Steps

The classic manipulation of difficulty in the Swaps task is to increase the number of steps. For instance, rather than requiring only two swaps to reach the solution (two steps), a more difficult problem may require three or even four swaps. Stankov (2000) found that the increase in Steps produced a smooth decrease in accuracy as steps increased, with the average percentage correct falling by approximately 8% for each additional step (from 90% at 1-step to 66% at 4-step). Although there was not a large enough range of steps in Stankov’s (2000) study to determine if this decrease plateaus, Bowman (2006) then provided additional data with steps ranging up to eight. Interestingly, Bowman found no plateauing effect, with the

steady decrease in accuracy continuing through to eight steps. This seems to indicate that attentional control demands do not simply ‘run out’ at some point (causing outright failure), as may be indicated by an attentional ‘capacity’, but rather, the steady increase is reflective of concomitant increases in the duration that attention must be kept controlled. This also means the increase in steps is unlikely to be simply due to a build-up of proactive interference (which may implicate binding capacity demands), because we would expect this proactive interference to become exponentially more detrimental as it accumulates throughout the problem.14 _{However, it must be cautioned that Bowman presented items in the Swaps task in} order of sequentially increasing steps (i.e., participants started with 1-step, then moved on to 2-step, and so on...). This means an asymptote related to attentional ‘capacity’ limits may have been mitigated by a learning effect (Jensen, 1977), as participants systematically learnt to deal with the steadily increasing demands (this point will become particularly relevant in the Discussion of this chapter).

Nonetheless, it appears that each additional step is more demanding of attentional control than of binding capacity, because attention must be kept active and controlled for longer for each increase in steps. This bodes well for an attentional control view of Gf, since both Bowman (2006) and Stankov (2000) found a linear covariance effect for the number of steps relating to Gf. That is, as the steps increased, so too did the relationship of the task to Gf. Stankov concluded that attentional control was the most likely WM demand linked to Gf. However, there are problems with this conclusion. For Bowman’s (2006) data, as discussed, the number of steps increased sequentially throughout the task (rather than being presented in a random order) and thus, the increase could be more related to a learning aspect (Jensen,

14 _{It is possible that the proactive interference demands remain consistent because they are replacing themselves} rather than growing but the potential combination of orders invariably increases as the number of steps increase. It takes a minimum of six steps to experience all possible combinations of three letter orders (six possible orderings) but this does not account for repeats, which can occur on every non-adjacent step.

1977) than to an increase in attentional control demands. Stankov (2000), meanwhile, did randomize the order of items, solving that concern for attentional control explanations. However, although the overall linear performance covariance of Steps with Gf was significant, a closer look at the correlations reveals the trend is not as smooth as the

performance effect. Rather, there is a large jump going from 1-step (r = .248) to 2-step (r = .401) but then it quickly plateaus at 3-step (r = .429) and 4-step (r = .414). Thus, there may be a qualitative difference between 1-step and 2-step unrelated to attentional control

occurring. This difference could be as simple as the visual presentation of the ordering for the first step. That is, in the first step, the letters to-be-rearranged are given on the screen. In every subsequent step, the letters to-be-rearranged are ‘presented’ only in the active, direct- access region of WM. Thus, 1-step problems may be qualitatively different in their

attentional control demands, not because they require a stepwise, linearly decreasing amount of attentional control; but because they only need to be enacted on a visually presented and accessible arrangement of letters. It is also possible the qualitative difference is an artefact of the ceiling effect occurring on 1-step items. Although the success rate of 1-step items is not at ceiling (90% accuracy), the task does appear quite simple and this deficit from perfect

performance may simply indicate a failure to understand the instructions. Regardless, to circumvent the confound of visual presentation,15 _{the current experiment included the} manipulation of steps with three levels, all requiring active representation of the letter arrangement in direct access: 2-step (2S), 3S, and 4S items. We expect to see a linear decrease in performance associated with the linear increase in steps, because the attentional control demands are prolonged as steps increase. However, we expect to see no covariance of

15 _{A pilot test also revealed the 1-step items were virtually unusable in the analyses, with near-perfect}

performance (M = 98%). Thus, although there was theoretical reason not to consider 1-step items, there was also a practical reason in maximizing the value of participant time.

this linear effect with Gf because research in prior chapters (Chapter III on the LST and Chapter V) have indicated that increasing attentional control demands are not related to Gf.