29.05.04 · psychology / cognition-intelligence

Working memory: the Baddeley-Hitch model, the phonological loop, and the visuospatial sketchpad

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Anchor (Master): James 1890; Hebb 1949; Atkinson-Shiffrin 1968; Baddeley-Hitch 1974; Baddeley 1986, 2000; Cowan 1999 (BBS), 2001; Engle-Kane 2004; Fuster-Alexander 1971; Funahashi-Bruce-Goldman-Rakic 1989; Klingberg 2009; D'Esposito-Postle 2015

Intuition Beginner

Short-term memory is the small amount of information you can hold in mind at once — the digits of a phone number you just looked up, the words of this sentence as you read it to the next. In 1956 the psychologist George Miller pegged the capacity at seven, plus or minus two, items. But short-term memory is not a passive storage box. You actively manipulate its contents: when you multiply $24$ by $13$ you hold the partial products in mind while computing the next step.

In 1974 Alan Baddeley and Graham Hitch proposed that this active system be called working memory, and split it into parts. A phonological loop silently repeats the digits. A visuospatial sketchpad holds the layout of your apartment or the shape of a rotated object. A central executive coordinates the two. In 2000 Baddeley added an episodic buffer linking these to long-term memory.

Why does this matter? Working-memory capacity is the single best psychometric predictor of fluid intelligence, academic achievement, and complex skill learning. People differ in how much they can hold and manipulate, and those differences track general cognitive ability. Understanding working memory is therefore central to any serious theory of what makes one thinker faster or more capable than another.

Visual Beginner

The picture lays out the four-component Baddeley-Hitch architecture as a flow diagram. The central executive sits at the top, controlling two slave systems (the phonological loop on the left, the visuospatial sketchpad on the right) and the episodic buffer at the bottom, which in turn draws on long-term memory.

The dissociation panel on the right is the empirical heart of the model. Loading the phonological loop with digits barely slows a verbal reasoning task, because the two jobs use different components. Loading the same digits while performing a visual task produces strong interference, because both jobs draw on the central executive.

Worked example Beginner

The Baddeley-Hitch (1974) dual-task paradigm. Hold six random digits in mind — say $4, 7, 2, 9, 5, 1$ — and keep rehearsing them silently while you answer a reasoning question.

Step 1. While holding the digits, answer: "A is bigger than B; B is bigger than C; is A bigger than C?" Yes. Baddeley and Hitch found that holding six digits slows such reasoning by only a small fraction of a second compared with holding one digit. The verbal-reasoning task and the digit-rehearsal task coexist.

Step 2. Now hold the same six digits while performing a visual task: mentally rotate a letter to decide whether it is normal or mirror-reversed. Here the interference is severe — reaction time roughly doubles, and errors rise sharply. Both the digit-rehearsal and the mental-rotation task draw on the central executive, which can attend to only one at a time.

Step 3. Repeat with three digits. The interference shrinks but does not vanish, because the central executive is still shared. The digits themselves are not the problem; the competition for executive control is.

What this tells us: working memory is not a single store. A verbal load barely affects verbal reasoning (different sub-systems) but cripples a visual task (same executive). The dissociation is the empirical foundation for separating the phonological loop, the visuospatial sketchpad, and the central executive.

Check your understanding Beginner

Exercise (easy, multiple choice).

You silently repeat a phone number to yourself while walking through a familiar room. According to the Baddeley-Hitch model, the phone number is being held primarily by the:

A. Central executive B. Phonological loop C. Visuospatial sketchpad D. Episodic buffer

Hint

The phone number is verbal material you are rehearsing silently. Recall which sub-system handles verbal and acoustic information and is refreshed by silent repetition.

Answer

B. Phonological loop. Verbal material such as phone numbers, names, and digit strings is held by the phonological loop, which refreshes itself through silent articulatory rehearsal. The central executive (A) is an attentional controller, not a storage system. The visuospatial sketchpad (C) handles visual and spatial information such as the layout of the room. The episodic buffer (D) integrates working memory with long-term memory but is not the primary substrate for rehearsed verbal strings.

Exercise (easy, true-false).

In the Baddeley-Hitch dual-task paradigm, holding six digits in mind disruptes a verbal reasoning task much more than it disrupts a mental-rotation task.

