Display size effects in visual search: Analyses of reaction time distributions as mixtures

Abstract

In a reanalysis of data from Cousineau and Shiffrin (2004) and two new visual search experiments, we used a likelihood ratio test to examine the full distributions of reaction time (RT) for evidence that the display size effect is a mixture-type effect that occurs on only a proportion of trials, leaving RT in the remaining trials unaffected, as is predicted by serial self-terminating search models. Experiment 1 was a reanalysis of Cousineau and Shiffrin's data, for which a mixture effect had previously been established by a bimodal distribution of RTs, and the results confirmed that the likelihood ratio test could also detect this mixture. Experiment 2 applied the likelihood ratio test within a more standard visual search task with a relatively easy target/distractor discrimination, and Experiment 3 applied it within a target identification search task within the same types of stimuli. Neither of these experiments provided any evidence for the mixture-type display size effect predicted by serial self-terminating search models. Overall, these results suggest that serial self-terminating search models may generally be applicable only with relatively difficult target/distractor discriminations, and then only for some participants. In addition, they further illustrate the utility of analysing full RT distributions in addition to mean RT.

Keywords:

• Visual search
• Mixture distribution
• Reaction time distributions

Acknowledgments

This research was supported by a grant from The Marsden Fund administered by the Royal Society of New Zealand. The authors thank Denis Cousineau for providing the data analysed in Experiment 1 and Denis Cousineau, Wolf Schwarz, and two anonymous reviewers for helpful comments on earlier versions of the article.

Notes

¹ In cognitive modelling the likelihood ratio can be used to (a) adjust the parameters of a model in order to maximize the likelihood of that model (e.g., Palmer, Huk, & Shadlen, 2005), or (b) choose the better of two competing models (e.g., Reddi, Asrress, & Carpenter, 2003; Schwarz, 2001). The procedure developed by Miller (2006) is an example of the latter use of likelihood ratios.

² For the sake of simplicity, we ignore for now the possibility that the scanning process can start with the target in more than half of the trials, as would be suggested by some guided search models (e.g., Wolfe, 1994).

³ Parallel models can often mimic serial ones (e.g., Townsend, 1990), so it is possible that certain parallel models would also be compatible with a mixture-type effect. The exact class of parallel models consistent with such an effect is beyond the scope of the present analysis.

⁴ The display size two distributions were not also checked, because the shapes of these distributions are not known in advance if a mixture effect is in fact present.

⁵ Consider, for example, the guided search model (Wolfe, 1994). If items were not selected randomly but instead on the basis of a preattentive assessment of their similarity to targets, then participants should examine the target first in more than half of the target-present display size two trials, because the preattentive assessment would tend to guide the search to the target more often than that to the distractor. If that happened, the DSE would actually only be present in the minority of trials in which the preattentive assessment rated the distractor as more target-like than the target.

⁶ We thank Denis Cousineau for raising these two issues.

⁷ The exclusion criterion was a p value of .05 or less using a chi-square goodness of fit test. An equivalent mixture analysis was carried out on the present data sets using the more lenient criterion of p value of .025, which allowed the inclusion of two additional data sets. The results of the analysis were essentially the same as those using the .05 cut-off criterion.

⁸ Our criterion for the presence of RT outliers was an estimated mixture probability of P < .1. Outliers seemed the most plausible cause of such low mixture probabilities, because a priori considerations suggest that the effect should be present in approximately half of the trials (i.e., with random sampling of the first display position inspected with display size two). Furthermore, inspection of the observed RT distributions for cases with P < .1 revealed two unusually long RTs that did not appear to fit with the rest of the distribution, and reanalysis of the data without these RTs produced reasonable estimates of P (i.e., approximately .5 or 1.0). The P < .1 outlier criterion was applied to the data sets from both the present experiment and the final experiment to be described in this paper.

⁹ As in Experiment 1, additional simulations were conducted to examine the power of the likelihood ratio test to detect a mixture effect (a) when effect-present slowing varies randomly from trial to trial, and (b) within a hybrid model in which some DSE is present in all trials. As is described in the Appendix, power did not decrease substantially for reasonable versions of these alternative models, so the overall conclusions remain the same taking these models into account.

¹⁰ As in the previous two experiments, additional simulations were conducted to examine the power of the likelihood ratio test to detect a mixture effect (a) when effect-present slowing varies randomly from trial to trial, and (b) within a hybrid model in which some DSE is present in all trials. As is described in the Appendix, power did not decrease substantially for reasonable versions of these alternative models, so the overall conclusions remain the same taking these models into account.

¹¹ We limited the simulations to P = .5 because this value is theoretically plausible and because power did not change rapidly as a function of P in simulations with the basic model (e.g., Table 5).