![]() Even though c and d describe conceptually separate performance aspects their sample estimates are not independent 2, whereas those of π H and π F (that is, H and F) are. Formally, this analysis may be interpreted as a transformation of the two independent probabilities π H = P(" yes"|s 1) and π F = P(" yes"|s 0) into the two indices d′ and c, which carry information about conceptually separate aspects characterizing the performance of the observer, at least within the framework of the classical model. In this model, d′ is the separation of the means of the distributions, and c is the location of the decision criterion, relative to these means. Varying the bias of the observer towards one decision or the other provides additional information, but in many applied studies extracting detection indices, only a single pair of observed hit ( H) and false alarm ( F) rates is obtained, and the present note focuses on this widely used “single-point design” (e.g., Rotello et al., 2008).Ī traditional and prominent approach for analyzing data in the format of Table Table1 1 is to extract estimates of the sensitivity and bias measures d′ and c (for detailed expositions, see, e.g., Macmillan & Creelman, 2005, Ch, 1–2 Stanislaw & Todorov, 1999) which are derived from the classical SDT model assuming internal stimulus representations which are normally distributed with equal variance 1. Especially in applied settings the trial numbers n 0, n 1 per observer and condition of interest are often quite small (typical sample sizes in applied studies are n 0 = n 1 = 10 as, e.g., in Köteles et al., 2013, or n 0 = n 1 = 20 as, e.g., in O’Connor et al., 2003), and the main interest often centers on whether the observer’s ability to detect or discriminate the signals under study is better than chance and if so, by how much. In the YN design generating the data format shown in Table Table1, 1, an observer is presented in each trial with either a signal ( s 1) or a noise ( s 0) stimulus, and indicates his/her decision about the nature of the stimulus presented by responding “yes” or “no” the Table represents a standard summary of potential results. The column totals m and n 0 + n 1 − m are called the response marginal, the row totals n 1 and n 0 form the stimulus marginal The observed hit rate is H = x/ n 1, the observed false alarm rate is F = ( m − x)/ n 0. Of all m “yes” responses, x were given in signal trials, m − x in noise trials. In all n 0 + n 1 trials the observer has given a total of m “yes” responses, and thus n 0 + n 1 − m “no” responses. The signal stimulus s 1 is presented in n 1 trials, the noise stimulus s 0 in n 0 trials. We relate the conditional approach to classical (logistic) detection models also leading to analyses of the odds ratio, compare its statistical power to that of the unconditional approach, and conclude by discussing some of its pros and cons. We describe in detail how the conditional approach leads to conditional maximum likelihood sample estimates of sensitivity, and to exact confidence intervals for the underlying (log) odds ratio. The conditional framework applied to single-point Yes/No detection studies is based on the noncentral hypergeometric sampling distribution and permits, for samples of any size, exact inference because it eliminates nuisance (i.e., bias) parameters by conditioning. It is closely related to, for example, Fisher’s exact test or the Rasch model in item response theory which have long been valuable and prominent in psychology. ![]() An alternative conditional approach to statistical inference emphasizes explicitly the conditional nature of the inferences drawn, and argues on the basis of the response marginal (the number of “yes” responses) that was actually observed. ( 2019, Medical Decision Making, 39, 21–31) presented general practitioners (GPs) with clinical vignettes of patients showing various cancer-related symptoms, and asked them to decide if urgent referral was required the standard discrimination index d′ was calculated for each GP. ![]() ![]() ![]() For example, Kostopoulou, Nurek, Cantarella et al. In many applied single-point Yes/No signal-detection studies, the main interest is to evaluate the observer’s sensitivity, based on the observed rates of hits and false alarms. ![]()
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