The persistence of wishful thinking: Response to "Updated thinking on   positivity ratios"
  This is a response to Barbara Fredrickson's comment [American Psychologist 68, 814-822 (2013)] on our article arXiv:1307.7006.   We analyze critically the renewed claims made by Fredrickson (2013) concerning positivity ratios and "flourishing", and attempt to disentangle some conceptual confusions; we also address the alleged empirical evidence for nonlinear effects. We conclude that there is no evidence whatsoever for the existence of any "tipping points", and only weak evidence for the existence of any nonlinearity of any kind. Our original concern, that the application of advanced mathematical techniques in psychology and related disciplines may not always be appropriate, remains undiminished. 
Nicholas J.L. Brown, Alan D. Sokal, Harris L. Friedman
stat.AP