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Introduction: The principle is, Whatever you do, somebody in psychometrics already did it long before. The new evidence comes from an article by Lawrence Hubert and Howard Wainer: There are several issues with the use of ecological correlations: They tend to be a lot higher than individual-level correlations, and assuming what is seen at the group level also holds at the level of the individual is so pernicious, it has been labeled the “ecological fallacy” by Selvin (1958). The term ecological correlation was popularized from a 1950 article by William Robinson (Robinson, 1950), but the idea has been around for some time (e.g., see the 1939 article by E. L. Thorndike, On the Fallacy of Imputing Correlations Found for Groups to the Individuals or Smaller Groups Composing Them).
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same-blog 1 1.0 1082 andrew gelman stats-2011-12-25-Further evidence of a longstanding principle of statistics
Introduction: The principle is, Whatever you do, somebody in psychometrics already did it long before. The new evidence comes from an article by Lawrence Hubert and Howard Wainer: There are several issues with the use of ecological correlations: They tend to be a lot higher than individual-level correlations, and assuming what is seen at the group level also holds at the level of the individual is so pernicious, it has been labeled the “ecological fallacy” by Selvin (1958). The term ecological correlation was popularized from a 1950 article by William Robinson (Robinson, 1950), but the idea has been around for some time (e.g., see the 1939 article by E. L. Thorndike, On the Fallacy of Imputing Correlations Found for Groups to the Individuals or Smaller Groups Composing Them).
2 0.30590197 1704 andrew gelman stats-2013-02-03-Heuristics for identifying ecological fallacies?
Introduction: Greg Laughlin writes: My company just wrote a blog post about the ecological fallacy. There’s a discussion about it on the Hacker News message board. Someone asks, “How do you know [if a group-level finding shouldn't be used to describe individual level behavior]?” The best answer I had was “you can never tell without the individual-level data, you should always be suspicious of group-level findings applied to individuals.” Am I missing anything? Are there any situations in which you can look at group-level qualities being ascribed to individuals and not have to fear the ecological fallacy? My reply: I think that’s right. To put it another way, consider the larger model with separate coefficients for individual-level and group-level effects. If you want, you can make an assumption that they’re equal, but that’s an assumption that needs to be justified on substantive grounds. We discuss these issues a bit in this paper from 2001. (I just reread that paper. It’s pre
Introduction: Psychologists talk about “folk psychology”: ideas that make sense to us about how people think and behave, even if these ideas are not accurate descriptions of reality. And physicists talk about “folk physics” (for example, the idea that a thrown ball falls in a straight line and then suddenly drops, rather than following an approximate parabola). There’s also “folk statistics.” Some of the ideas of folk statistics are so strong that even educated people–even well-known researchers–can make these mistakes. One of the ideas of folk statistics that bothers me a lot is what might be called the “either/or fallacy”: the idea that if there are two possible stories, the truth has to be one or the other. I have often encountered the either/or fallacy in Bayesian statistics, for example the vast literature on “model selection” or “variable selection” or “model averaging” in which it is assumed that one of some pre-specified discrete set of models is the truth, and that this true model
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Introduction: I’ve had a couple of email conversations in the past couple days on dependence in multivariate prior distributions. Modeling the degrees of freedom and scale parameters in the t distribution First, in our Stan group we’ve been discussing the choice of priors for the degrees-of-freedom parameter in the t distribution. I wrote that also there’s the question of parameterization. It does not necessarily make sense to have independent priors on the df and scale parameters. In some sense, the meaning of the scale parameter changes with the df. Prior dependence between correlation and scale parameters in the scaled inverse-Wishart model The second case of parameterization in prior distribution arose from an email I received from Chris Chatham pointing me to this exploration by Matt Simpson of the scaled inverse-Wishart prior distribution for hierarchical covariance matrices. Simpson writes: A popular prior for Σ is the inverse-Wishart distribution [ not the same as the
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Introduction: Howard Wainer writes : When we focus only on the differences between groups, we too easily lose track of the big picture. Nowhere is this more obvious than in the current public discussions of the size of the gap in test scores that is observed between racial groups. It has been noted that in New Jersey the gap between the average scores of white and black students on the well-developed scale of the National Assessment of Educational Progress (NAEP) has shrunk by only about 25 percent over the past two decades. The conclusion drawn was that even though the change is in the right direction, it is far too slow. But focusing on the difference blinds us to what has been a remarkable success in education over the past 20 years. Although the direction and size of student improvements are considered across many subject areas and many age groups, I will describe just one — 4th grade mathematics. . . . there have been steep gains for both racial groups over this period (somewhat steeper g
