Archive for the Bad Statistics Category

Bad Statistics, Bad Science

Posted in Bad Statistics, Science Politics, The Universe and Stuff with tags , , on July 2, 2015 by telescoper

I saw an interesting article in Nature the opening paragraph of which reads:

The past few years have seen a slew of announcements of major discoveries in particle astrophysics and cosmology. The list includes faster-than-light neutrinos; dark-matter particles producing γ-rays; X-rays scattering off nuclei underground; and even evidence in the cosmic microwave background for gravitational waves caused by the rapid inflation of the early Universe. Most of these turned out to be false alarms; and in my view, that is the probable fate of the rest.

The piece goes on to berate physicists for being too trigger-happy in claiming discoveries, the BICEP2 fiasco being a prime example. I agree that this is a problem, but it goes fare beyond physics. In fact its endemic throughout science. A major cause of it is abuse of statistical reasoning.

Anyway, I thought I’d take the opportunity to re-iterate why I statistics and statistical reasoning are so important to science. In fact, I think they lie at the very core of the scientific method, although I am still surprised how few practising scientists are comfortable with even basic statistical language. A more important problem is the popular impression that science is about facts and absolute truths. It isn’t. It’s a process. In order to advance it has to question itself. Getting this message wrong – whether by error or on purpose -is immensely dangerous.

Statistical reasoning also applies to many facets of everyday life, including business, commerce, transport, the media, and politics. Probability even plays a role in personal relationships, though mostly at a subconscious level. It is a feature of everyday life that science and technology are deeply embedded in every aspect of what we do each day. Science has given us greater levels of comfort, better health care, and a plethora of labour-saving devices. It has also given us unprecedented ability to destroy the environment and each other, whether through accident or design.

Civilized societies face rigorous challenges in this century. We must confront the threat of climate change and forthcoming energy crises. We must find better ways of resolving conflicts peacefully lest nuclear or conventional weapons lead us to global catastrophe. We must stop large-scale pollution or systematic destruction of the biosphere that nurtures us. And we must do all of these things without abandoning the many positive things that science has brought us. Abandoning science and rationality by retreating into religious or political fundamentalism would be a catastrophe for humanity.

Unfortunately, recent decades have seen a wholesale breakdown of trust between scientists and the public at large. This is due partly to the deliberate abuse of science for immoral purposes, and partly to the sheer carelessness with which various agencies have exploited scientific discoveries without proper evaluation of the risks involved. The abuse of statistical arguments have undoubtedly contributed to the suspicion with which many individuals view science.

There is an increasing alienation between scientists and the general public. Many fewer students enrol for courses in physics and chemistry than a a few decades ago. Fewer graduates mean fewer qualified science teachers in schools. This is a vicious cycle that threatens our future. It must be broken.

The danger is that the decreasing level of understanding of science in society means that knowledge (as well as its consequent power) becomes concentrated in the minds of a few individuals. This could have dire consequences for the future of our democracy. Even as things stand now, very few Members of Parliament are scientifically literate. How can we expect to control the application of science when the necessary understanding rests with an unelected “priesthood” that is hardly understood by, or represented in, our democratic institutions?

Very few journalists or television producers know enough about science to report sensibly on the latest discoveries or controversies. As a result, important matters that the public needs to know about do not appear at all in the media, or if they do it is in such a garbled fashion that they do more harm than good.

Years ago I used to listen to radio interviews with scientists on the Today programme on BBC Radio 4. I even did such an interview once. It is a deeply frustrating experience. The scientist usually starts by explaining what the discovery is about in the way a scientist should, with careful statements of what is assumed, how the data is interpreted, and what other possible interpretations might be and the likely sources of error. The interviewer then loses patience and asks for a yes or no answer. The scientist tries to continue, but is badgered. Either the interview ends as a row, or the scientist ends up stating a grossly oversimplified version of the story.

