Random walks describe stochastic processes characterized by a sequence of unpredictable changes in a random variable with no correlation to past changes. This report describes the random walk component of a clinical sensory test of olfactory performance. The precise definition of this stochastic process allows the establishment of precise diagnostic cut-offs for the identification of olfactory loss. Within the Sniffin`Sticks olfactory test battery, odor discrimination (D) and odor identification (I) are assessed by four- and three-alternative forced-choice designs, respectively. Meanwhile, the odor threshold (T) test integrates a three-alternative forced-choice paradigm within a staircase paradigm with seven turning points. We explored this paradigm through computer simulations and provided a formal description. The odor threshold assessment test consists of two sequential components, the first of which sets the starting point for the second. Both parts can be characterized as biased random walks with significantly different probabilities of moving to higher (11%) or lower (89%) values. The initial odor concentration step for the first phase of the test and the length of the subsequent random walk in the second phase significantly affect the probability of randomly achieving high test scores. Changing the odor concentration from where the starting point determination for the second test part begins has raised the current cut-off for anosmia, represented as T + D + I < 16, from the 87th quantile of random test scores to the 97th quantile. Analogous findings are likely applicable to other sensory tests that use the staircase paradigm characterized as random walk.
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