Visuo-spatial working memory measures.

These tasks were designed to test visual working memory at varying levels of precision and capacity. None of these involve classic dual-task (i.e., “maintenance” plus “manipulation”) working memory tasks due to the relative difficulty of implementing these complex tasks in child populations. However, at high difficulty levels, previous work suggests a commonality between dual- and single-tasks’ relations to matrix reasoning measures [17,44]. Indeed, in populations of children and older adults, single-task spans are often utilized as measures of working memory (e.g., [45–48]).

1] N-Back task (see Fig 1A): The N-back task is a common running span measure in which a series of stimuli are presented and the participant has to compare the current stimulus to the stimulus that was presented N items prior; for example, on 2-back trials, participants are required to compare the identity of the third item to the first item, the fourth item to the second item, the fifth item to the third item, and so on [49]. We utilized a variation of the standard N-back working memory task that has previously been used to assess differences across distinct groups or across the lifespan [50–52]. Minor modifications were made to the standard design to ensure the task was easily understood by children. In this task, the screen space was evenly divided into 7 columns from left to right, and 21 rows from top to bottom. Although the column/row divisions were not explicitly displayed on the screen, the participants were made aware of this fact during the task explanation and this setup aided participants in keeping track of the temporal position of items [50]. Each trial began by indicating the number of columns that were going to be used on that trial (the ‘N’ in the N-back–i.e., on a 2-back trial, 2 columns would be used; see Fig 1]; this allowed the vertical spatial alignment of items to serve as a cue for which items should be compared. For ease of exposition, we will briefly describe a 2-back trial–with the other levels of ‘N’ being simple extrapolations of this base description.

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Fig 1. Examples of tasks.

Examples of 3 tasks. All parameters remained the same for both children and adults except set size. Children were given the verbal prompts shown here, while adults were given instructions prior to the tasks. (A) In the N-back task, a series of cartoon animals were presented in an invisible grid. Participants responded whether the item that had appeared above the current item was the same or different than the current item. Set size (i.e., ‘N’) was identical to the number of columns. (B) In the Spatial Span task, participants saw a series of items filled in within a randomly-generated set of squares. They then reproduced the sequence they saw. (C) In Multiple Object Tracking (MOT), participants tracked several blue target faces moving amidst many yellow distractor faces. The targets then became identical to the distractors and all items continued to move. After 4 seconds of motion, one item was cued and the participant had to identify whether the cued item started as a blue or yellow face.

https://doi.org/10.1371/journal.pone.0221353.g001

Participants pressed a key to begin each run. After 1 s, a cartoon animal was presented on a blue background in the first column of the first row. All the animals were visually distinct and presented in nameable different colors (brown beaver, blue fish, red crawfish, tan clam, yellow duck, green turtle) and subtended approximately 1.3° of visual angle. Then, after 2 s, the first animal disappeared and a new animal appeared in the second column of the first row. After a 2 s delay, the second animal disappeared and an animal was presented in the first column of the second row. The participant then indicated via a keypress whether this animal matched the one that had appeared directly above it (i.e., the animal that had been presented in the first column of the first row, or 2-back). After the participant entered a response, the third animal disappeared and an animal appeared in the next location (second column of the second row), with the response now indicating whether the animal matched that which had been presented in the second column of the first row. The next animal appeared in the first column of the third row, and so on until the participant had made a total of 20 responses. The other values of “N” progressed in the same manner across N number of columns. Adults completed set sizes (“N”) 1 through 7 followed by 7 through 1 [20 trials per run), while children completed set sizes 1 through 5 followed by 5 through 1 (15 trials per run). Overall percent correct was then calculated from all trials.

2] Spatial span task (see Fig 1B): The spatial span task that was utilized was a variant of the Corsi block-tapping task, a classic measure of visuospatial short-term memory [53–56]. Each trial began with the presentation of an array of outlined squares (each subtended 1.25° visual angle) in 12 locations selected pseudo-randomly from a virtual 5 x 5 grid of possible locations on a blue (RGB = 153, 217, 234) background. Then, a subset of these squares (corresponding to set size) were briefly filled in, one at a time, for 0.6 s before turning back to unfilled. After the final square changed back to unfilled, the participant was prompted to use the mouse to click on the squares in the order that they had changed color (with the squares changing color when clicked to verify each choice). Children completed 25 trials consisting of 5 each of set sizes 2 through 6. Adults completed 20 trials consisting of 4 each of set sizes 4 through 8. In both age groups, set sizes were randomly shuffled and intermixed.

