View source for Critical positivity ratio

{{Short description|Discredited statistical finding in positive psychology}}
{{lead rewrite | reason = lead violates WP:INTRO and other guidelines in presenting unique content (being the article) rather than summarizing it | date = February 2022}}
{{Update|date=April 2020}}
The '''critical positivity ratio''' (also known as the "Losada ratio" or the "Losada line"{{citation needed lead|date=February 2022}})<!--NO CITATION anywhere on this, and no mention in the article.--> is a largely discredited concept in [[positive psychology]] positing an exact ratio of positive to negative emotions which distinguishes "flourishing" people from "languishing" people.{{citation needed|date = February 2022}}<!--Prior Guardian citation does NOT support KEY element of sentence, the "largely discredited" assertion. This must be from a citation, and it is not in the Guardian.--> The ratio was proposed by psychologists [[Barbara Fredrickson]] and [[Marcial Losada]], who believed that they had identified an experimental measure of [[affect (psychology)|affect]] whose model-derived positive-to-negative ratio of 2.9013 defined a critical separation between flourishing and languishing individuals, as reported in their 2005 paper in ''[[American Psychologist]]''.<ref name="positive"/>{{primary source inline|date = February 2022}} This concept of a critical positivity ratio was widely embraced by academic psychologists and the lay public; Fredrickson and Losada's paper had been cited more than 320 times by January 2014,<ref name=BowerSciNews130812/><ref name="guardian"/><ref name=CitationCountNote>Will Wilkinson, writing for ''[[The Daily Beast]]'', see citation following, states that Fredrickson & Losada (2005) "garnered almost 1,000 citations in less than a decade", which places it at odds with ''The Guardian'', who interviews Brown and suggests it had been cited ca. 350 times by January 2014 (which is at about at the same one decade mark). Likewise, the ''Science News'' source, see preceding, quoting Sokal, sets the number just above 320. ''The Guardian'' interview with Brown's and the ''Science News'' with Sokal's more conservative numbers are the basis for the statement here.</ref> and Fredrickson wrote a popular book expounding the concept of "the 3-to-1 ratio that will change your life".<ref name=":6"/> In it she wrote, "just as zero degrees Celsius is a special number in thermodynamics, the 3-to-1 positivity ratio may well be a magic number in human psychology."<ref name="guardian"/>

The first consequential re-evaluation of the mathematical modeling behind the critical positivity ratio was published in 2008 by a group of Finnish researchers from the Systems Analysis Laboratory at [[Aalto University]] (Jukka Luoma, [[Raimo Hämäläinen]], and [[Esa Saarinen]]).<ref name=LuomaHämäläinenSaarinen2008/> The authors noted that "only very limited explanations are given about the modeling process and the meaning and interpretation of its parameters... [so that] the reasoning behind the model equations remains unclear to the reader"; moreover, they noted that "the model also produces strange and previously unreported behavior under certain conditions... [so that] the predictive validity of the model also becomes problematic."<ref name=LuomaHämäläinenSaarinen2008/> Losada's 1999 modeling article was also critiqued by Andrés Navas in a French language publication, a note in the [[CNRS]] publication, ''Images des Mathématiques''.<ref name = Navas/><ref name="brown-response"/> Neither of these articles received broad attention at the times of their publication.{{citation needed|date = February 2022}}

Later, but of critical importance, the Fredrickson and Losada work on modeling the positivity ratio aroused the skepticism of Nick Brown, a graduate student in applied positive psychology, who questioned whether such work could reliably make such broad claims, and perceived that the paper's mathematical claims underlying the critical positivity ratio were suspect.<ref name="chronicle"/> Brown contacted and ultimately collaborated with physics and maths professor [[Alan Sokal]] and psychology professor Harris Friedman on a re-analysis of the paper's data<ref name="chronicle"/> (hereafter the Brown-Sokal-Friedman rebuttal<ref name="wishful"/>). They argued that Losada's earlier work on positive psychology and Fredrickson and Losada's 2005 critical positivity ratio paper contained "numerous fundamental conceptual and mathematical errors",<ref name="wishful"/> errors of a magnitude that completely invalidated their claims.{{citation needed|date = February 2022|reason=This needs to be a secondary source that describes what Brown-Sokal-Friedman say; that is, it needs to avoid [[WP:OR ]] interpretation of primary sources by Wikipedia editors.}}