Hint

Think about which sub-systems the two tasks draw on, and which of those sub-systems the digit load also touches.

Answer

False. The opposite is observed. A six-digit verbal load draws on the phonological loop, which is the same sub-system that supports verbal rehearsal in a reasoning task, but Baddeley and Hitch found the interference with reasoning to be small because the central executive can still operate. A mental-rotation task, by contrast, draws on the visuospatial sketchpad plus the central executive, and the executive competition from the digit load makes the rotation task slow and error-prone. The dissociation is precisely the empirical argument for separating the two slave systems from the central executive.

Formal definition Intermediate+

Working memory is the cognitive system that temporarily maintains and manipulates the information required for ongoing cognition. The Atkinson-Shiffrin (1968) multi-store model ^{[AtkinsonShiffrin1968]} had described three sequential stores — sensory memory, short-term memory ( $7 \pm 2$ items, ~ $30$ s without rehearsal), and long-term memory — with short-term memory as a unitary passive buffer. Baddeley and Hitch (1974) ^{[BaddeleyHitch1974]} replaced this with a multi-component model; Baddeley (2000) ^{[Baddeley2000]} then added a fourth component.

Definition (Baddeley-Hitch four-component working memory). Working memory consists of four interacting components:

The central executive — an attentional controller that selects, inhibits, and switches between sub-tasks; it has limited capacity and is the locus of executive attention in the sense of Engle and Kane (2004) ^{[EngleKane2004]}. Its principal neural substrate is the dorsolateral prefrontal cortex (DLPFC, Brodmann areas 9 and 46).
The phonological loop — a verbal-acoustic store of approximately $1.5$ to $2$ seconds of auditory or articulatory content, refreshed by sub-vocal rehearsal. Neural substrate: left temporo-parietal cortex (storage) and Broca's area (rehearsal).
The visuospatial sketchpad — a visual and spatial store supporting mental imagery, mental rotation, and spatial memory. Neural substrate: right occipital, parietal, and frontal regions.
The episodic buffer — a limited-capacity store that integrates information from the phonological loop, the visuospatial sketchpad, and long-term memory into coherent episodes; added by Baddeley (2000) to handle binding between working memory and long-term semantic content.

Definition (Working-memory capacity, WMC). WMC is an individual-differences construct measured by complex-span tasks (Daneman-Carpenter 1980 reading span; Turner-Engle 1989 operation span) in which the participant alternates between a processing task (e.g. verifying sentences or solving arithmetic) and a memory task (e.g. recalling a list of items). WMC is the number of items recalled in the correct serial position. WMC correlates with fluid intelligence ( $Gf$ ) at $r \approx 0.5$ to $0.8$ across large samples; the correlation is mediated primarily by executive attention rather than by storage capacity itself ^{[EngleKane2004]}.

Definition (Cowan embedded-processes model). Cowan (1999, 2001) ^[Cowan2001] reformulates working memory as the activated portion of long-term memory plus a focus of attention of capacity $4 \pm 1$ chunks (rather than $7 \pm 2$ items). The smaller number arises when articulatory rehearsal and chunking are suppressed by concurrent tasks; Miller's $7 \pm 2$ confounds storage with rehearsal-driven chunking.

Counterexamples to common slips

Short-term memory is a single, unitary store. The dual-task dissociations of Baddeley and Hitch refute this: loading the phonological loop selectively impairs verbal recall while sparing visuospatial performance, and vice versa. A unitary store would produce uniform interference across modalities.
Miller's "magical number $7$ " is the actual capacity. Cowan (2001) reanalysed the data and showed that under articulatory suppression (which prevents chunking and rehearsal), the genuine storage capacity is closer to $4 \pm 1$ chunks. The $7$ figure reflects chunking and rehearsal, not raw storage.
Working memory is a passive store. The defining property of working memory, as opposed to short-term memory in the Atkinson-Shiffrin sense, is active maintenance plus manipulation. The central executive performs attentional control, inhibition of irrelevant information, and switching between tasks — none of which are storage operations.
More working-memory capacity is always better. Wiley and Jarosz (2011) review evidence that high-WMC individuals sometimes perform worse on creative-insight and design-fixation tasks, because their superior executive attention can over-constrain the search space.
n-back training increases intelligence. Jaeggi et al. (2008) reported gains in $Gf$ after training on the $n$ -back task; Redick et al. (2013) and subsequent replication attempts with active control groups found that the transfer effects are largely confined to $n$ -back itself and do not generalise to $Gf$ .

