An Algorithm for Identifying Nonsystematic Delay-Discounting Data

Matthew W. Johnson, Warren K. Bickel

Research output: Contribution to journalArticlepeer-review

271 Scopus citations


Several previous discounting studies have use the R2 measure to identify data sets with poor fits to a mathematical discounting model as nonsystematic data to be eliminated before further analyses are conducted. Data from three previous delay-discounting studies (six separate groups, with a total of 161 individuals) were used to demonstrate why using R2 to assess the fits of discounting data is problematic. A significant, positive correlation between discounting rate parameter and R2 was found in most groups, showing that R2 is more stringent as a measure of fit for low discounting rates than for high discounting rates. Furthermore, it is suggested that identifying nonsystematic data based on any measure of fit to a mathematical discounting model may be problematic because it confounds discounting rate comparison with the issue of discounting model assessment. Therefore, a model-free method to identify nonsystematic data is needed. An algorithm for identifying nonsystematic data is presented that is based on the expectation of a monotonically decreasing discounting function. This algorithm identified 13 cases out of the 161 reanalyzed data sets as nonsystematic. These nonsystematic data are presented, along with examples of data not identified as nonsystematic. This algorithm, or modifications of it, may be useful in a variety of human and nonhuman animal discounting studies (e.g., delay discounting, probability discounting) as an alternative to the R2 measure for identifying nonsystematic data. The algorithm may be used in empirical investigations to improve discounting methodology, and may be used to identify outliers to be removed from analyses.

Original languageEnglish (US)
Pages (from-to)264-274
Number of pages11
JournalExperimental and clinical psychopharmacology
Issue number3
StatePublished - Jun 2008


  • R
  • delay discounting
  • hyperbolic discounting
  • outliers
  • probability discounting

ASJC Scopus subject areas

  • Pharmacology
  • Psychiatry and Mental health
  • Pharmacology (medical)


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