john hawks weblog

paleoanthropology, genetics and evolution

statistics

  • Unraveling Fisher's mysteries

    Wed, 2013-04-10 09:11 -- John Hawks

    Haldane's Sieve has a great post by James Lee giving context to a new preprint from him and Carson Chow: "Our paper: The causal meaning of Fisher’s average effect".

    This paradox continued to bother me over the next several years. Soon after my daughter was born, I indulged one of those wild impulses that strike the sleepless: I emailed my questions regarding this matter to Anthony W. F. Edwards, the last student of the great Fisher himself. Anthony very generously sent me some of his unpublished work and also his correspondence with Falconer about the very article that had spurred my thoughts. This correspondence spanned a period of more than 20 years, and it provided a very poignant portrait of Douglas Falconer as a scientist (Hill and Mackay, 2004). I did not immediately find the answers to my questions in the materials that Anthony sent to me, but they set me on the path toward finding the answers. These are presented in the paper, which will shortly appear in Genetics Research.

    Fisher invented a lot of statistical concepts, many of which are used universally by everybody, even far outside genetics. But he also invented some that nobody else has been able to understand. The "average effect" of an allele is one of them. The concept was central in the development of his "Fundamental Theorem" of natural selection, but why it works is not obvious. Lee's post does a great job explaining why this was an interesting and useful project to undertake.

  • Dino size estimation

    Sun, 2013-02-24 21:02 -- John Hawks

    I know I'm linking a four-year-old post about dinosaurs, but I got this SV-POW post on my feed this morning and it is very relevant to those of us who think about variation among fossil hominins: "Brachiosaurus: both bigger and smaller than you think". Let's call it upcycling.

    Maybe the most interesting thing about this is that, so far as we can tell, XV2 was almost exactly the same size as the holotype individual of Sauroposeidon. So anything I or anyone else has written about Sauroposeidon being bigger, absolutely, than Brachiosaurus, is bobbins. Sauroposeidon still had a considerably longer neck, 11.5 meters to XV2′s 9.5, but the cervical skeleton weighed about the same thanks to the higher air space proportion in Sauroposeidon. In fact, if the higher ASP of Sauroposeidon applied to the rest of the vertebral column, then the holotype individual of Sauroposeidon might have weighed less than XV2!

    Much was published about the body size of australopithecines before a good male skeleton was found. Attempts to estimate body mass from single skeletal elements in hominins have a large associated estimation error. Human body size estimation by regression is very different from that within other ape species, because our different locomotor patterns load the hindliimb differently.

    In this light, it is always frustrating to see very many conclusions based upon the body size estimate of any single skeleton. This is an argument made most effectively by Richard Smith, who wrote a classic review paper on the errors of interpretation that can spring from neglecting the error associated with body size estimation [1]. Individuals do not evolve. They are imperfect representations of variable populations.


    References

    1. Smith RJ. Biology and body size in human evolution. Current Anthropology. 1996;37:451–481.
  • Mailbag: Jury regression

    Tue, 2011-12-13 09:41 -- John Hawks

    Re: Jury science

    I have followed your blog with inerest for a while now, and I was looking through your
    twitter stream and saw this, attributed to Kahneman:

    "if a court case hinges on regression to the mean, the side that has to explain this to the jury
    will lose."

    I was immediately intrigued by the idea of coming up with a good explantion for a
    jury, and here is what I came up with:

    Its like poker hands - even if daddy has 4 kings and mommy has 4 queens, the kids
    aren't going to average much better than two pair, kings over queens.

    This simplifies and glosses over a lot, but its memorable and avoids the dreaded
    'eyes glaze over' effect so common with math explanations for laymen. Perhaps it might be
    useful in teaching.

    Thanks! That does seem appealing. I do regression to the mean over the course of a whole lecture, using data that my students measure on themselves to replicate Galton's work on stature. I wouldn't envy anyone who had to do it under a time constraint!

  • "False-positive psychology"

    Fri, 2011-11-11 21:05 -- John Hawks

    Razib Khan conveys a list of suggestions from a recent paper by Joseph Simmons and colleagues [1], concerned with reducing reporting biases in research papers. The article is directed toward psychology research, but many of the observations hold true in paleoanthropology and genetics.

    The central point is that every research paper is a product of a course of inquiry that may come to include many kinds of questions, most of which are unanswered or answered negatively by results and data. When scientists report results, they focus on those that meet some statistical threshold. The threshold ostensibly makes results "significant" but the actual probability of seeing such a result depends on how many things the scientists looked at, not only on those they choose to report:

    In this article, we show that despite the nominal endorsement of a maximum false-positive rate of 5% (i.e., p ≤ .05), current standards for disclosing details of data collection and analyses make false positives vastly more likely. In fact, it is unacceptably easy to publish “statistically significant” evidence consistent with any hypothesis.