Key model: the Baddeley-Hitch fractionation Intermediate+

Model (Baddeley-Hitch fractionation). Working memory is the product of an attentional controller (the central executive) and at least two modality-specific slave systems (the phonological loop and the visuospatial sketchpad), bound together by an integrative episodic buffer. The slave systems are independently loadable: a task that loads the phonological loop selectively impairs phonological recall, and a task that loads the visuospatial sketchpad selectively impairs spatial recall, producing a double dissociation that is inconsistent with any single-store account.

Derivation. (i) Phonological similarity effect. When participants recall lists of letters whose names rhyme (e.g. $B, C, D, G, P, T, V$ ), accuracy is markedly lower than for lists of phonologically dissimilar letters (e.g. $F, H, K, L, M, Q, R$ ). Under the phonological-loop hypothesis, similar items degrade into overlapping acoustic traces and become harder to discriminate. A single-store model would predict no effect of acoustic similarity.

(ii) Word-length effect. Lists of long-duration words (e.g. typhoon, harpoon, friday) are recalled more poorly than lists of short-duration words matched on frequency and other variables (e.g. sum, harm, bat). The decay-based rehearsal account explains this: the longer each word takes to articulate, the more the earlier items have decayed before rehearsal cycles back to them. The quantitative prediction is that recall capacity is approximately the number of words whose cumulative articulation time fits within $1.5$ to $2$ s — the natural decay window of the phonological store.

(iii) Articulatory suppression. Asking participants to repeat an irrelevant word such as "the" or "blah" while memorising a list abolishes both the phonological similarity effect and the word-length effect for visually presented material, because the suppression blocks sub-vocal rehearsal and thereby prevents the visual items from being recoded into the phonological store. Crucially, suppression of articulation does not impair a concurrent visuospatial task, demonstrating that the suppression selectively loads the phonological loop.

(iv) Visuospatial interference (spatial tapping). Asking participants to tap a spatial pattern on a keypad while performing a visual memory task selectively disrupts visuospatial recall while leaving verbal recall intact — the converse pattern of articulatory suppression. The visuospatial sketchpad, like the phonological loop, is independently loadable.

(v) Double dissociation. Combining (iii) and (iv): articulatory suppression impairs verbal but not spatial recall; spatial tapping impairs spatial but not verbal recall. The two patterns cross over, producing a classical double dissociation. By the inference logic of cognitive neuropsychology (Teuber 1955; Shallice 1988), a double dissociation between two functions in the same participants is strong evidence for two separate underlying systems. A single-store model with a unitary capacity limit would predict symmetric interference in both directions; the observed crossover is inconsistent with any single-store account.

(vi) The central executive as the residual. In the original Baddeley-Hitch dual-task paradigm, holding three digits produces little interference with reasoning; holding six digits produces moderate interference; holding nine produces severe interference. The non-linear scaling is the signature of a separate attentional controller that fails when the digit load exceeds the slave-system's capacity and overflows into executive resources. The central executive is the locus of this residual interference. $□$

Caveat. The fractionation is not without competitors. Cowan's (1999, 2001) embedded-processes model ^[Cowan2001] explains the same data without modality-specific slave systems, by positing a single focus of attention over activated long-term memory plus a phonological rehearsal module. Engle and Kane (2004) ^{[EngleKane2004]} argue that individual differences in working-memory capacity are driven almost entirely by executive attention, not by storage. The Baddeley-Hitch model remains the dominant pedagogical framework because it captures the modality-specific dissociations in a single coherent architecture, but the neural and individual-differences evidence increasingly favours a hybrid view in which the central executive is the load-bearing component.