The dependent variable for this task was calculated using two criteria. The ‘strict’ criterion credited only exact location/temporal matches between the presentation and response (i.e., a response out of order was considered incorrect). The ‘lax’ criterion credited responses that corresponded to any item from the presentation, regardless of order. This measure recognizes that, for example, a participant may forget the first item but then reproduce the sequence accurately starting with the second item. Such a response would result in a score of 0 using the strict criterion, but clearly indicates some memory for the array. For all statistics, we used the average (per trial) between strict and lax scores; however, we note that the results are not qualitatively different when using only strict or lax scores.

3] Visual array change detection (CD): One-shot visual change detection involves the sequential presentation of two arrays of colored items, with the participant’s task being to detect the presence of a change between the two arrays [25,57,58]. Here stimuli were cartoon fish, subtending 1.8° of visual angle wide and separated by at least 0.9° on a blue background, drawn without replacement from the following colors (R,G,B): white [236, 236, 236], red [255, 0, 4], purple [136, 12, 146], orange [255, 127, 39], green [98, 249, 44], blue [0, 35, 255], yellow [255, 255, 0], brown [113, 56, 0]. Stimuli were randomly placed at locations in a virtual grid (adults: 5 x 5, children: 4 x 4] and presented for 250 ms immediately after a brief auditory cue. All stimuli then disappeared for a 1-s delay, after which a test array was presented until the participant responded. The test array was either identical to the first array, in which case participants were instructed to press a key labeled “same,” or one item changed color, in which case participants were instructed to press a key labeled “different.” Children completed 4 “different” trials and 4 “same” trials each for set sizes 2, 3, 4, 5, and 6, and adults completed 6 “different” and 6 “same” trials each for set sizes 2 through 7. Trial order was randomized. Overall percent correct was calculated and used in all analyses; A’ measures were also calculated [59] but the results were not qualitatively different than percent correct, so we report the simpler measure (percent correct) here.

4] Change detection task with distracting irrelevant items (“CD filter” task): This was based on the change detection task described above, but manipulated the number of distracting items rather than target items [25,60]. The target set size was fixed at 3 for children and 4 for adults on all trials. In addition to the colored cartoon fish targets on the screen there were circles with the same dimensions as the fish. These circles were described as “rocks” to participants, and were drawn from a non-overlapping color set from the fish. Adults completed 80 trials and children completed 60 trials, which were evenly divided between high-distractor (adults = 10, children = 6] and low-distractor (adults = 3, children = 2) condition. The dependent measure was the percent correct on low-distractor trials minus the percent correct on the high-distractor trials, indicating a decrement in change detection ability with additional task-irrelevant distractors.

5a-c) Delayed Match to Sample (position, color, orientation): Three separate visual short-term memory precision tasks were completed (memory for color, position, and full-contrast Gabor orientation respectively; see [61]). In the position memory task, participants saw a circle on the screen for 1000 ms, which was followed by a blank screen. After a delay of 500 ms, an identical circle appeared offset 0, .2, .7, and 1.5 degrees to the right or left. Participants pressed arrow keys to identify the direction of offset, and completed 80 of these trials. The dependent variable in this task was a 79% threshold calculated from a logistic fit to responses. The color and orientation tasks followed the general procedure of [61], with timing identical to the position memory task. In these two memory tasks, the post-delay stimulus could be the same or different than the original stimulus; if different, the difference was defined by either an orientation offset or an offset in a standardized 360-degree color space (see [61]). Offsets increased when participants responded that the stimuli were the same and decreased when participants responded that the stimuli were different, according to the procedure in [61]. The dependent variable on these tasks was the mean of the smallest color space distances for which participants responded that the colors were different.

Attention measures.

1] Visual enumeration task: The visual enumeration task required participants to identify the number of stimuli that were briefly presented. While many foundational applications of this paradigm have emphasized the speed with which participants could identify the correct number of items (e.g., [62–65]), we were instead interested in participants' ability to correctly identify the number of items after a short presentation [66]. On each trial, a number of yellow cartoon fish (modeled after [67] were presented in random locations within a virtual 5x5 grid in the middle of the screen for 250 ms (children) or 150 ms (adults) on a blue background. Each fish stimulus was 1.9° of visual angle wide, and at least 0.95° of visual angle separated each stimulus. After stimulus presentation, participants responded by typing the number of fish they saw using the number keys on a standard keyboard. All participants completed four trials per set size (one through ten, randomly intermixed), and the percent correct for all trials was used as the aggregate performance score.