Some scientists offer the oversimplified version at the outset, of course, and these are the ones that contribute to the image of scientists as priests. Such individuals often believe in their theories in exactly the same way that some people believe religiously. Not with the conditional and possibly temporary belief that characterizes the scientific method, but with the unquestioning fervour of an unthinking zealot. This approach may pay off for the individual in the short term, in popular esteem and media recognition – but when it goes wrong it is science as a whole that suffers. When a result that has been proclaimed certain is later shown to be false, the result is widespread disillusionment.

The worst example of this tendency that I can think of is the constant use of the phrase “Mind of God” by theoretical physicists to describe fundamental theories. This is not only meaningless but also damaging. As scientists we should know better than to use it. Our theories do not represent absolute truths: they are just the best we can do with the available data and the limited powers of the human mind. We believe in our theories, but only to the extent that we need to accept working hypotheses in order to make progress. Our approach is pragmatic rather than idealistic. We should be humble and avoid making extravagant claims that can’t be justified either theoretically or experimentally.

The more that people get used to the image of “scientist as priest” the more dissatisfied they are with real science. Most of the questions asked of scientists simply can’t be answered with “yes” or “no”. This leaves many with the impression that science is very vague and subjective. The public also tend to lose faith in science when it is unable to come up with quick answers. Science is a process, a way of looking at problems not a list of ready-made answers to impossible problems. Of course it is sometimes vague, but I think it is vague in a rational way and that’s what makes it worthwhile. It is also the reason why science has led to so many objectively measurable advances in our understanding of the World.

I don’t have any easy answers to the question of how to cure this malaise, but do have a few suggestions. It would be easy for a scientist such as myself to blame everything on the media and the education system, but in fact I think the responsibility lies mainly with ourselves. We are usually so obsessed with our own research, and the need to publish specialist papers by the lorry-load in order to advance our own careers that we usually spend very little time explaining what we do to the public or why.

I think every working scientist in the country should be required to spend at least 10% of their time working in schools or with the general media on “outreach”, including writing blogs like this. People in my field – astronomers and cosmologists – do this quite a lot, but these are areas where the public has some empathy with what we do. If only biologists, chemists, nuclear physicists and the rest were viewed in such a friendly light. Doing this sort of thing is not easy, especially when it comes to saying something on the radio that the interviewer does not want to hear. Media training for scientists has been a welcome recent innovation for some branches of science, but most of my colleagues have never had any help at all in this direction.

The second thing that must be done is to improve the dire state of science education in schools. Over the last two decades the national curriculum for British schools has been dumbed down to the point of absurdity. Pupils that leave school at 18 having taken “Advanced Level” physics do so with no useful knowledge of physics at all, even if they have obtained the highest grade. I do not at all blame the students for this; they can only do what they are asked to do. It’s all the fault of the educationalists, who have done the best they can for a long time to convince our young people that science is too hard for them. Science can be difficult, of course, and not everyone will be able to make a career out of it. But that doesn’t mean that it should not be taught properly to those that can take it in. If some students find it is not for them, then so be it. I always wanted to be a musician, but never had the talent for it.

I realise I must sound very gloomy about this, but I do think there are good prospects that the gap between science and society may gradually be healed. The fact that the public distrust scientists leads many of them to question us, which is a very good thing. They should question us and we should be prepared to answer them. If they ask us why, we should be prepared to give reasons. If enough scientists engage in this process then what will emerge is and understanding of the enduring value of science. I don’t just mean through the DVD players and computer games science has given us, but through its cultural impact. It is part of human nature to question our place in the Universe, so science is part of what we are. It gives us purpose. But it also shows us a way of living our lives. Except for a few individuals, the scientific community is tolerant, open, internationally-minded, and imbued with a philosophy of cooperation. It values reason and looks to the future rather than the past. Like anyone else, scientists will always make mistakes, but we can always learn from them. The logic of science may not be infallible, but it’s probably the best logic there is in a world so filled with uncertainty.



Still Not Significant

Posted in Bad Statistics with tags , on May 27, 2015 by telescoper

I just couldn’t resist reblogging this post because of the wonderful list of meaningless convoluted phrases people use when they don’t get a “statistically significant” result. I particularly like:

“a robust trend toward significance”.

