Statistical significance testing with mahalanobis distance for thresholds estimated from constant stimuli method

Takehiro Nagai, Takahiro Hoshino, Keiji Uchikawa

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

The t-test and the analysis of variance are commonly used as statistical significance testing methods. However, they cannot assess the significance of differences between thresholds within individual observers estimated from the constant stimuli method; these thresholds are not defined as averages of samples, but they are rather defined as functions of parameters of psychometric functions fitted to participants' responses. Moreover, the statistics necessary for these statistical testing methods cannot be derived. In this paper, we propose a new statistical testing method to assess the statistical significance of differences between thresholds estimated from the constant stimuli method. The new method can assess not only threshold differences but also main effects and interactions in multifactor experiments, exploiting the asymptotic normality of maximum likelihood estimators and the characteristics of multivariate normal distributions. This proposed method could be used in similar cases to the analysis of variance for thresholds estimated from the adjustment method and the staircase method. Finally, we present some data on simulations in which we tested assumptions, power and type I error of the proposed method.

Original languageEnglish
Pages (from-to)91-124
Number of pages34
JournalSeeing and Perceiving
Volume24
Issue number2
DOIs
Publication statusPublished - 2011 Oct 6
Externally publishedYes

Keywords

  • Constant stimuli method
  • Monte Carlo simulation
  • Psychophysics
  • Statistical hypothesis testing

ASJC Scopus subject areas

  • Experimental and Cognitive Psychology
  • Ophthalmology
  • Sensory Systems
  • Computer Vision and Pattern Recognition
  • Cognitive Neuroscience

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