The Slopes Remain the Same: Reply to Wolfe (2016)

Wolfe (2016) responds to my article (Kristjánsson, 2015), arguing among other things, that the differences in slope by response method in my data reflect speed accuracy trade-offs. But when reaction times and errors are combined in one score (inverse efficiency) to sidestep speed accuracy trade-offs, slope differences still remain. The problem that slopes, which are thought to measure search speed, differ by response type therefore remains.

size in the critical conditions that I report, and that this data involve a ''classic speed accuracy trade-off [SAT].'' Wolfe is right that there is evidence of SATs in the data but the important question is whether SATs account for all the differences in slope by response method reported in Kristja´nsson (2015).
There is no single agreed upon way of assessing whether SATs account for condition differences, and a definitive way may not exist (Bruyer & Brysbaert, 2011). But any such assessment must almost certainly involve some convolution of RTs and error rates. Inverse efficiency scores (IES; Townsend & Ashby, 1978) have been used to combine RTs and error rates in one score to compensate for differences in error rates (e.g., Bruyer & Brysbaert, 2011;Vandierendonck, 2016). IES involve multiplying mean RT by error rates yielding a single score (IES ¼ Mean RT/1 À Mean error rate). Slopes of IES and set size can then be measured. If there are still slope differences between response conditions in Kristja´nsson (2015), then the problem for the RT by set size methodology remains. Table 1 shows the results of applying IES scores to RTs and error rates in Kristja´nsson (2015) and also to data from Wang, Kristja´nsson, and Nakayama (2005) where a similar slope difference by response method was reported. The IES transform does not affect the patterns in the results in any fundamental way. For easy conjunction search, there are still condition differences of 5 ms per added item to the set size. This means that the search is 5 ms slower per added item for the more traditional present/absent task than the Go No-Go task. This is also the case for easy conjunction search from Wang et al. (2005). The slope differences for the difficult conjunction search are, however, smaller than in the original data. In sum, SATs do not easily account for slope differences by response method suggesting that slopes are not straightforward measures of search rate.
There are also notable intercept differences. Intercept differences are often ignored in visual search studies, based on the assumption that they involve a separate processing stage from the actual search (Sternberg, 1969), which also relies on the questionable assumption that slopes are the true measure of search. In any case, outright dismissal of intercept differences as irrelevant to visual search is unhelpful, but further speculation is beyond the current scope.
In the end, I do not think that Wolfe and I disagree on very much. And we agree that taskbased differences in slope are a challenge to the RT Â Set size methodology. We may disagree on whether SATs account for the task-based slope differences, but I think that the current analysis makes clear that they cannot easily be dismissed as SATs.
There are likely other ways of assessing SATs, but it is hard to see that they would involve anything else than taking both error rates and RTs in to account as inverse efficiency scores do, although weights assigned to each could be varied. This issue deserves more detailed analysis. Inverse efficiency scores are not uncontroversial and carry a number of assumptions (Bruyer & Brysbaert, 2011;Vandierendonck, 2016). Recent studies highlight the usefulness of analyzing RT distributions (Antoniades et al., 2013;Burnham, Cilento, & Hanley, 2015;Kristja´nsson & Jo´hannesson, 2014;Palmer, Horowitz, Torralba, & Wolfe, 2011;Wolfe, Palmer, & Horowitz, 2010). Testing whether RT distributions differ by response method could shed further light on the issue. Currently, my coworkers and I are collecting large data sets with varied response methods that will enable such detailed analyses.

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