Fredrickson wrote a response in which she conceded that the mathematical aspects of the critical positivity ratio were "questionable" and that she had "neither the expertise nor the insight" to defend them, but she maintained that the empirical evidence for the existence of a critical positivity ratio was solid.<ref name="updated"/> Brown, Sokal, and Friedman, the rebuttal authors, published their response to Fredrickson's "Update" the next year, maintaining that there was no evidence for a critical positivity ratio.<ref name="brown-response"/> Losada declined to respond to the criticism (indicating to the ''Chronicle of Higher Education'' that he was too busy running his consulting business).<ref name="chronicle"/>{{verification needed|date = February 2022}} Hämäläinen and colleagues responded later, passing over the Brown-Sokal-Friedman rebuttal claim of failed criteria for use of differential equations in modeling, instead arguing that there were no fundamental errors in the mathematics itself, only problems related to the model's justification and interpretation.<ref name=HämäläinenLuoma2014Response/>{{primary source inline|date = February 2022}}

A formal retraction for the mathematical modeling elements of the Losada and Fredrickson (2005) paper was issued by the journal,  ''American Psychologist'', concluding that both the specific critical positivity ratio of 2.9013 and its upper limit were invalid.<ref name="correction"/> The fact that the problems with the paper went unnoticed for years despite the widespread adulatory publicity surrounding the critical positivity ratio concept contributed to a perception of social psychology as a field lacking scientific soundness and rigorous critical thinking.<ref name="beast"/><ref name="chronicle"/><ref name="scientist"/> Sokal later stated, "The main claim made by Fredrickson and Losada is so implausible on its face that some red flags ought to have been raised",<ref name="chronicle"/> as would only happen broadly in graduate student Brown's initiating the collaboration that resulted in the Brown-Sokal-Friedman rebuttal.<ref name="chronicle"/>

