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Statistical Significance Testing with Mahalanobis Distance for Thresholds Estimated from Constant Stimuli Method

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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.

Affiliations: 1: Department of Information Processing, Tokyo Institute of Technology, 4259- G2-1 Nagatsuta-cho, Midori-ku, Yokohama 226-8502, Japan, Department of Computer Science and Engineering, Toyohashi University of Technology, 1-1 Hibarigaoka Tenpaku, Toyohashi, Aichi 441-8580, Japan;, Email:; 2: Graduate School of Economics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japan; 3: Department of Information Processing, Tokyo Institute of Technology, 4259- G2-1 Nagatsuta-cho, Midori-ku, Yokohama 226-8502, Japan


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