2] Multiple Object Tracking (MOT; see Fig 1C): The MOT task involves attending to a number of moving targets amidst identical distractors [23]. The version employed here was a child-friendly version of the task similar to that which has been described previously [68]. Fourteen cartoon faces (each subtending .8° of visual angle) for child participants, or sixteen cartoon faces for adult participants, were presented inside a gray circle on the screen that subtended 10° of visual angle from its center. All faces were yellow circles with black lines depicting a ‘happy face’, except for a variable number of faces, which were blue circles with black lines depicting a ‘sad’ face. The blue ‘sad’ faces were identified as the targets that the participant should track (and thus the yellow ‘happy’ faces were distractors). Each trial consisted of all the cartoon faces moving within the gray circle at a speed of 5 deg/s, with direction of movement determined stochastically. The faces never overlapped or touched, and were programmed to ‘bounce’ off each other and the walls of the gray circle. After 2 s, the blue target faces changed to match the yellow, happy distractor faces. After an additional 4 s of movement, the faces halted and a white circle containing a question mark replaced one of the faces. The question mark had a 50% chance of appearing over a target face. Participants were required to indicate whether the indicated face had been a blue target face at the onset of the trial. Children were tested on 10 trials each of set sizes 1, 2, 3, and 4 targets. Adults were tested on 5 trials of set size 1 and 10 trials each of set sizes 2, 3, and 4, and 5. These set sizes were chosen to ensure that no participants would perform at chance, due to tracking 1 item being very easy, but capacity-related individual differences would be evident at higher set sizes. Trial order was fully randomized. Overall percent correct was calculated and used in all analyses.

3] The Attentional Network Task (ANT; [67,69]: The ANT is a measure of several dimensions of visual attention involving a directional response to an oriented central stimulus that is flanked by response-compatible or response-incompatible stimuli. These central and flanking stimuli are presented in combinations of location cues as well as response-compatible and response-incompatible distractors. Subtracted mean response times (e.g., incompatible-distractor trials minus compatible-distractor trials), normalized by individual participants’ overall mean response time, are intended to index attentional orienting, alerting and conflict resolution. We utilized a 96-trial version of the task adapted from [56] using yellow fish as the directional stimuli. All task parameters (e.g., size of stimuli) were modeled directly from [56].

4] The Useful Field of View (UFOV) visual search task: The UFOV task [70] is designed to test individuals’ ability to identify briefly-presented peripheral information. In this task participants see a display of items (white squares) arranged in two concentric circles and along 8 lines radiating from the center of the screen. The participant must identify the line on which an oddball item (a white star) occurred. A concurrent task, designed to encourage central fixation and ensure the peripheral nature of the main task, involved an identification of a central stimulus, a small cartoon face, as having long hair or short hair. Adults and children each completed 50 trials of a 3 down/1 up adaptive staircase. The staircase procedure converges on a threshold value; these threshold values were log-transformed to approximate normality then sign-flipped to make better performance be associated with higher values for consistency with other tasks.

Intelligence measures.

1] Raven's Progressive Matrices were utilized as our measure of fluid intelligence. These matrices are a measure of reasoning commonly used in cognitive training paradigms (e.g., [71–73] as well as cross-sectional studies of the cognitive bases of reasoning [74]. Despite the fairly small number of trials, Raven’s Matrices have long been the gold standard for reasoning measures. Nonetheless, our use of only one measure of this construct does limit the conclusions we can draw.

In this task, a series of pattern completion problems are presented to the participant. The rules for the patterns (e.g., perceptual matching, mutual exclusivity) become more difficult as items progress later in the series. We presented a selection of 4 items from set A, 6 items each from sets B, C and D, and 4 items from set E of Raven's Standard Progressive Matrices to children (26 items total), and even-numbered items from Raven's Advanced Progressive Matrices to adults (18 items total). All participants were limited to 10 minutes in completing the task, although as they completed items they were unaware of the amount of time remaining. The adults’ selection was patterned from previous cognitive training work that divided reasoning tests into two halves for pre- and post-tests [17,71], while the children's selection was designed to maximize individual differences by presenting a large range of difficulty in stimuli in a relatively brief amount of time. Our outcome measure for this task was percent correct of the total items.