==Background==
Building on research by [[Barbara Fredrickson]] suggesting that individuals with a higher ratio of positive to negative emotions tend to have more successful life outcomes,<ref>E.g., see {{cite journal | author = Fredrickson, B. L. | date = 2004 | title = The Broaden-and-Build Theory of Positive Emotions | journal = Philos. Trans. R. Soc. Lond., B, Biol. Sci. | volume = 359 | issue = 1449| pages = 1367–1377 | doi = 10.1098/rstb.2004.1512 | pmid = 15347528 | pmc = 1693418 }}</ref> and on studies by [[Marcial Losada]] applying [[differential equations]] from [[fluid dynamics]] to human emotions,{{citation needed|date = February 2022}} Fredrickson and Losada proposed as informative a ratio of positive to negative [[affect (psychology)|affect]] derived from [[nonlinear dynamics]] modelling (based on [[Lorenz system]]s), which appeared in 2005 in a paper in ''[[American Psychologist]]''.<ref name="positive">{{cite journal | journal=[[American Psychologist|Am. Psychol.]] | title=Positive affect and the complex dynamics of human flourishing. | vauthors=Fredrickson BL, Losada MF | volume=60 | issue = 7 | year=2005 | pages=678–86 | doi=10.1037/0003-066X.60.7.678 | pmid=16221001 | pmc=3126111}}{{Erratum|doi=10.1037/a0034435|pmid=16221001|http://retractionwatch.com/2013/09/19/fredrickson-losada-positivity-ratio-paper-partially-withdrawn/ ''Retraction Watch''}}</ref> The derived combination of expressions and default parameters led them to conclude that a critical ratio of positive to negative affect of exactly 2.9013 separated flourishing from languishing individuals, and to argue that the ideal [[positivity/negativity ratio]] lies between 2.9013 and an upper limit ratio of 11.6346. Hence, they claimed that their model predicted cut-off points for the minimum and maximum positivity ratios within which one should observe qualitative changes in an individual's level of flourishing, specifically, that those within this range of ratios would "flourish", and those outside would "languish".<ref name="positive"/>{{primary source inline|date = February 2022|reason=Needs to be presenting descriptions of primary source aims and conclusions from secondary sources, and using primary sources as supplemental citations—and not presenting editor [[WP:OR]] interpretations as article text.}} As of January 2014, the 2005 Fredrickson and Losada's paper had been cited more than 320 times in the psychology literature.<ref name=BowerSciNews130812>{{cite news | author= Bower, Bruce | date=August 12, 2013 | title=Ratio for a Good Life Exposed as 'Nonsense' | work=[[Science News|Sci. News]] | url=https://www.sciencenews.org/article/ratio-good-life-exposed-nonsense | access-date=2013-08-15 | quote = 'What’s shocking is not just that this piece of pseudomathematical nonsense received 322 scholarly citations and 164,000 web mentions, but that no one criticized it publicly for eight years, not even supposed experts in the field,' Sokal says.}}</ref><ref name="guardian">{{cite news | work = [[The Guardian]] | title = Interview: The British Amateur Who Debunked the Mathematics of Happiness | date = 18 January 2014 | first = Andrew | last = Anthony | url = https://www.theguardian.com/science/2014/jan/19/mathematics-of-happiness-debunked-nick-brown |access-date = February 10, 2022 | quote = Fredrickson subsequently removed the critical chapter that outlines Losada's input from further editions of Positivity. She has avoided speaking to... the press but in an email ... maintained that "on empirical grounds, yes, tipping points are highly probable" in relation to positive emotions and flourishing.}}</ref><ref name=CitationCountNote/>{{better source|date = February 2022}}

==Criticism==
===Initially ignored questioning===
The first critical evaluation of the mathematical modeling behind the critical positivity ratio was published by a group of Finnish researchers—Luoma, [[Raimo Hämäläinen|Hämäläinen]], and [[Esa Saarinen|Saarinen]] of the Systems Analysis Laboratory at [[Aalto University]]—in 2008.<ref name=LuomaHämäläinenSaarinen2008>{{Cite journal|last1=Luoma|first1=Jukka|last2=Hämäläinen|first2=Raimo P.|last3=Saarinen|first3=Esa|date=2008-08-27|title=Perspectives on team dynamics: Meta learning and systems intelligence|journal=[[Systems Research and Behavioral Science|Syst. Res. Behav. Sci.]]| volume=25| issue=6| pages=757–767| url = https://onlinelibrary.wiley.com/doi/epdf/10.1002/sres.905 | url-access = subscription | access-date = February 11, 2022 | doi=10.1002/sres.905|issn=1092-7026}}</ref> The authors noted that "[o]nly very limited explanations are given about the modeling process and the meaning and interpretation of its parameters... [so that] the reasoning behind the model equations remains unclear to the reader"; moreover, they noted that "the model also produces strange and previously unreported behavior under certain conditions... [so that] the predictive validity of the model also becomes problematic."<ref name=LuomaHämäläinenSaarinen2008/> Not widely impactful at the time,{{citation needed|date = February 2022}}<!--The evidence that this work only becan receiving attention, after the Brown-Sokal-Friedman rebuttal needs to be cited here.--> Losada's earlier modeling article was also critiqued by Andrés Navas in a French language publication, a note in the [[CNRS]] publication, "Images des Mathématiques",<ref name = Navas>{{cite journal | author = Navas, Andrés | date = 2011 | title = Un cas d'inconscience (?) [A case of unconsciousness (?)] | journal = Images des Mathématiques | url = http://images.math.cnrs.fr/Un-cas-d-inconscience,1004.html | access-date = February 11, 2022  | language = fr | quote = Outre le fait qu'il n'y a pas de justification théorique du modèle proposé, sa pertinence peut être mise en cause par le fait que les enregistrements auxquels on se réfère ne sont pas fournis dans l'article plus risquées. [Besides the fact that there is no theoretical justification for the proposed model, its relevance can be questioned by the fact that the records to which reference is made are not provided in the article.]}} For the full machine translation, by Google Translate, on February 11, 2022, see [https://images-math-cnrs-fr.translate.goog/Un-cas-d-inconscience-1004?lang=es&id_forum=4154&_x_tr_sch=http&_x_tr_sl=fr&_x_tr_tl=en&_x_tr_hl=en&_x_tr_pto=sc this link].</ref> which also failed to attract a wide readership.{{citation needed|date = February 2022}}<!--See last in-text note.--> In their followup to Fredrickson's immediate response to the rebuttal, Brown, Sokal, and Friedman note as a footnote to their submission:<blockquote>After the publication of Brown et al. (2013), Andrés Navas kindly drew our attention to his article (Navas, 2011) in which a very similar (though briefer) critique of Losada (1999) was made. [This footnote was unfortunately omitted from the published version of this article, due to space limitations.]<ref name="brown-response"/></blockquote>

