The current experiment was designed to further specify the demands associated with binding capacity and attentional control in WM. Specifically, we aimed to uncouple the
frequently seen overlap between binding capacity and attentional control. In aim of this goal, we also consider the important role of systematicity, which we identified in Chapter IV as an important determinant relating to the true binding capacity demands of the task. As with studies in prior chapters, the approach was to experimentally manipulate the core task (the Swaps task) to differ in theoretical demands and observe how these experimental
manipulations changed the variance in prototypical tasks representing key constructs such as Gf. Unlike prior experiments the manipulations (Letters and Steps) in the Swaps task are expected to be quantitative in nature.16 Thus, rather than using each condition as separate predictors in a linear regression, we use an analysis of covariance (ANCOVA) for each hypothesis, with the expectation that the Letters and Steps manipulations can be plotted as linear functions. We then compare how latent variables of Gf and WM covary with these linear functions.
For Steps (attentional control), we hypothesized a linear decrease in performance associated with increases in the number of steps (2S > 3S > 4S), as seen in Stankov (2000). However, unlike Stankov (2000), we do not predict that steps will covary with Gf, because the lack of 1-step items removes the qualitative difference that occurs as a result of arranging letters visually presented (as opposed to those only in the direct-access region). In other words, although attentional control demands increase consistently and linearly with increases in Steps (as they require longer attentional control), these demands are hypothesized to be not related to Gf. Thus, increased steps will not increase the relationship to Gf. Similarly,
Bowman’s (2002) sequential ordering of Steps means the linear covariance with Gf observed by him may simply be due to learning (Jensen, 1977). However, attentional control demands
16 RC in the LST is theorized to be, and was expected to be, a quantitative manipulation also, with the pattern of 2D > 3D > 4D. However, the analyses consistently revealed a pattern more like 2D = 3D > 4D, and the task breakdown provided in discussions indicate a more qualitative difference between 4D items and the other two RC levels. For the RMT, the same, different, and ascending conditions were never theorized to be a continuous scale, only that the binding demands in different were theorized to be higher than those in same and ascending, though same and ascending still differed in the visual similarity of the elements to-be-integrated.
are more likely to be tapped through traditional WM tasks such as complex spans (used often by, e.g., Engle, 2018), so we do expect this linear function of Steps to covary with our WM factor.
For Letters (capacity), we hypothesized a linear decrease in performance associated with increases in the number of letters involved in the problems (3L > 4L > 5L). Although this is a novel manipulation, the prediction comes from increased binding load on the direct access region. Previous chapters have observed a decrease in performance related to
increased binding demands (access-random vs. access-fixed in the ACT; different vs. same in the RMT).
Unlike Steps, we do expect to see a covarying effect of Gf, such that increases in letters are associated with concomitant increases in the relationship to Gf. This covariation has been somewhat seen in earlier chapters. Although this has not been consistently
demonstrated, various reasons have been explored for why this is not showing consistently, including that Gf tasks may not necessarily differ in binding capacity demands, even though they do, more generally, tap a fundamental binding function. The overall implication of binding theory is that relational integration demands acts upon both WM and Gf (the relational integration hypothesis). Although these demands are assumed to be through the number of active bindings in the direct access region (Oberauer et al., 2007), it is not yet clear whether this can be most appropriately observed through linear increases in binding
‘capacity’ demands (as Chapter V failed to find this difference between same vs. different). In the current experiment, we assume they are (Oberauer et al., 2007) and expect to see the linear effect of Letters leading to concomitant increases in covariation with both Gf and WM.