    The culprit is a construct we refer to as researcher degrees of freedom. In the course of collecting and analyzing data, researchers have many decisions to make: Should more data be collected? Should some observations be excluded? Which conditions should be combined and which ones compared? Which control variables should be considered? Should specific measures be combined or transformed or both?

    It is rare, and sometimes impractical, for researchers to make all these decisions beforehand. Rather, it is common (and accepted practice) for researchers to explore various analytic alternatives, to search for a combination that yields “statistical significance,” and to then report only what “worked.” The problem, of course, is that the likelihood of at least one (of many) analyses producing a falsely positive finding at the 5% level is necessarily greater than 5%.

    "Researcher degrees of freedom" sounds erudite, but all they're really describing is tinkering. When the data lead you to a result, they do so by leading you along a drunkard's path of new analytical biases.

    Razib has presented the authors' suggestions for researchers and reviewers, to try to reduce the tinkering bias. I think if we followed those suggestions in paleoanthropology, our discipline would be stronger in some ways, weaker in others. For example, the authors suggest rejecting any paper with fewer than 20 observations in a cell of a test of association. Clearly, if we rigidly enforced such a rule, we'd have a lot more work done on comparative collections, and that would be a good thing. On the other hand, we'd have a lot more papers like the ones I like to write, about how the data are insufficient to test a hypothesis. Our science would shift even further toward description, which would benefit some kinds of research and punish others.

    One may object that there are many cases in paleoanthropology where a single observation is fundamentally important. I would just point out that such cases are most evident where the single observation is a many-sigma outlier to some pre-existing hypothesis. If we have a new radiocarbon date that's a three-sigma outlier above previous dates, it will either cause us to change our hypothesis or challenge the date's accuracy. There are biases even so -- for example, when we find outlier radiocarbon dates on otherwise-uncontroversial things, we tend to just ignore the outliers.

    What I most liked about this paper was that the authors anticipated various objections. For example, many researchers would claim that a Bayesian statistical approach would eliminate or reduce the bias from "researcher degrees of freedom". Here's the authors' response:

    Although the Bayesian approach has many virtues, it actually increases researcher degrees of freedom. First, it offers a new set of analyses (in addition to all frequentist ones) that authors could flexibly try out on their data. Second, Bayesian statistics require making additional judgments (e.g., the prior distribution) on a case-by-case basis, providing yet more researcher degrees of freedom.

    That's my observation as well. Researchers adopt Bayesian methods for more ways to tinker. I also appreciate this comment:

    We are strongly supportive of all journals requiring authors to make their original materials and data publicly available. However, this is not likely to address the problem of interest, as this policy would impose too high a cost on readers and reviewers to examine, in real time, the credibility of a particular claim. Readers should not need to download data, load it into their statistical packages, and start running analyses to learn the importance of controlling for father’s age; nor should they need to read pages of additional materials to learn that the researchers simply dropped the “Hot Potato” condition.

    Furthermore, if a journal allows the redaction of a condition from the report, for example, it would presumably also allow its redaction from the raw data and “original” materials, making the entire transparency effort futile.

    All in all, the article is a good reminder of Feynman's first principle, "You must not fool yourself, and you are the easiest person to fool."


    References

    Synopsis: 
    Three psychologists look for solutions to researcher biases in publishing results.
  • Mailbag: Statistics and future evolution

    Mon, 2009-08-24 09:16 -- John Hawks

    I was trying to find out more
    about recent research predicting a relative convergence of racial features in
    future generations (but I don't know anything about "rapid evolution by drift"
    or things like that). I'm aware of debunked claims (inc. your debunking) from
    media reports, but I'm not aware of research that actually contains enough
    scientific merit to make a valid prediction. I decided to write to you after reading
    your review of a lecture by UCL geneticist Steve Jones.

    If there is any reference you can give to someone like me who has very little genetic
    training (past Mendel, anyway) I would greatly appreciate it.

    I'll be glad to help if I can. Population genetics shouldn't be too much of a challenge for you; it's basically statistics (e.g., evolution by genetic drift is modeled by repeated binomial sampling).

    We have a very high rate of gene flow between "racial" or geographic groups today compared to the past, and so we can predict that gene frequencies should converge in the future. But there are two issues -- first, the rate of change by chance in very large populations is very slow; and second, some genes may be (or recently have been) subject to selection processes that maintain diversity. That second is a complicated problem because selection pressures may be different for every gene.

