Abstract
We investigated the effects of old age on search, subitizing, and counting of difficult-to-find targets. In Experiment 1, young and older adults enumerated targets (Os) with and without distractors (Qs). Without distractors, the usual subitization-counting function occurred in both groups, with the same subitization span of 3.3 items. Subitization disappeared with distractors; older adults were slowed more overall by their presence but enumeration rates were not slowed by ageing either with or without distractors. In contrast, search rates for a single target (O among Qs) were twice as slow for older as for young adults. Experiment 2 tested and ruled out one account of age-equivalent serial enumeration based on the need to subvocalize numbers as items are enumerated. Alternative explanations based on the specific task differences between detecting and enumerating stimuli are discussed.
Acknowledgments
This work was funded by a grant awarded to the first and second authors from the Economic and Social Research Council of Great Britain (R000239180). We are grateful to Lana Trick and two anonymous reviewers for helpful comments on an earlier version of the paper.
Notes
It is notable that the slope associated with subitizing is considerably larger than that obtained in parallel or even classic serial search tasks. Trick and Pylyshyn (Citation1994) suggest that the slope could arise at the stage of binding FINSTs to items or at the response stage. Reviewing the literature, they conclude that the majority of the slope is attributable to the response stage as a result of each bound FINST being associated with a number name, which is a serial process (see Trick & Pylyshyn, Citation1994, p. 88).
The reduced degrees of freedom reflect adjustments for unequal variances across age groups.
We note that Watson, Maylor, and Manson (Citation2002) reported the screen resolution to be 640 × 480 pixels and the screen grid to be 10 × 10. In fact the screen resolution was 800 × 600 pixels and the display grid was 6 × 6.
This starting point for the initial model state was chosen so as to reduce the possibility of the model settling on unrealistic solutions due to local minima. We note that starting the model with subitizing slopes based on numerosities 1 to 2 or 2 to 4 and counting slopes based on numerosities 4 to 7 or 6 to 8, respectively, or fixed typical subitizing/counting rates and intercepts, produced very similar results.
As in Watson et al. (2002), it is apparent that the faster subitizing rate for the older participants in the absence of distractors is due to older participants being relatively slow at numerosity 1. To assess this, we reanalysed the data with numerosity 1 excluded. Without distractors, the subitizing slopes were now 28.1 ms/item (older) and 46.1 ms/item (young), and with distractors they were 226.7 (older) and 225.6 (young). Neither a 2 × 2 × 7 (Age × Distractor Presence × Numerosity 2–8) nor a 2 × 2 × 2 (Age × Distractor Presence × Numerosity 2–3) mixed ANOVA found a significant Age × Numerosity interaction or a three-way interaction (all Fs = 1.5, ps > .25). Thus without numerosity 1, there was no age-selective difference in enumeration rates for either small or large numerosities. We also remodelled the data to determine the subitizing span in the absence of distractors with numerosity 1 excluded. The bilinear model remained a very good fit to the data (median R 2 values of.991 for the young and.990 for the older adults) and again showed no age-related difference in the subitizing spans (M = 3.44, SD = 0.42, for the young, and M = 3.58, SD = 0.44, for the older observers), t(66) = 1.26, p > .2.
The most appropriate comparison is between subvocalizing rates for the range 5–8 and visual enumeration without distractors (rather than when distractors were present). This is because the presence of distractors in the visual enumeration task may have caused a more exhaustive processing if guidance to the target features was not strong, and this would have led to artificially shallower enumeration functions.
The subvocalizing rates observed in this study are considerably faster than those obtained by Maylor and Wing (Citation1996) (∼175 ms/number compared to∼400 ms/number). This is most likely because participants in Maylor and Wing's study enumerated from 1 to 100, and so the majority of subvocalizing responses would have been to two-digit numerals, which would take longer to subvocalize than the single-digit numerals (1–9) presented here.