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Critical positivity ratio
The critical positivity ratio (also known as the Losada ratio or the Losada line) is a largely discredited concept in positive psychology positing an exact ratio of positive to negative emotions which distinguishes "flourishing" people from "languishing" people. The ratio was proposed by Marcial Losada and psychologist Barbara Fredrickson, who identified a ratio of positive to negative affect of exactly 2.9013 as separating flourishing from languishing individuals in a 2005 paper in ''American Psychologist''. The concept of a critical positivity ratio was widely embraced by both academic psychologists and the lay public; Fredrickson and Losada's paper was cited nearly 1,000 times, and Fredrickson wrote a popular book expounding the concept of "the 3-to-1 ratio that will change your life". Fredrickson 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."〔
In 2013, the critical positivity ratio aroused the skepticism of Nick Brown, a graduate student in applied positive psychology, who felt that the paper's mathematical claims underlying the critical positivity ratio were fundamentally flawed. Brown collaborated with physicist Alan Sokal and psychologist Harris Friedman on a re-analysis of the paper's data. They found that Fredrickson and Losada's paper contained "numerous fundamental conceptual and mathematical errors", as did Losada's earlier work on positive psychology, which completely invalidated their claims. Losada declined to respond to the criticism, indicating that he was too busy running his consulting business.〔 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 was solid. Brown and colleagues, whose response was published the next year, maintain that there is no evidence for the critical positivity ratio.
In response, ''American Psychologist'' formally retracted the mathematical modeling elements of Fredrickson & Losada's paper, including the specific critical positivity ratio of 2.9013, as invalid. The fundamental nature of the mathematical errors, which went unnoticed for years despite the widespread publicity surrounding the critical positivity ratio, contributed to a perception that social psychology as a field lacked scientific soundness and rigorous critical thinking.〔〔 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."〔
==Concept==
Building on research by Barbara Fredrickson indicating that individuals with a higher ratio of positive to negative emotions tend to have more successful life outcomes,〔Fredrickson, B. L. (2004). (The broaden-and-build theory of positive emotions ). Philosophical Transactions of the Royal Society of London, Series B: Biological Sciences, 359, 1367-1377.〕 and on studies by Marcial Losada applying differential equations from fluid dynamics to human emotions, Fredrickson and Losada used nonlinear dynamics modelling (based on Lorenz systems) to argue that the ideal positivity/negativity ratio lies between 2.9013 and 11.6346. They argued that those with ratios within this range will "flourish", whereas those with values outside it will "languish". They claimed that their model predicted cut-off points for the maximum and minimum positivity ratios within which one should observe qualitative changes in an individual's level of flourishing.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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