It’s scary to think that these were all taken from peer-reviewed scientific journals…

Probable Error


What to do if your p-value is just over the arbitrary threshold for ‘significance’ of p=0.05?

You don’t need to play the significance testing game – there are better methods, like quoting the effect size with a confidence interval – but if you do, the rules are simple: the result is either significant or it isn’t.

So if your p-value remains stubbornly higher than 0.05, you should call it ‘non-significant’ and write it up as such. The problem for many authors is that this just isn’t the answer they were looking for: publishing so-called ‘negative results’ is harder than ‘positive results’.

The solution is to apply the time-honoured tactic of circumlocution to disguise the non-significant result as something more interesting. The following list is culled from peer-reviewed journal articles in which (a) the authors set themselves the threshold of 0.05 for significance, (b) failed to achieve that threshold value for…

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One More for the Bad Statistics in Astronomy File…

Posted in Bad Statistics, The Universe and Stuff with tags , , , , , on May 20, 2015 by telescoper

It’s been a while since I last posted anything in the file marked Bad Statistics, but I can remedy that this morning with a comment or two on the following paper by Robertson et al. which I found on the arXiv via the Astrostatistics Facebook page. It’s called Stellar activity mimics a habitable-zone planet around Kapteyn’s star and it the abstract is as follows:

Kapteyn’s star is an old M subdwarf believed to be a member of the Galactic halo population of stars. A recent study has claimed the existence of two super-Earth planets around the star based on radial velocity (RV) observations. The innermost of these candidate planets–Kapteyn b (P = 48 days)–resides within the circumstellar habitable zone. Given recent progress in understanding the impact of stellar activity in detecting planetary signals, we have analyzed the observed HARPS data for signatures of stellar activity. We find that while Kapteyn’s star is photometrically very stable, a suite of spectral activity indices reveals a large-amplitude rotation signal, and we determine the stellar rotation period to be 143 days. The spectral activity tracers are strongly correlated with the purported RV signal of “planet b,” and the 48-day period is an integer fraction (1/3) of the stellar rotation period. We conclude that Kapteyn b is not a planet in the Habitable Zone, but an artifact of stellar activity.

It’s not really my area of specialism but it seemed an interesting conclusions so I had a skim through the rest of the paper. Here’s the pertinent figure, Figure 3,


It looks like difficult data to do a correlation analysis on and there are lots of questions to be asked  about  the form of the errors and how the bunching of the data is handled, to give just two examples.I’d like to have seen a much more comprehensive discussion of this in the paper. In particular the statistic chosen to measure the correlation between variates is the Pearson product-moment correlation coefficient, which is intended to measure linear association between variables. There may indeed be correlations in the plots shown above, but it doesn’t look to me that a straight line fit characterizes it very well. It looks to me in some of the  cases that there are simply two groups of data points…

However, that’s not the real reason for flagging this one up. The real reason is the following statement in the text:



No matter how the p-value is arrived at (see comments above), it says nothing about the “probability of no correlation”. This is an error which is sadly commonplace throughout the scientific literature, not just astronomy.  The point is that the p-value relates to the probability that the given value of the test statistic (in this case the Pearson product-moment correlation coefficient, r) would arise by chace in the sample if the null hypothesis H (in this case that the two variates are uncorrelated) were true. In other words it relates to P(r|H). It does not tells us anything directly about the probability of H. That would require the use of Bayes’ Theorem. If you want to say anything at all about the probability of a hypothesis being true or not you should use a Bayesian approach. And if you don’t want to say anything about the probability of a hypothesis being true or not then what are you trying to do anyway?

If I had my way I would ban p-values altogether, but it people are going to use them I do wish they would be more careful about the statements make about them.

The Law of Averages

Posted in Bad Statistics, Crosswords with tags , , on March 4, 2015 by telescoper

Just a couple of weeks ago I found myself bemoaning my bad luck in the following terms

A few months have passed since I last won a dictionary as a prize in the Independent Crossword competition. That’s nothing remarkable in itself, but since my average rate of dictionary accumulation has been about one a month over the last few years, it seems a bit of a lull.  Have I forgotten how to do crosswords and keep sending in wrong solutions? Is the Royal Mail intercepting my post? Has the number of correct entries per week suddenly increased, reducing my odds of winning? Have the competition organizers turned against me?