  • Quote: Fisher defining epistasis

    Fri, 2009-06-05 18:19 -- John Hawks

    People often complain that R. A. Fisher wrote in a hard-to-read style; unnecessarily verbose and indirect. Either I don't tend to mind, or I find that the style makes me read with greater care. In either case, there are select passages from his writings that stand out as very clear to me. His description of epistasis and dominance as deviations from additivity, in his famous 1918 paper (p. 404), is one of them:

    The steps from recessive to heterozygote and from heterozygote to dominant are genetically identical, and may change from one to the other in passing from father to son. Somatically the steps are of different importance, and the soma to some extent disguises the true genetic nature. There is in dominance a certain latency. We may say that the somatic effects of identical genetic changes are not additive, and for this reason the genetic similarity of relations is partly obscured in the statistical aggregate. A similar deviation from the addition of superimposed effects may occur between different Mendelian factors. We may use the term Epistacy to describe such deviation, which although potentially more complicated, has similar statistical effects to dominance. If the two sexes are considered as Mendelian alternatives, the fact that other Mendelian factors affect them to different extents may be regarded as an example of epistacy.

    The terms we use today are familiar by use. A biologist doesn't necessary consider how idiosyncratic is the genetic use of term "additive". When I read a passage like this, it brings to mind a long-ago time when the select group of people using a term all had read the same papers. I wonder how many geneticists still read Fisher during their training. I can tell you this: the bound volume of the Proceedings of the Royal Society of Edinburgh in our library didn't look like it's been picked up for 30 years. I mean, serious dust on the cover.

    I wrote last month about how Fisher invented "variance", and noted the very useful property that the variance is a sum of contributions from different causes. It seems remarkable that Fisher could arrive at statistical framework for identifying the interactions of multiple genes on a trait, at a time when only a relative handful of "Mendelian factors" had yet been found.

    Now that we are able to find Mendelian factors in whole-genome association studies, it's remarkable that Fisher's framework is so often forgotten!

    References:

    Fisher RA. 1918. The correlation between relatives on the supposition of Mendelian inheritance. Proc R Soc Edinburgh 52:399-433.

  • NY Times: Veterinarian-disguised Mengele brought twins to Brazilian village

    Mon, 2009-02-23 16:09 -- John Hawks

    A reader sent along this NY Times article about the town in Brazil with an unusual concentration of twins. Naturally, it's a Boys from Brazil type of scenario:

    Some researchers have suggested the darker possibility that Josef Mengele, the Nazi physician known as the Angel of Death, was involved. Mengele, residents say, roamed this region of southern Brazil, posing as a veterinarian, in the 1960s, about the time the twins explosion began. In a book published last year, an Argentine journalist, Jorge Camarasa, suggested that Mengele conducted experiments with women here that resulted in the higher rate of twins, many of them with blond hair and light-colored eyes. The experiments, locals said, may have involved new types of drugs and preparations, or even the artificial insemination Mengele claimed to know about, regarding cows and humans.

    But neither Mr. Camarasa nor any other adherent of the Mengele theory has been able to prove the escaped Nazi conducted any experiments here. Mengele, who died in Brazil in 1979, was notorious for his often deadly experiments on twins at Auschwitz, ostensibly in an effort to produce a master Aryan race for Hitler.

    Because everyone knows that's where twins come from. Nazi experiments.

    The most interesting observation is that the unusual number of twins (10 percent of births from 1990-1994) is accompanied by an unusual fraction of identical twins. However, I'd like to see a simple plot showing all similar-sized towns in Brazil. 10 percent of births across a limited time span is not very exciting if we have thousands of towns and pick out the most extreme value.

    Statistics, people. Oh yeah, I suppose the Nazis invented that, too!

  • R profiled in NY Times

    Thu, 2009-01-08 07:45 -- John Hawks

    If you do much statistics and haven't worked with R, you should try it out. The NY Times profiled the software yesterday:

    R is similar to other programming languages, like C, Java and Perl, in that it helps people perform a wide variety of computing tasks by giving them access to various commands. For statisticians, however, R is particularly useful because it contains a number of built-in mechanisms for organizing data, running calculations on the information and creating graphical representations of data sets.

    ...

    What makes R so useful — and helps explain its quick acceptance — is that statisticians, engineers and scientists can improve the software’s code or write variations for specific tasks. Packages written for R add advanced algorithms, colored and textured graphs and mining techniques to dig deeper into databases.

    The graphs are pretty, and it's free software. The article describes it as a "lingua franca" for grad students. Maybe not, but I wouldn't invest my time learning anything less powerful.

  • Bolt and Johnson as statistical outliers

    Mon, 2008-08-25 22:30 -- John Hawks

    An interesting post from Justin Wolfers about statistical outliers and sprinters, referencing a New York Times story about Usain Bolt, along with a key graphic showing Bolt's and Michael Johnson's records versus the 249 other fastest 200 meter sprint times in history. Wolfers:

    Not only does this not look like a normal distribution, it doesn’t even look like the tail of any standard distribution I’ve ever seen.

    It should be clear from this chart why few thought that the previous world record would be broken anytime soon.

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