Finally, for Systematicity (fixedness of letters and bigrams throughout 4L and 5L problems, respectively), we predict that systematic items will lead to higher performance than non-systematic items, and this effect will be amplified for items benefitting the most from
systematicity, which is those of higher steps. This performance increase should put systematic 4L and 5L items on the same performance level as 3L items, minus any deficit associated with carrying the fixed letters across the problem steps or reintegrating them with the final step (these demands are anticipated to be minimal). In line with the results from the ACT (Chapter IV), we also hypothesize that items with systematicity OFF will correlate more with Gf than items with systematicity ON, because they increase the binding demands of the problem (in line with the prior ‘capacity’ hypothesis). Specifically, systematic 4L and 5L items should correlate with Gf similarly to 3L items, while non-systematic 4L and 5L items will correlate more with Gf in correspondence with the increasing binding capacity demands. 6.2. Method
6.2.1. Participants
There were 106 participants who participated in exchange for course credit. The mean age was 19.90 (SD = 3.85) and there were 74 females (69.8%). This is the same dataset from Experiment 3 of Chapter III on the LST, though the focus of the analyses in that chapter are on the LST rather than the Swaps task.
6.2.2. Measures Swaps Task
Participants completed 36 items of the Swaps Task as described in Stankov (2000). On each item, participants were presented a problem page with a set of letters (e.g., B K M) arranged towards the top of the screen and below, several lines of instructions (steps) that instructed the participants to swap the order of letters (e.g., “Swap 1 with 2 | Swap 1 with 3”).
The number of Letters varied between three to five. The number of Steps varied between two to four. Letter arrangements were randomly generated by selecting from any of the consonants of the English alphabet with the only constraint that all letters in a problem had to be unique. Swap steps were generated randomly with one constraint: two consecutive
swaps could never cancel each other out (i.e., “Swap 1 with 3” could never be followed by “Swap 1 with 3” or “Swap 3 with 1”). This constraint meant that step generation would naturally prioritise using letter positions that had not previously been used. There were 12 of each number of letters (3L/4L/5L) and 12 of each number of swaps (2S/3S/4S) generated to make up the 36 items for each participant, mixed evenly across the two variables (i.e., there were four 3L2S items, four 3L3S items, and so on) and presented in a random order.
The final manipulation was systematicity. When systematicity was off, the items were generated randomly using the above logic. When systematicity was on, the same logic was applied except that 4L and 5L items used the steps generation of 3L items to produce the instructions, such that only three of the four/five letters were actually used in the problem. An additional constraint ensured that the one/two excluded letters were chosen randomly from all available letters rather than always excluding the far-right letters. For 5L items, the two excluded letters were always adjacent, making it an excluded bigram. Systematicity was applied evenly, such that half of each type of item (e.g., half of 4L, half of 2S) had systematicity off and half had systematicity on (for 3L items, systematicity being on does nothing because it uses the same 3L logic either way).
When participants were ready to respond, they pressed spacebar which progressed the program to a response page that was blank apart from a textbox where they could type and submit their response. This is different from previous research (e.g., Bowman, 2006) which presented the possible response options (all possible orderings) to choose from. The current method was preferred to prevent guessing and because it would be unpractical to display the 120 possible combinations of letters for the novel 5L items (as opposed to only six
Gf Tasks
The same 20-item version of Raven’s APM from earlier chapters was included. The same Letter Series from earlier chapters was included. The LST from Chapter III
(Experiment 3) was also administered but the data is not included in the analyses presented here, primarily because the lack of rule induction makes it unsuitable as a Gf task (as described in Chapter II).
WM Tasks
The same spatial n-back, Operation Span (OSPAN) and Symmetry Span (SSPAN) from earlier chapters were included. For both OSPAN and SSPAN, the dependent variable was total number of elements (letters/squares) recalled across the task and the processing cut- off was set at 80% accuracy. Scores below this threshold were removed and set as missing data.
6.2.3. Procedure
Participants were tested in groups of one to ten in computer labs at the University of Sydney. The testing sessions were 90-minutes long and participants were instructed to complete as many of the seven tasks as possible in the 90 minutes. The tasks were presented in a random order, except for SSPAN which was always presented last. This was because the SSPAN was thought to be the most disposable in the analyses, considering the OSPAN was already included. In total, 80 of the 106 participants completed all tasks including the SSPAN, while a small amount (two to four participants) completed five of the seven tasks, missing one other task. The implications of this missing data on the SSPAN are described in the Results.
6.3. Results