===The Brown-Sokal-Friedman rebuttal===
The Fredrickson and Losada work on modeling the positivity ratio aroused the skepticism of Nick Brown, a graduate student in applied positive psychology, who questioned whether such work could reliably make such broad claims, and perceived that the paper's mathematical claims were suspect.<ref name="chronicle">{{cite web | work = [[Chronicle of Higher Education|Chron. High. Educ.]] | title = The Magic Ratio That Wasn't | first = Tom | last = Bartlett | url = http://chronicle.com/blogs/percolator/the-magic-ratio-that-wasnt/33279 | date = 5 August 2013 | access-date = February 11, 2022 }}</ref> Brown contacted and ultimately collaborated with physics and maths professor [[Alan Sokal]] and psychology professor Friedman on a re-analysis of the paper's data.<ref name="chronicle"/> The result was a strong critique of the critical positivity ratio in its entirety by Brown, Sokal, and Friedman, that appeared in a 2013 article in ''[[American Psychologist]]'', here referred to as the Brown-Sokal-Friedman rebuttal.<ref name="wishful">{{cite journal | journal=[[American Psychologist|Am. Psychol.]] | title=The complex dynamics of wishful thinking: the critical positivity ratio. | vauthors=Brown NJ, Sokal AD, Friedman HL | volume=68 | issue = 9 | year=2013 | pages=801–13 | doi=10.1037/a0032850 | pmid=23855896| arxiv=1307.7006 | s2cid=644769 }}</ref> These authors argued that Losada's conclusions in previous papers using modelling from fluid dynamics, and those in his paper co-authored with Fredrickson, were not only based on poorly reported experiments, but also that it was difficult to draw conclusions from Losada's previous cited studies because critical details were omitted, "interpretations of results [were] made with little or no justification", and that elementary errors were made in the application of differential equations.<ref name="wishful"/>

