods of getting the same answer, we tend to go with the framework we are used
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