On the theoretical error bound for estimating psychometric functions

Huanping Dai, Virginia M. Richards

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


The theoretical limits to the amount of error, or the Cramer-Rao bounds, were derived for estimating psychometric functions. These theoretical error bounds were compared with the variability of psychometric functions estimated from human as well as computer-simulated observers. For the simulated observers, due to the limited efficiency of the sampling strategies, including the placement of the signals and the distribution of the trials, the variances of the estimated parameters are seven times the theoretical bound for threshold and 22 times that for slope. For the human observers, the variance is 18 times the theoretical bounds for threshold and 80 times that for slope. Therefore, a major portion of the variances (60% for threshold and 73% for slope) for the human observers is associated with factors other than sampling strategies. Further improvement of the accuracy for estimating psychometric functions will depend on not only optimizing the sampling strategy, but also better understanding the various sources of error related to the behavior of human observers.

Original languageEnglish (US)
Pages (from-to)919-926
Number of pages8
JournalAttention, Perception, and Psychophysics
Issue number3
StatePublished - 2011


  • Cramer-Rao bound
  • Psychometric function

ASJC Scopus subject areas

  • Language and Linguistics
  • Experimental and Cognitive Psychology
  • Sensory Systems
  • Linguistics and Language


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