Among the severe flaws claimed by Brown et al. in the positivity-ratio theory and its presentation were that:<ref name="wishful"/>
* data used by Losada in several analyses do not meet basic criteria for the use of differential equations (such as the use of continuous variables that evolve smoothly and deterministically over time);
* differential equations used by Losada to calculate the critical positivity ratio use parameters taken directly from [[Edward Lorenz|Lorenz]]'s simplified, illustrative, and arbitrary models for fluid dynamics, with Losada giving no rationale for his choice of parameters;
* use of different arbitrary parameters would give different positivity ratios, thus the precise values for the lower and upper critical ratios based on the arbitrary parameters, Fredrickson and Losada's 2.9013 to 11.6346 ratios, are meaningless;
* the [[Butterfly effect|butterfly]]-like first figure provided by Fredrickson and Losada is not a model of the data taken from their human participants, but "the results of computer simulations of the Lorenz equations, nothing more"; and
* based on the maths, even if precise positivity/negativity ratios could be derived, several "windows" of desirable and undesirable positivity/negativity ratios above a certain value should exist, rather than a simple range of ratios in which "flourishing" should occur. 
With regard to these, and especially the last, the Brown-Sokal-Friedman rebuttal argues that it is likely that Fredrickson and Losada did not fully grasp the implications of applying nonlinear dynamics to their data.<ref name="wishful"/> Brown, Sokal, and Friedman state that one can:<blockquote>only marvel at the astonishing coincidence that human emotions should turn out to be governed by exactly the same set of equations that were derived in a celebrated article several decades ago as a deliberately simplified model of convection in fluids, and whose solutions happen to have visually appealing properties. An alternative explanation – and, frankly, the one that appears most plausible to us – is that the entire process of "derivation" of the Lorenz equations has been contrived to demonstrate an imagined fit between some rather limited empirical data and the scientifically impressive world of nonlinear dynamics.</blockquote> They "urge future researchers to exercise caution in the use of advanced mathematical tools, such as nonlinear dynamics".<ref name="wishful"/>

==Responses to the Brown-Sokal-Friedman rebuttal==
{{expand section | with = a more fully developed presentation of responses to the 2003 rebuttal, including updates regarding the continuing suggestions of the value of the ratio from Fredrickson, and a more complete presentation of the views of others than Fredrickson and Brown-Sokal-Friedman | small = no | date = February 2022}}

===Fredrickson and ''Am. Psychol.''  retraction===
Fredrickson responded to the critique by agreeing that Losada's mathematical modelling was "questionable" and did not show that there are precise values of the ratio, but also arguing that the evidence for the benefits of a high positivity/negativity ratio is solid. Fredrickson noted that Losada declined to respond to the criticism.<ref name="updated">{{cite journal | journal=[[American Psychologist|Am. Psychol.]] | title=Updated thinking on positivity ratios. | author=Fredrickson BL | volume=68 | issue = 9 | year=2013 | pages=814–22 | doi=10.1037/a0033584 | pmid=23855895| s2cid=29283230 }}</ref> The ''American Psychologist'' proceeded to formally retract as invalid the mathematical modeling elements of Fredrickson and Losada's paper, including the specific critical positivity ratios of 2.9013 and its upper limit.<ref name="correction">{{cite journal | journal = [[American Psychologist|Am. Psychol.]] | title = Correction to Fredrickson and Losada (2005) | year = 2013 | volume = 68 | issue = 9 | pages = 822 | url = https://doi.apa.org/doiLanding?doi=10.1037%2Fa0034435 | url-access = subscription | access-date = February 10, 2022 | doi = 10.1037/a0034435| last1 = Fredrickson | first1 = Barbara L. | last2 = Losada | first2 = Marcial F. }}</ref>

