Ratio for a good life exposed as ‘nonsense’

Tuesday, August 13th 2013. | Science News

Highly touted measure of emotional health criticized as math disaster

By Bruce Bower

Web edition: August 12, 2013

A 52-year-old, part-time graduate student with no previous training in psychology and little math education beyond high school has knocked a celebrated measure of the emotional mix needed to live well off its mathematical pedestal.

Nicholas Brown, who is completing a master’s degree in applied positive psychology at the University of East London in England, teamed up with two colleagues to demolish the math at the heart of a widely cited October 2005 American Psychologist paper that claimed to identify the precise ratio of positive to negative emotions that enables life success. The researchers’ takedown of what’s known as the critical positivity ratio appears July 15 in American Psychologist.

“It’s slightly worrying to discover that a leading journal could publish an article with so many obvious errors in it,” Brown says.

His report joins a movement in psychology to clean up research practices (SN: 6/1/13, p. 26).

One of Brown’s coauthors is physicist Alan Sokal of New York University. Sokal gained notoriety in 1996 by publishing an intentionally nonsensical paper in a leading peer-reviewed journal of cultural studies.

Psychologist Barbara Fredrickson of the University of North Carolina at Chapel Hill and psychologist Marcial Losada, head of Losada Line Consulting in Brasilia, Brazil, coauthored the 2005 paper. In a response published alongside the new critique, psychologist Fredrickson acknowledges that their paper employed “now questionable mathematics.” But she devotes most of her response to shoring up the argument of the 2005 paper by describing evidence that people do best when positive feelings exceed negative feelings by a factor of about 3 to 1 — roughly equivalent to the contested critical positivity ratio.

Responding to a request for comment, Fredrickson told Science News that she’s “not speculating any further on these issues.” Losada, whose firm uses the ratio when advising companies on improving employee productivity, declined to write a response to Brown’s paper.

Brown first read Fredrickson and Losada’s paper in November 2011 as a class assignment. The study used mathematical equations known as Lorenz equations to calculate how positive and negative human emotions change over time. In 1963, the mathematician Edward Lorenz published the equations  to model how fluids change over time. Fredrickson and Losada used the equations with emotion data from volunteers tracked for 28 days. The researchers determined that creativity, helpfulness to others and other elements of “flourishing” characterized people who displayed a ratio of positive to negative emotions above 2.9013:1 and below 11.6346:1.

People whose balance of emotions fell outside that range “languished” in an unproductive state, the two psychologists concluded. Their report emphasized the lower ratio as the critical threshold to cross in order to flourish in life.

Upon reading a 1963 paper on Lorenz equations “with some difficulty,” Brown realized that the equation Fredrickson and Losada used to calculate the critical positivity ratio had no connection to their emotion data: Regardless of the volunteers’ data points, the equation would simply generate the same, meaningless number.

Brown then asked Sokal and psychologist Harris Friedman of the University of Florida in Gainesville to analyze the 2005 paper more completely.

“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.

Brown and his colleagues’ sacking of the critical positivity ratio is on the mark, comments mathematician Colin Sparrow of the University of Warwick in England, who studies Lorenz equations.

The equations belong to the field of nonlinear dynamics, which describes how small changes in a few variables that evolve independently — mainly in physics and chemistry — can lead to complex consequences.

In the 2005 report, Fredrickson and Losada failed to show how individuals’ self-reported feelings could be mathematically described as quantities that vary smoothly over time, as the Lorenz equations require, Sokal says. Two earlier papers by Losada that examined emotional changes in groups suffered from the same problem, he adds.

Losada and Fredrickson also plugged into key parts of their calculation values that had been adopted by Lorenz for his fluid analysis, Sokal says. There’s no reason to assume those values also apply to emotional changes, rendering the critical positivity ratio “entirely fanciful,” he concludes.

No retraction of the 2005 paper is planned, says psychologist Norman Anderson, editor-in-chief of American Psychologist and CEO of the American Psychological Association in Washington, D.C.

Related For Ratio for a good life exposed as ‘nonsense’