In fact, statistically speaking, there’s nothing significant in this gap. Even if my grids are all correct, the number of correct grids has remained constant, and the winner is pulled at random  from those submitted (i.e. in such a way that all correct entries are equally likely to be drawn) , then a relatively long unsuccessful period such as I am experiencing at the moment is not at all improbable. The point is that such runs are far more likely in a truly random process than most people imagine, as indeed are runs of successes. Chance coincidence happen more often than you think.

Well, as I suspected would happen soon my run of ill fortune came to an end today with the arrival of this splendid item in the mail:


It’s the prize for winning Beelzebub 1303, the rather devilish prize cryptic in the Independent on Sunday Magazine. It’s nice to get back to winning ways. Now what’s the betting I’ll now get a run of successes?

P.S. I used the title “Law of Averages” just so I could point out in a footnote that there’s actually no such thing.

Uncertainty, Risk and Probability

Posted in Bad Statistics, Science Politics with tags , , , , , , , , on March 2, 2015 by telescoper

Last week I attended a very interesting event on the Sussex University campus, the Annual Marie Jahoda Lecture which was given this year by Prof. Helga Nowotny a distinguished social scientist. The title of the talk was A social scientist in the land of scientific promise and the abstract was as follows:

Promises are a means of bringing the future into the present. Nowhere is this insight by Hannah Arendt more applicable than in science. Research is a long and inherently uncertain process. The question is open which of the multiple possible, probable or preferred futures will be actualized. Yet, scientific promises, vague as they may be, constitute a crucial link in the relationship between science and society. They form the core of the metaphorical ‘contract’ in which support for science is stipulated in exchange for the benefits that science will bring to the well-being and wealth of society. At present, the trend is to formalize scientific promises through impact assessment and measurement. Against this background, I will present three case studies from the life sciences: assisted reproductive technologies, stem cell research and the pending promise of personalized medicine. I will explore the uncertainty of promises as well as the cunning of uncertainty at work.

It was a fascinating and wide-ranging lecture that touched on many themes. I won’t try to comment on all of them, but just pick up on a couple that struck me from my own perspective as a physicist. One was the increasing aversion to risk demonstrated by research funding agencies, such as the European Research Council which she helped set up but described in the lecture as “a clash between a culture of trust and a culture of control”. This will ring true to any scientist applying for grants even in “blue skies” disciplines such as astronomy: we tend to trust our peers, who have some control over funding decisions, but the machinery of control from above gets stronger every day. Milestones and deliverables are everything. Sometimes I think in order to get funding you have to be so confident of the outcomes of your research to that you have to have already done it, in which case funding isn’t even necessary. The importance of extremely speculative research is rarely recognized, although that is where there is the greatest potential for truly revolutionary breakthroughs.

Another theme that struck me was the role of uncertainty and risk. This grabbed my attention because I’ve actually written a book about uncertainty in the physical sciences. In her lecture, Prof. Nowotny referred to the definition (which was quite new to me) of these two terms by Frank Hyneman Knight in a book on economics called Risk, Uncertainty and Profit. The distinction made there is that “risk” is “randomness” with “knowable probabilities”, whereas “uncertainty” involves “randomness” with “unknowable probabilities”. I don’t like these definitions at all. For one thing they both involve a reference to “randomness”, a word which I don’t know how to define anyway; I’d be much happier to use “unpredictability”. Even more importantly, perhaps, I find the distinction between “knowable” and “unknowable” probabilities very problematic. One always knows something about a probability distribution, even if that something means that the distribution has to be very broad. And in any case these definitions imply that the probabilities concerned are “out there”, rather being statements about a state of knowledge (or lack thereof). Sometimes we know what we know and sometimes we don’t, but there are more than two possibilities. As the great American philosopher and social scientist Donald Rumsfeld (Shurely Shome Mishtake? Ed) put it:

“…as we know, there are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns – the ones we don’t know we don’t know.”