2] As a test of verbal knowledge that could covary with Raven’s scores (particularly in children), each participant completed a non-progressive selection of items from the Peabody Picture Vocabulary Test (PPVT; [75], a standardized 4-alteranative-choice test of vocabulary. Stimuli were presented on the full screen and a recording was played directing the participant to choose a certain cartoon picture (e.g., the participant would see 4 pictures on the screen and would hear a phrase like “point to cupola”). Children were provided the opportunity to ask the experimenter to repeat the word if they desired. Children completed items 109–156 while adults completed items 169–216.

Analytical approach.

We first used the full covariance structure of our data to test for the presence of a positive manifold. We examined the magnitudes of bivariate correlations as well as the degree to which our data could be explained by a single underlying latent variable. These two methods provided evidence regarding the hypothesis that a positive manifold in task performance was present. If correlations between tasks were uniformly large and positive, and if the majority of variation could be explained with a single latent variable, that would be evidence for the classic general-ability definition of fluid intelligence [6,39]

In contrast, if cognitive tasks were not generally positively correlated with Raven’s scores, this would be evidence for some degree of process-specificity of reasoning (i.e., that reasoning is not reliably related to all possible tasks–which was our a priori assumption). Indeed, our methods involved the intentional inclusion of a wide variety of cognitive tasks which themselves were designed to demand a variety of processes. Process-level heterogeneity by design should lead to a performance covariance structure that is likewise heterogeneous, and we did not expect a strong positive manifold or single-component latent variable structure. However, our analyses in this section also provide initial evidence for which tasks that are most related to our measure of reasoning, Raven’s. We end this section by examining the evidence for a subset of reasoning-related tasks, which can then inform more specific model comparisons in the next section.

Bivariate correlations.

As an initial measure of a positive manifold, we calculated the proportion of all pairwise correlations that were higher than a series of possible thresholds. We did this by resampling our dataset 10,000 times with replacement and calculating the percent of above-threshold product-moment correlations for each threshold. Task scores were sign-flipped, if necessary, so that larger values would indicate better performance in these analyses.

When this threshold was restricted to only correlations that were positive (i.e., > 0), a slight majority of correlations appeared to demonstrate a positive manifold (see Fig 2). In contrast, if a threshold was introduced such that tasks must share just 1% of their variance (i.e., correlation at or above 0.1), then fewer than 50% of correlations satisfied the expectation of a positive manifold. Bootstrapped Spearman rank-order correlations followed the same qualitative pattern (see S3 File). Since there was no clear positive manifold, with many very small correlations in our data, it was more likely that certain key tasks should be the focus of our comparisons here. Indeed, only a sub-set of measures appeared to be related to domain-general fluid intelligence ability. This was the expected result, in that some tasks were chosen for the battery that were unlikely to load particularly strongly on fluid intelligence abilities.

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Fig 2. Test of positive manifold in children and adults.

As the threshold for identifying a “positive manifold” increased, the number of correlations that satisfy that threshold decreased. Error bands denote 95% percentiles from 10,000 bootstrapped samples for each of 26 evenly spaced correlation thresholds. Thresholds for statistical significance, at alpha = .05, are r = 0.304 (children) and r = 0.219 (adults).

https://doi.org/10.1371/journal.pone.0221353.g002

Latent variable decompositions.

In order to confirm the lack of a positive manifold found above we conducted a second analysis to test the extent to which a single factor could explain performance across all tasks in the battery. To this end, we examined the components produced by an eigenvalue decomposition of the correlation matrices when excluding Raven’s (i.e., Principal Components Analysis; PCA). This analysis was able to provide evidence supporting our observed lack of a positive manifold. In addition, we used this analysis to identify certain tasks most likely to be related to fluid intelligence.

As was true in the general patterns seen in the bivariate correlation matrices, PCA also did not support a single-component latent structure. In the dataset including both children and adults and looking only at tasks other than Raven’s, 5 eigenvalues were above 1, with 2 being above the parallel-analysis cutoffs (actual eigenvalues: 2.96, 1.44). Yet, while 2 components survive the parallel analysis cutoff, we feel caution is warranted in interpreting these components [76,77]. For instance, when splitting the data by age group, only one component in each age group survived a parallel-analysis component comparison. This implied a possible dissociation between adults’ and children’s patterns of cognitive correlates of intelligence. Age-related differences between the tasks associated with high first-component loadings would provide evidence for developmental changes in the relations of cognitive abilities. Below, we examine each age group’s first-component loadings in order to understand these patterns in more detail.