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Introduction: Andrew has pointed to Jonathan Livengood’s analysis of the correlation between poverty and PISA results, whereby schools with poorer students get poorer test results. I’d have written a comment, but then I couldn’t have inserted a chart. Andrew points out that a causal analysis is needed. This reminds me of an intervention that has been done before: take a child out of poverty, and bring him up in a better-off family. What’s going to happen? There have been several studies examining correlations between adoptive and biological parents’ IQ (assuming IQ is a test analogous to the math and verbal tests, and that parent IQ is analogous to the quality of instruction – but the point is in the analysis not in the metric). This is the result (from Adoption Strategies by Robin P Corley in Encyclopedia of Life Sciences): So, while it did make a difference at an early age, with increasing age of the adopted child, the intelligence of adoptive parents might not be making any difference
Introduction: Dan Kahan writes: We all know it’s ridiculous to be able to go on an fMRI fishing trip & resort to post hoc story-telling to explain the “significant” correlations one (inevitably) observes (good fMRI studies *don’t* do this; only bad ones do– to the injury of the reputation of all the scholars doing good studies of this kind). But now one doesn’t even need correlations that support the post-hoc inferences one is drawing. This one’s good. Kahan continues: Headline: Religious Experiences Shrink Part of the Brain text: ” … The study, published March 30 [2011] in PLoS One, showed greater atrophy in the hippocampus in individuals who identify with specific religious groups as well as those with no religious affiliation … The results showed significantly greater hippocampal atrophy in individuals reporting a life-changing religious experience. In addition, they found significantly greater hippocampal atrophy among born-again Protestants, Catholics, and those with no religiou
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Introduction: The principle is, Whatever you do, somebody in psychometrics already did it long before. The new evidence comes from an article by Lawrence Hubert and Howard Wainer: There are several issues with the use of ecological correlations: They tend to be a lot higher than individual-level correlations, and assuming what is seen at the group level also holds at the level of the individual is so pernicious, it has been labeled the “ecological fallacy” by Selvin (1958). The term ecological correlation was popularized from a 1950 article by William Robinson (Robinson, 1950), but the idea has been around for some time (e.g., see the 1939 article by E. L. Thorndike, On the Fallacy of Imputing Correlations Found for Groups to the Individuals or Smaller Groups Composing Them).
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Introduction: The following is an essay into a topic I know next to nothing about. As part of our endless discussion of Dilbert and Charlie Sheen, commenter Fraac linked to a blog by philosopher Edouard Machery, who tells a fascinating story : How do we think about the intentional nature of actions? And how do people with an impaired mindreading capacity think about it? Consider the following probes: The Free-Cup Case Joe was feeling quite dehydrated, so he stopped by the local smoothie shop to buy the largest sized drink available. Before ordering, the cashier told him that if he bought a Mega-Sized Smoothie he would get it in a special commemorative cup. Joe replied, ‘I don’t care about a commemorative cup, I just want the biggest smoothie you have.’ Sure enough, Joe received the Mega-Sized Smoothie in a commemorative cup. Did Joe intentionally obtain the commemorative cup? The Extra-Dollar Case Joe was feeling quite dehydrated, so he stopped by the local smoothie shop to buy
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Introduction: Michael Gilligan, Eric Mvukiyehe, and Cyrus Samii write : We [Gilligan, Mvukiyehe, and Samii] use original survey data, collected in Burundi in the summer of 2007, to show that a World Bank ex-combatant reintegration program implemented after Burundi’s civil war caused significant economic reintegration for its beneficiaries but that this economic reintegration did not translate into greater political and social reintegration. Previous studies of reintegration programs have found them to be ineffective, but these studies have suffered from selection bias: only ex-combatants who self selected into those programs were studied. We avoid such bias with a quasi-experimental research design made possible by an exogenous bureaucratic failure in the implementation of program. One of the World Bank’s implementing partners delayed implementation by almost a year due to an unforeseen contract dispute. As a result, roughly a third of ex-combatants had their program benefits withheld for reas
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