When searching for a vertical blue bar among a set of horizontal blue bars and vertical yellow bars, we would expect to find a display size function in which:

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First, restating the scenario helps frame the reasoning: when searching for a distinct target (a vertical blue bar) among distractors that are horizontal blue bars and vertical yellow bars, researchers often examine how search difficulty scales with display size by comparing reaction times (RT) across target-present and target-absent conditions.
Option 1: 'Mean RT is a linear function of display size with the slope for target-present displays around twice that for target-absent displays.' This aligns with classic findings in standard display size search tasks, where adding more items generally leads to longer RTs, and the increase is steeper when the target is present because observers initiate a search and identify the target, adding a processing cost that scales with more items. The ~2x slope difference reflects the common observation that target-present searches incur an additional processing step (verification) compared to target-absent searches.
Option 2: 'Mean RT is a linear function of display size with the same slopes for target-absent and target-present displays.' If the slopes were identical, it would imply that detecting the target does not add extra processing cost as display size grows, which contradicts the well-established finding that target-present trials typically exhibit higher search costs due to target verification ority. Hence this is unlikely in standard visual search data.
Option 3: 'Mean RT is roughly constant for displays of different size and is the same for target-present and target-absent displays.' A flat RT across varying display sizes would suggest no influence of display size on search performance, which is inconsistent with the core principle of many visual search experiments that increasing display size adds more items to scan and increases RT, especially in target-present cases.
Option 4: 'Mean RT is a linear function of display size with the slope for target-absent displays around twice that for target-present displays.' This is the reverse of the typical pattern observed in many searches. If target-absent slopes were steeper, it would indicate that missing the target imposes greater RT costs as display size grows, which contradicts standard findings where target presence generally imposes greater incremental cost because observers must locate and verify the target when present, not simply conclude absence from scanning more items.
In summary, the reasoning across options hinges on whether RT increases with display size (a linear relationship is common) and whether the slope is steeper for target-present or target-absent conditions. The conventional expectation is that target-present searches incur a larger incremental cost with more items due to the need to locate and verify the target, yielding a steeper slope for target-present than for target-absent, roughly by a factor near two. The other options either deny the size effect, claim equal slopes, or invert the slope relationship, which misaligns with established visual search literature.

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When searching for a vertical blue bar among a set of horizontal blue bars and vertical yellow bars, we would expect to find a display size function in which:

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