How to correctly put the "subsequent" in subsequent search miss errors

Visual search, finding targets among distractors, is theoretically interesting and practically important as it involves many cognitive abilities and is vital for several critical industries (e.g., radiology, baggage screening). Unfortunately, search is especially error prone when more than one target is present in a display (a phenomenon termed the satisfaction of search effect or the subsequent search miss effect). The general effect is that observers are more likely to miss a second target if a first was already detected. Unpacking the underlying mechanisms requires two key aspects in analysis and design. First, to speak to the "subsequent" nature of the effect, the analyses must compare performance on single-target trials to performance for a second target in dual-target displays after a first has been found. Second, the design must include single-target displays that are matched in difficulty to each dual-target display to enable fair comparisons. However, it is not clear that prior research has met these two standards simultaneously. Work from academic radiology has primarily used designs with well-matched single- and dual-target trials, but most employed analyses that do not focus solely on performance after a first target has been detected. Work from cognitive psychology has generally performed the correct analyses, but relied on unmatched single- and dual-target trials, introducing a confound that could distort the results. In the current paper, we demonstrate the impact of this confound in empirical data and provide a roadmap for proper study design and analyses.