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Description: _ Sometimes, sensitivity measure d’ of detection theory is explained to be given by (1)____d’=z(H)-z(F), where z(H) and z(F) are z-scores (Hautus, Macmillan, & Creelman (2022, p. 7). However, the right hand side of Eq. (1) includes the value of criterion for judgment under a general case of detection theory, i.e., an unequal variance Gaussian model, as is shown by eq. (4) in Okamoto (2023). For more details, check the file cmmnt_ZH_ZF.pdf in the Files box below. Swets discusses cases, where variances of the noise and signal stimuli are not equal (Swets, J. A. 1996. “Signal detection theory and ROC analysis in psychology and diagnostics: Collected papers.” Lawrence Erlbaum Associations, Publishers. pp. 52-54). Simple examples of visual presentation of relation between mean and variance (standard deviation) for a single data point are shown in the file MuSigma.pdf in the Files box below. For fixed distance between the noise and signal stimuli, d’ given by eq. (1) varies depending on the standard deviation of the signal stimulus, as shown in Figure 1 of Okamoto (2023). So, we need the estimate of the standard deviation of the signal stimulus to estimate the sensitivity. Moreover, Okamoto (2023) shows by simulation that some experimental designs cause severe problems of estimation, i.e., very large overestimation. Ways to avoid these problems are suggested by simulations in Okamoto (2023). He recommends a rating method with more than three judgment categories in case of 1AFC task (Tables 1 and 2). Drastic effects of width of category on estimation bias are shown in the case of Yes/No task (Tables 3 and 4). For scripts for Bayesian analysis of 1AFC task, check the file ReadMe_1AFCRating.pdf, or the website http://y-okamoto-psy1949.la.coocan.jp/Python/en2/SDT_1AFC_Rating/ _ When you estimate variance of sensation of a signal stimulus, you need sufficient amount of data, because data of small size may support a wrong equal variance model. For details, check the file comp_waic.pdf in the Files box below. _ Wixted (2020) says (p. 201): Such developments suggest that signal detection theory is one of the most useful theories. _ Wixted's appreciation recommends usage of signal detection theory. But, a most useful theory should be used correctly. _ Program files used in Okamoto (2023) are archived with the document file ReadMe.pdf in the file prgs_doc.zip in the Files box below. Program files for Bayesian analysis of 1AFC rating task data are archived in the zip file ScriptFiles_1AFCRating.zip in the Files box below. For a document of the program, check the pdf file ReadMe_1AFCRating.pdf in the Files box below. _ References Hautus, M. J., Macmillan, N. A., & Creelman, C. D (2022). Detection Theory: A user’s guide, third edition. Okamoto, Y. (2023). Experimental problems about estimation of sensitivity measure d′. The Japanese Journal of Psychonomic Science, 41, 107-114. DOI https://doi.org/10.14947/psychono.41.16 or https://www.jstage.jst.go.jp/article/psychono/41/2/41_41.16/_article/-char/en Wixted, J. T. (2020). The forgotten history of signal detection theory. Journal of Experimental Psychology: Learning, Memory, and Cognition, 2020, 46, 2, 201-233. _