===Other respondents===
{{expand section | with = at least one summary sentence for each published 2014 response | small = no | date = February 2022}}
In a follow-up to the 2013 papers—the Brown-Sokal-Friedman rebuttal, and the Fredrickson response—''American Psychologist'' published further scholarly responses, mostly supportive, but some critical of at least some aspects of the rebuttal.{{citation needed|date = February 2022}}<!--We know about these, in this article, only through the Brown, Sokal, and Friedman (2014) response, and it is inadequate to only provide the views of Nickerson, Hämäläinen, etc. only through the eyes of Brown et al. They need to be described independently, here.--> The series of responses culminated in a further response to these from Brown, Sokal, and Friedman.<ref name="brown-response"/> C.A. Nickerson, an independent scholar formerly at the [[University of Colorado, Boulder]],{{citation needed|date = February 2022}} concurred with the Brown-Sokal-Friedman rebuttal conclusion of the lack of empirical evidence for a critical positivity ratio, and noted the necessity of distinguishing between within-person-across-time versus within-time-across-persons theories.<ref>{{cite journal | author = Nickerson, C. A. | date = 2014 | title = No empirical evidence for critical positivity ratios | journal = [[American Psychologist|Am. Psychol.]] | volume = 69 | issue = 6 | pages = 626–628 | url =  | access-date =  | doi = 10.1037/a0036961| pmid = 25197846 }}</ref>{{verification needed|date = February 2022}} Emeritus professor Raimo Hämäläinen and colleagues responded, passing over the Brown-Sokal-Friedman rebuttal claims of failed criteria for use of differential equations in modeling, instead arguing that there were no fundamental errors in the mathematics itself, only problems related to the model's justification and interpretation.<ref name=HämäläinenLuoma2014Response>{{Cite journal|last1=Hämäläinen|first1=Raimo P.|last2=Luoma|first2=Jukka|last3=Saarinen|first3=Esa|date=2014|title=Mathematical modeling is more than fitting equations.|journal=[[American Psychologist|Am. Psychol.]]|volume=69|issue=6|pages=633–634|url=https://doi.apa.org/doiLanding?doi=10.1037%2Fa0037048| url-access=subscription | access-date = February 10, 2022 | doi=10.1037/a0037048 | pmid=25197850 | issn=1935-990X}}</ref> 

===Follow-up from Brown, Sokal, and Friedman===
The original rebuttal authors were openly critical about Fredrickson's partial retraction, and ''American Psychologist'' published their response to it in 2014, where they emphatically argued that there was no evidence whatsoever, as of that date, for the existence of a critical positivity ratio (i.e., a tipping-point for positivity).<ref name="brown-response">{{cite journal |vauthors=Brown NJ, Sokal AD, Friedman HL |title=The Persistence of Wishful Thinking |journal=[[American Psychologist|Am. Psychol.]] |volume=69 |issue=6 |pages=629–32 |year=2014 |pmid=25197848 |doi=10.1037/a0037050 |arxiv=1409.4837 |s2cid=12697463 }}</ref> In 2014, the rebuttal authors also responded to comments from others on their 2013 work,
* noting Nickerson's concurrence regarding the lack of empirical evidence for a critical positivity ratio, and lauding her distinction between the within-person and within-time types of theories, noting that "[b]oth types of theories are valuable... but... conceptually distinct and by no means equivalent" and that they believed that "this distinction deserves to be more widely discussed in the literature on research methods".<ref name="brown-response"/> 
* noting that Hämäläinen, Luoma, and Saarinen "concede our main point, namely the complete lack of justification for the use of the Lorenz equations in modeling the time evolution of human emotions",<ref name = BrownSokalFriedman2014response>{{cite journal |vauthors=Brown NJ, Sokal AD, Friedman HL |title=Positive psychology and romantic scientism |journal=[[American Psychologist|Am. Psychol.]] |volume=69 |issue=6 |pages=636–7 |year=2014 |pmid=25197852 |doi=10.1037/a0037390 |arxiv=1409.5172 |s2cid=207577657 }}</ref> but confronting the "no clear mathematical errors" assertion, stating that<blockquote>Among the purely mathematical errors clearly noted... are Fredrickson and Losada's assertion that the r = 22 data (alleged to be characteristic of “medium-performance teams”) end up in a limit cycle... and their implicit claims concerning the absence of chaotic attraction at large values of r...  But we are happy to agree with Hämäläinen et al. that the central flaws in Fredrickson and Losada (2005) and its predecessor articles are logical and conceptual, not narrowly mathematical. And they are, as we have demonstrated, overwhelming.<ref name = BrownSokalFriedman2014response/></blockquote>