Identifying target cognitive tasks.

Examining the first component in each age group, it was clear that tasks with high working memory demands had consistently large loadings (see Table 1). In addition, several attentional tasks had high loadings as well, with enumeration loading the most strongly onto this first component.

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Table 1. PCA component-1 task loadings for each age group.

https://doi.org/10.1371/journal.pone.0221353.t001

The construct of fluid intelligence describes a latent general ability to perform on tasks, particularly novel ones on which prior knowledge would not help. The tasks in this battery overwhelmingly fit this description (apart from PPVT, which is specifically designed to test prior knowledge, a central aspect of crystallized intelligence). As such, the general component just described should be related to a general performance factor such as fluid intelligence. Further evidence may be derived from an examination of bivariate correlations. Specifically, we were interested in whether correlations between cognitive measures and Raven’s scores were high for the same tasks with high component-1 loadings. Further, differences between children’s and adults’ correlations would provide initial evidence for development-related qualitative differences in the cognitive correlates of reasoning. To test this, we examined the correlations between each task and Raven’s scores (see Table 2; see S2 File for the full correlation matrices). In particular, we compared these correlations to the patterns seen in the component analysis reported above, and we statistically test the differences between children’s and adults’ correlations.

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Table 2. Correlations of cognitive tasks with Raven’s, separated by age group.

https://doi.org/10.1371/journal.pone.0221353.t002

As Table 2 shows, the tasks with the highest correlations with Raven’s generally had the highest loadings on the common component. These included spatial span, N-back, enumeration, and MOT. Despite this qualitative pattern of similarity, neither the enumeration nor the MOT correlations reached conventional statistical significance in adults. The correlations between these four tasks generally were similar between age groups, while certain other correlations are quite different. Most notably, the correlation of PPVT scores and Raven’s scores was significantly higher in children than adults (p < .01).

Of these four top tasks that were both correlated with Raven’s and loaded highly onto the common latent component, two were canonical memory tasks (i.e., spatial span and N-back) and two were canonical attention tasks (i.e., enumeration and MOT; note that UFOV had relatively high component loadings while having weak correlations with Raven’s). This provided evidence that the relations between cognitive tasks and intelligence measures are not divisible into strictly memory or attention categories, but specific processing demands of tasks may be related to measured intelligence. Further analyses explored these tasks in greater detail.

Analytical approach.

Each of the following analyses was the output of one Bayesian regression using the brms package in R [78]. A beta response distribution was used because Raven’s accuracy scores are bounded between 0 and 1, and for interpretability coefficients are reported on log-odds scales. Results are reported here in terms of two numbers, the regression coefficient (i.e., expected value [b]) and the proportion of the posterior distribution with the same sign as that expected value (congruent density [cD], e.g, a positive expected value is paired with the percent of posterior samples that were positive). This provides a simple and intuitive sense of the probability of the hypothesis that a given parameter is non-zero. We adopt a threshold value of cD = 0.975, roughly corresponding to a two-tailed frequentist alpha = 0.05. Note that the main effect of age is not reported in this section because it is likely to be a theoretically-unimportant artifact of task-difficulty differences across ages. More detailed information about each model’s results can be found in tables in S3 File.

Each of these regressions sampled 5 chains for 20,000 samples each, with the first 10,000 of each chain’s samples being discarded as warm-up. A thinning interval of 2 was implemented. Default priors from brms were used in each model. In every case, the precision parameter phi was estimated as a random effect that varied by age, thereby controlling for age-related distributional differences in Raven’s scores. All models converged with r-hat values below 1.02, indicating a very small potential scale reduction factor across chains.

In S3 File frequentist fits of these models are reported. Also, reported there are bootstrapped frequentist estimates of parameters from models which randomly sample an equal number of children and adults, thereby mitigating possible bias in parameter estimates due to unequal sample sizes (see S3 File).

Predicting reasoning using measures of visuospatial working memory.