There may be a proper Bayesian formulation of the distinction between “risk” and “uncertainty” that involves a transition between prior-dominated (uncertain) and posterior-dominated (risky), but basically I don’t see any qualititative difference between the two from such a perspective.

Anyway, it was a very interesting lecture that differed from many talks I’ve attended about the sociology of science in that the speaker clearly understood a lot about how science actually works. The Director of the Science Policy Research Unit invited the Heads of the Science Schools (including myself) to dinner with the speaker afterwards, and that led to the generation of many interesting ideas about how we (I mean scientists and social scientists) might work better together in the future, something we really need to do.

Digit Ratio Survey

Posted in Bad Statistics, Biographical with tags , , , on February 9, 2015 by telescoper

I was intrigued by an article I found at the weekend which reports on a (no doubt rigorous) scientific study that claims a connection between the relative lengths of index and ring fingers and the propensity to be promiscuous. The assertion is that people whose ring finger is longer than their index finger like to play around, while those whose index finger is longer than their ring finger are inclined to fidelity. Obviously, since the study involves the University of Oxford’s Department of Experimental Psychology, there can be do doubt whatsoever about its reliablity or scientific credibility, just like the dozens of other things supposed to be correlated with digit ratio. Ahem.

I do remember a similar study some time ago that claimed that men with with a longer index finger (2D) than ring finger (4D) (i.e. with a 2D:4D digit ratio greater than one) were much more likely to be gay than those with a digit ratio lower than one. Taken with this new finding it proves what we all knew all along: that heterosexuals are far more likely to be promiscuous than homosexuals.

For the record, here is a photograph of my left hand (which, on reflection, is similar to my right, and which clearly shows a 2D:4D ratio greater than unity):


Inspired by the stunning application of the scientific method described in the report, I have decided to carry out a rigorous study of my own. I have heard that, at least among males, it is much more common to have digit ratio less than one than greater than one but I can’t say I’ve noticed it myself. Furthermore previously unanswered question in the literature is whether there is a connection between digit ratio and the propensity to read blogs. I will know subject this to rigorous scientific scrutiny by inviting readers of this blog to complete the following simply survey. I look forward to publishing my findings in due course in the Journal of Irreproducible Results.

PS. The actual paper on which the report was based is by Rafael Wlodarski, John Manning, and R. I. M. Dunbar,

Doomsday is Cancelled…

Posted in Bad Statistics, The Universe and Stuff with tags , on November 25, 2014 by telescoper

Last week I posted an item that included a discussion of the Doomsday Argument. A subsequent comment on that post mentioned a paper by Ken Olum, which I finally got around to reading over the weekend, so I thought I’d post a link here for those of you worrying that the world might come to an end before the Christmas holiday.

You can find Olum’s paper on the arXiv here. The abstract reads (my emphasis):

If the human race comes to an end relatively shortly, then we have been born at a fairly typical time in history of humanity. On the other hand, if humanity lasts for much longer and trillions of people eventually exist, then we have been born in the first surprisingly tiny fraction of all people. According to the Doomsday Argument of Carter, Leslie, Gott, and Nielsen, this means that the chance of a disaster which would obliterate humanity is much larger than usually thought. Here I argue that treating possible observers in the same way as those who actually exist avoids this conclusion. Under this treatment, it is more likely to exist at all in a race which is long-lived, as originally discussed by Dieks, and this cancels the Doomsday Argument, so that the chance of a disaster is only what one would ordinarily estimate. Treating possible and actual observers alike also allows sensible anthropic predictions from quantum cosmology, which would otherwise depend on one’s interpretation of quantum mechanics.

I think Olum does identify a logical flaw in the argument, but it’s by no means the only one. I wouldn’t find it at all surprising to be among the first “tiny fraction of all people”, as my genetic characteristics are such that I could not be otherwise. But even if you’re not all that interested in the Doomsday Argument I recommend you read this paper as it says some quite interesting things about the application of probabilistic reasoning elsewhere in cosmology, an area in which quite a lot is written that makes no sense to me whatsoever!



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