The original rebuttal authors conclude this salvo by lamenting that the "unbridled romanticism" of which humanist psychology has been accused has not been replaced with a rigorous evidence-based psychology—as [[Martin Seligman|Seligman]] and [[Mihaly Csikszentmihalyi|Csikszentmihalyi]] promised in their founding manifesto of positive psychology—rather, the widespread acceptance of the critical positivity ratio shows that positive psychology has betrayed this promise, stating that "the sin is now romantic scientism rather than pure romanticism is not, in our view, a great advance."<ref name = BrownSokalFriedman2014response/>

==''[[Journal of Humanistic Psychology|J. Humanist. Psychol.]]'' special issue, and other follow-up==
{{expand section | with =  full description of the content of the 2018 ''J Humanist Psychol'' special issue, and of other more recent followup citations addressing the rebuttal controversy | small = no | date = February 2022}}
As of January 2014, as Andrew Anthony notes from his preparation for his article in ''[[The Observer]]'' from that period, Fredrickson continued to maintain "on empirical grounds" that "tipping points [in relation to positive emotions and flourishing] are highly probable", as communicated to him via email.<ref name="guardian"/>

In 2018, the ''[[Journal of Humanistic Psychology]]'' published a special issue focused on the aftermath to the rebuttal of the original Fredrickson and Losada article, where Harris L. Friedman and Nicholas J. L. Brown served as monitoring editors.<ref>{{cite journal | author = Friedman, Harris L. |author2=Brown, Nicholas J. L. | date = 2018 | title = Implications of Debunking the "Critical Positivity Ratio" for Humanistic Psychology: Introduction to Special Issue | journal = [[Journal of Humanistic Psychology|J. Humanist. Psychol.]] | volume = 58 | issue = 3 | pages = 239–261 | doi = 10.1177/0022167818762227 | pmc = 5898419 | pmid = 29706664 }}</ref>

As of this date,{{when|date = February 2022}} the 2005 report of Fredrickson and Losada has been described as discredited.{{citation needed|date = February 2022}}<!--This is placed here, because the same is stated in the opening sentence of the lead. If removing it here, remove it also from the lead, because it is not sourced in either place.-->

==Popular discussion==
{{expand section | with = information on the fate of published popular books, following the rebuttal, and other updates to popular perspective | small = no | date = February 2022}} 
The concept of a critical positivity ratio advanced by Fredrickson and Losada in 2005 was embraced by the lay public.{{clarify|date = February 2022}}<!--What does this mean, and what is the presented evidence?--><ref name="beast">{{cite news | newspaper = [[Daily Beast]] | title = Barbara Fredrickson's Bestselling 'Positivity' Is Trashed by a New Study | url = http://www.thedailybeast.com/articles/2013/08/16/barbara-fredrickson-s-bestselling-positivity-is-trashed-by-a-new-study.html | date = 16 August 2013 | first = Will | last = Wilkinson}}</ref>{{verification needed|date = February 2022}} Prior to the appearance of the Brown-Sokal-Friedman rebuttal and the ensuing retraction, Fredrickson had written a popular book, ''Positivity: Top-Notch Research Reveals the 3-to-1 Positivity Ratio that Will Change Your life''.<ref name=":6">{{cite book | last = Fredrickson | first = Barbara | author-link = Barbara Fredrickson | year = 2009 |title = Positivity: Top-notch research reveals the 3-to-1 ratio that will change your life | publisher = Harmony | isbn = 9780307393746}}</ref> Andrew Anthony, writing for ''[[The Guardian]]'' in January 2014, noted that in it, Fredrickson had written, "Just as zero degrees Celsius is a special number in thermodynamics, the 3-to-1 positivity ratio may well be a magic number in human psychology."<ref name="guardian"/> Anthony also noted that following the Brown-Sokal-Friedman rebuttal, Fredrickson has "removed the critical chapter that outlines Losada's input from further editions of Positivity", and that she has largely avoided engaging the popular press.<ref name="guardian"/>

