Positivity: Retract The Bathwater, Save The Baby

By Neuroskeptic | July 28, 2013 7:24 am

Last week I covered a new paper Brown et al (2013) in the journal American Psychologist.

The article was strongly critical of a highly-cited paper that appeared in the same journal 8 years ago, Positive affect and the complex dynamics of human flourishing, by Barbara Fredrickson and Marcial Losada.

See my original post – or better yet, the papers in question – for details, but in a nutshell, the argument was that Fredrickson and Losada misused mathematics. They presented a nonlinear series of equations (a Lorenz system) and claimed that it provided insight into the dynamics of human emotion and group performance.

Brown et al accused that model of being flawed on an elementary level.

The story has attracted a lot of interest – my post has received 8,000 pageviews so far and still going strong. For responses, see e.g. here and here.

I was criticized for describing Fredrickson & Losada (2005) as “complete rubbish”. But I challenge anyone to read that paper, and then Brown et al. (2013), and come away with a qualitatively different conclusion.

I’ve yet to see a defence of the equations. For instance, in her response to Brown et al, Fredrickson herself repeatedly describes the mathematics as “questionable”, and makes no attempt to rebut the mathematical criticisms:

I’ve come to see sufficient reason to question the particular mathematical framework Losada and I adopted to represent and test the concept of a [positivity ratio]…

Fredrickson’s argument is that her psychological theory (‘positivity ratios’) is sound without the mathematical model.

The claims Losada and I made… were supported by three interwoven elements: psychological theory, mathematical modelling, and quantitative data. Here I unthread the now-questionable element of mathematical modelling from this braid…

She describes the equations in less than flattering terms:

Research on the full value of positivity ratios remains in its infancy.

Although in the wake of Brown and colleagues’ (2013) work, this infant may seem a bit sullied, in my estimation a good scrubbing reveals a healthy baby well worth letting grow up. Losada’s mathematical work, which to date he has elected not to defend, may well be the smudge that needs removing.

Whereas Brown and colleagues’ article revealed this smudge, my hope is that the present article effectively washes it away. Perhaps we can now toss out the muddied bath water…

Note that I said nothing about Fredrickson’s research as a whole, or her theory of how positive emotion promotes flourishing. Neither did Brown et al. What I called ‘complete rubbish’ was the paper based on the mathematical work that even the first author now calls a “smudge” on her baby.

As for Losada, American Psychologist approached him for comment, but did not choose to respond. So it appears that neither of the original authors has confidence in the mathematical model – which formed about two thirds of the text of the 2005 paper as well as determining the title (‘complex dynamics’).


Well – ‘complete rubbish’, then? I was blunt, but I can’t see anyone who disagrees with the sentiment, only with my phrasing of it. I don’t generally write about academic papers in those terms, but this is an exceptional case.

Fredrickson’s response piece is, itself, a kind of argument that we should treat the 2005 mathematical model as an exceptional case – an exceptionally weak strand of her positivity research. She presents a review of the empirical psychology literature supporting her theories and says that, those Lorenz equations aside, everything else stands up to scrutiny.

If so, I suggest she considers making a clean break. I mean: retracting Fredrickson & Losada (2005) on the grounds that she no longer has confidence in the work presented.

She doesn’t have to retract it. The paper is no worse now than it was when it passed peer review (whatever this says about the original peer review), so I would say that the authors have a right to leave it there if they want. But if so, it will remain out there, the single most cited paper about ‘positivity ratios’ (I think), and one of Fredrickson’s most cited works. The smudge would remain.

I would advise that, in the interests of saving that baby, the bathwater should be drained as thoroughly as possible. If the Losada model was truly an exception, exceptional action is called for.

ResearchBlogging.orgFredrickson BL, & Losada MF (2005). Positive affect and the complex dynamics of human flourishing. The American psychologist, 60 (7), 678-86 PMID: 16221001

Fredrickson BL (2013). Updated Thinking on Positivity Ratios American Psychologist DOI: 10.1037/a0033584

  • S.T.

    I don’t know if I agree with retracting the F & L article on the grounds that one no longer has confidence in the work. Reasoning from the perspective that science is a process, I wonder if that would then also imply that when findings do not turn out to be true (leaving aside if, and how then, this can ever really be concluded) that the corresponding articles would all have to be retracted?