We start by looking at relations between working memory measures and Raven’s as moderated by age (see Fig 3). Given the lack of age-related differences in the previous analyses, despite our expectation of reliable main effects of cognitive predictors, we did not expect any reliable interactions between cognitive measures and age group. When predicting Raven’s scores spatial span scores and age group, spatial span scores were a reliable predictor (b = 2.089, cD = 0.997) while the interactions between spatial span score and age were not reliable (b = 0.872, cD = 0.801). When predicting Raven’s scores with N-back scores and age group, N-back scores were a reliable predictor (b = 3.845, cD = 0.976) while the interactions between N-back score and age were not reliable (b = 0.538, cD = 0.594).

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Fig 3. Effects of key working memory measures in predicting Raven’s scores.

Main effects of each memory measure were reliably predictive of reasoning scores. No interactions with age were reliable.

https://doi.org/10.1371/journal.pone.0221353.g003

Bivariate relations between task scores (e.g., between N-back and Raven’s) are influenced by task-specific random variation; we mitigated this variation by calculating a composite score. We calculated composite scores as geometric means in order to minimize the effects of distributional differences between predictor tasks. When predicting Raven’s scores using a working memory (WM) composite score (i.e., geometric mean of N-back and spatial span scores) and age group, WM composite scores were a reliable predictor (b = 3.424, cD = 0.999) while the interactions between WM composite score and age were not reliable (b = 1.228, cD = 0.797). This composite score regression provides further support for close and developmentally-stable links between working memory and reasoning.

Predicting reasoning scores using measures of visual attention.

Next, we examined the relations between age, Raven’s scores, and attention measures (see Fig 4]. When predicting Raven’s scores using enumeration scores, and age group, enumeration scores were a reliable predictor (b = 1.606, cD = 0.979) while the interactions between enumeration score and age were not reliable (b = -0.375, cD = 0.65). When predicting Raven’s scores using MOT scores and age group, MOT scores were a reliable predictor (b = 3.729, cD = 0.991) while the interactions between MOT score and age were not reliable (b = -2.265, cD = 0.887). When predicting Raven’s scores using attention composite (i.e., geometric mean of enumeration and MOT scores) and age group, attention composite scores were a reliable predictor (b = 1.653, cD = 0.999) while the interactions between attention composite and age were not reliable (b = -0.737, cD = 0.817). As we found with working memory measures, attention is also linked to reasoning in a developmentally-stable pattern.

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Fig 4. Effects of key attention measures in predicting Raven’s scores.

Main effects of each attention measure were reliably predictive of reasoning scores. No interactions with age were reliable.

https://doi.org/10.1371/journal.pone.0221353.g004

Does working memory mediate the relations between attention and reasoning?

Next we tested whether attention measures are uniquely related to Raven’s scores or whether their relations are mediated by the same capacity constraints as the working memory measures. Theories of memory and intelligence (e.g., [26]), suggest that the relations between attention and reasoning would be mediated by working memory scores. To test this hypothesis we fit Bayesian mediation models, using the same basic modeling methods described above, to estimate the degree to which relations between WM composite scores explain the effects of enumeration and MOT predicting reasoning scores. Age was included as a covariate for both expected value and precision parameters, but the interaction between age and other predictors was omitted in order to simplify model interpretation and because no interactions were evident in previous analyses.

The model parameters are reported in each of the tables below, which provide evidence that the relations between attention measures and reasoning scores are in fact mediated by a common ability captured by the WM composite scores (see Tables 3 and 4). Each of the indirect effects were reliably above zero, the proportions mediated were essentially 100%, and the direct effects of attention measures on reasoning scores was reduced to be indistinguishable from zero.

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Table 3. Effect of enumeration on Ravens when mediated by WM composite, controlling for age-related main effects.

https://doi.org/10.1371/journal.pone.0221353.t003

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Table 4. Effect of MOT on Ravens when mediated by WM composite, controlling for age-related main effects.

https://doi.org/10.1371/journal.pone.0221353.t004

Importantly, the reverse mediation effect was not observed (see S3 File for full tables). The direct effects of N-back and MOT on Raven’s each remained reliable. The reliability was lower for the effect of attention composite scores mediating the relations between memory measures and Raven’s scores. The estimated proportion mediated in these models was approximately 50%. Because links between attention and reasoning were fully mediated by memory, but not the reverse, this implies a hierarchical structure of cognition and reasoning in which attentional processes underlie working memory, which in turn underlies higher-level abilities.