Reporting from a variety of sources, including ''[[The Chronicle of Higher Education]]'' and ''[[The Scientist (magazine)|The Scientist]]'', the fact that the problems with the critical positivity ratio paper and concept went unnoticed for years (despite widespread adulatory publicity) contributed to a public perception of social psychology being a field that lacks scientific soundness and rigorous critical thinking.<ref name="beast"/><ref name="chronicle"/><ref name="scientist">{{cite web | work = [[The Scientist (magazine)|The Scientist]] | url = http://www.the-scientist.com/?articles.view/articleNo/36910/title/-Positivity-Ratio--Debunked/ | title = 'Positivity Ratio' Debunked | first = Dan | last = Cossins | date = August 7, 2013 | url-access = registration | access-date = February 11, 2022}}</ref> Sokal would state that the paper's "main claim... is so implausible on its face that some red flags ought to have been raised",<ref name="chronicle"/> as would only happen broadly with graduate student Brown's initiating the collaboration that resulted in the Brown-Sokal-Friedman rebuttal.<ref name="guardian"/><ref name="chronicle"/>

==References==
{{Reflist|2}}

==Further reading==
===Scholarly sources===
* {{cite journal | author = Losada, M. | date = 1999 | title = The Complex Dynamics of High Performance Teams | journal = [[Mathematical and Computer Modelling|Math. Comput. Model.]] | volume = 30 |issue = 9–10 | pages = 179–192 | doi = 10.1016/S0895-7177(99)00189-2 | url = | access-date = | doi-access =  }}{{full|date = February 2022}}
* {{cite journal | author = Losada, M. |author2= Heaphy, E. | date = 2004 | title = The Role of Positivity and Connectivity in the Performance of Business Teams: A Nonlinear Dynamics Model | journal = [[American Behavioral Scientist|Am. Behav. Sci.]] | volume = 47 |issue = 6 | pages = 740–765 |doi= 10.1177/0002764203260208 |s2cid= 54020643 | url = http://mattselker.org/Documents/positive%20to%20negative%20attractors%20in%20business%20teams.pdf | url-status = dead | archive-url = https://web.archive.org/web/20100602052915/http://mattselker.org/Documents/positive%20to%20negative%20attractors%20in%20business%20teams.pdf | archive-date =2010-06-02  | access-date = February 11, 2022}}{{Expression of Concern|doi=10.1177/0002764214537204|http://retractionwatch.com/2014/07/29/positivity-ratio-research-now-subject-to-an-expression-of-concern/ ''Retraction Watch''|http://retractionwatch.com/2019/10/09/i-decline-to-respond-but-take-this-history-to-undermine/ ''Retraction Watch''}}
===Popular sources===
* {{cite web | author= Marlier, Didier | date=November 1, 2009 | title= Marcial Losada Explains his Research for our Blog Readers | work=[[EnablersNetwork.com]] | url=https://www.enablersnetwork.com/2009/marcial-losada-explains-his-research-for-our-blog-readers/ | access-date=February 11, 2022 | quote = }}
* {{cite news | author= Bower, Bruce | date=August 12, 2013 | title=Ratio for a Good Life Exposed as 'Nonsense' | work=[[Science News|Sci. News]] | url=https://www.sciencenews.org/article/ratio-good-life-exposed-nonsense | access-date=2013-08-15 | quote = 'What’s shocking is not just that this piece of pseudomathematical nonsense received 322 scholarly citations and 164,000 web mentions, but that no one criticized it publicly for eight years, not even supposed experts in the field,' Sokal says.}}

==External links==
* [http://blogs.discovermagazine.com/neuroskeptic/2013/07/28/notes-on-positivity-ratio/#more-4171 July 28, 2013 blog post by independent science writer "Neuroskeptic", entitled "Positivity: Retract the Bathwater, Save the Baby".] {{Webarchive|url=https://web.archive.org/web/20130801064952/http://blogs.discovermagazine.com/neuroskeptic/2013/07/28/notes-on-positivity-ratio#more-4171 |date=August 1, 2013 }}

[[Category:Group processes]]
[[Category:Positive psychology]]
[[Category:Pseudoscience]]