    I think retraction of papers in case of data-fabrication for instance is usefiul, but I am trying to find the borders regarding other issues, like faulty math, and note that I find this hard to do.

    Maybe this F & L-situation does indicate that continuous post-publication peer-review could be useful: when people would read the article, for possible subsequent citing, they would then have information regarding its possible flaws and can take this into account.

    • http://blogs.discovermagazine.com/neuroskeptic/ Neuroskeptic

      It’s a very good question, but my point was not that the article ought to be retracted – on grounds of principle – but that it would be a good idea to retract it, in this case, because it would help the theory (and positive psychology as a whole) ‘move on’.

      • S.T.



        “This study examines citations to retracted papers in the scientific literature and the context of these citations. Citations to 211 articles, published between 1996 and 2000, were analyzed; about 30% of the citations occurred after the articles had been retracted. An in-depth analysis of the context of four selected articles was conducted. Most of the citations were
        affirmative; only five of the 137 citations we re negative. It is concluded that, with electronic publication and in electronic databases, retractions should be more closely linked with the article retracted.”

        Maybe closely linked retraction information also fits in with the idea of post-publiication peer-review in the sense that relevant information is directly tied to the original source.

      • Eric Charles

        I think there is a big difference between retracting an article because the conclusions were later found to be wrong (i.e., further science supported an alternative) and retracting an article because you now believe it is seriously flawed (i.e., the original science was just bad). The later should certainly be encouraged.

  • Dale Barr

    We have been discussing this over at Rolf Zwaan’s blog as well. http://rolfzwaan.blogspot.co.uk/2013/07/the-gains-and-pains-of-joint-authorship.html

    I think it is important to keep in mind during the discussion that this paper is not “wrong” in the conventional scientific sense of having flawed assumptions, erroneous statistical methods, confounds in the design, being a Type I error, etc. In fact, there is nothing “wrong” with the paper apart from being chock full of mathematical nonsense to make the ideas sound weighty and impressive.

    The blame for Fredrickson and Losada falls not only on the authors. Let us not forget that there was an editor who decided to publish this paper. Mistakes happen, of course, and editors are busy people and so things can slip through. However, the integrity of a journal is defined not only by the papers they choose to accept, but also by what they allow to let stand.

    Papers like this get published all the time, but usually in obscure, low tier journals. But American Psychologist is what might be called the “flagship” journal of the American Psychological Association, the major scholarly association for psychology in the US. People pay attention to what gets published there. It is the journal where APA prizes, honors, awards, etc are announced. It is also the journal that published Kahneman’s Nobel Prize Keynote speech.

    It is an embarrassment to the APA to let this article stand, and it is also an embarrassment to the field of psychology.

  • Lisa Sansom

    Well I’m honoured! I’ve never had a comment referenced before! I’d like to clarify that it wasn’t so much the “rubbish” that I was worried about – it was that you were only critiquing without adding to the discourse. Very easy to criticize – less easy to say what should be done in a positive and productive direction. Should all psychologists now start learning theoretical mathematics as well? But I am glad that you have also reviewed Fredrickson’s side. I can’t say anything about the math. Not my field. I asked a physicist to explain it to me, and we didn’t get very far. I am concerned that Losada has not come out and made any comments – that does not speak well for the modelling either. Yet Fredrickson does also say (and I don’t have the paper in front of me to cite directly) something along the lines of how psychology does need to embrace non-linear math / modelling to be able to more accurately understand the complexities of human behaviour. Perhaps the Losada model was misguided, and may now be termed as “rubbish” but what an interesting line of inquiry and scrutiny has opened up! I would be wonderful, as Fredrickson suggests, to clean up the baby and let it mature a bit.

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  • andrés navas

    Dear all,

    much before this I posted a Note in the french scientific site “Images des Mathematiques” of the CNRS:

    From a mathematical point of view, all of this is nonsense.

    • http://blogs.discovermagazine.com/neuroskeptic/ Neuroskeptic

      That’s extremely interesting…thanks for commenting!

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Neuroskeptic is a British neuroscientist who takes a skeptical look at his own field, and beyond. His blog offers a look at the latest developments in neuroscience, psychiatry and psychology through a critical lens.


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