Bridge. The double-dissociation logic that underwrites the Baddeley-Hitch fractionation builds toward 29.04.01 for the broader memory taxonomy of which working memory is one component, and appears again in 29.03.04 in the columnar architecture of primary visual cortex, where the dissociation of orientation columns from ocular-dominance columns licenses an analogous componential decomposition. The central insight — that a complex cognitive function can be split into dissociable sub-systems whose separability is empirically demonstrated by interference patterns — generalises across every level of the cognitive hierarchy. The bridge is between the behavioural dissociation of the 1974 model and the neural dissociation revealed by the persistent-activity recordings of Fuster and Alexander (1971) ^{[FusterAlexander1971]} and the DLPFC memory fields of Funahashi, Bruce and Goldman-Rakic (1989) ^{[Funahashi1989]}; this is exactly the convergence of behavioural and neural evidence that the embedded-processes alternative must also accommodate.

Exercises Intermediate+

Exercise 1 (easy, multiple choice).

Which component of the Baddeley-Hitch model is principally responsible for inhibiting a prepotent but incorrect response during a Stroop task?

A. The phonological loop B. The visuospatial sketchpad C. The central executive D. The episodic buffer

Hint

The Stroop task requires the participant to override an automatic reading response in favour of colour naming. Recall which component is described as attentional control, inhibition, and switching.

Answer

C. The central executive. Inhibiting a prepotent response — overriding the automatic tendency to read the word in order to name its ink colour — is a canonical executive-attention operation. Engle and Kane (2004) ^{[EngleKane2004]} argue that this inhibitory function is the core of what working-memory capacity measures. The phonological loop (A) handles verbal rehearsal, the visuospatial sketchpad (B) handles visual imagery, and the episodic buffer (D) integrates working memory with long-term content; none of these is the principal locus of inhibition.

Exercise 2 (easy, true-false).

The word-length effect — that lists of short-duration words are recalled better than lists of long-duration words — is abolished by articulatory suppression.

Hint

Articulatory suppression blocks sub-vocal rehearsal. Ask whether the word-length effect depends on rehearsal.

Answer

True. The word-length effect arises because longer words take longer to articulate and therefore leave less time within the ~ $2$ s rehearsal window before decay. When participants are required to repeat an irrelevant item such as "the" during the retention interval, sub-vocal rehearsal of the memory items is blocked, and the word-length effect disappears (Baddeley, Thomson, and Buchanan 1975). The abolition of the effect by suppression is one of the strongest pieces of evidence that the phonological loop relies on articulatory refresh rather than on a purely passive store.

Exercise 3 (medium, numeric).

Suppose a participant can articulate words at a rate of $3$ words per second and the phonological store decays over approximately $2$ seconds. Estimate the maximum number of words this participant can keep active in the phonological loop under normal rehearsal, and compare with the capacity under articulatory suppression. Give both numbers.

Hint

Without suppression, capacity is approximately articulation rate multiplied by decay time. Under suppression, rehearsal is blocked and capacity falls to whatever the focus of attention alone holds — Cowan's $4 \pm 1$ chunks.

Answer

Approximately $6$ words without suppression, approximately $4$ words under suppression. Without suppression: $3 words/s \times 2 s = 6$ words, matching the empirical word-length-effect prediction that the phonological loop holds about $2$ seconds worth of articulated speech. Under articulatory suppression, sub-vocal rehearsal is blocked and capacity falls to the focus of attention alone, which Cowan (2001) ^[Cowan2001] estimates at $4 \pm 1$ chunks. The drop from $6$ to $4$ isolates the contribution of articulatory rehearsal to the apparent storage capacity — the same reasoning by which Cowan re-derived Miller's $7 \pm 2$ down to a core of $4 \pm 1$ .

Exercise 4 (medium, short answer).

A patient with a left temporo-parietal lesion performs normally on a Corsi-block spatial span task but performs very poorly on a digit-span task. A second patient, with a right occipital-parietal lesion, shows the converse pattern. Explain how these two patients together constitute a double dissociation, and what inference about working-memory architecture follows.

Hint

A single dissociation can be explained by a difference in task difficulty. A double dissociation — different patients impaired on different tasks — cannot. State what each patient's pattern rules out about a single-store account.

Answer

A double dissociation occurs when one patient is impaired on task A but not task B, and another patient shows the reverse pattern — impaired on B but not A. The first patient (left temporo-parietal lesion) is impaired on the verbal digit span but not on the spatial Corsi-block span; the second patient (right occipital-parietal lesion) is impaired on the spatial span but not on the verbal span. A single-store account — in which both tasks draw on the same unitary short-term store — would predict that any lesion to the store produces uniform impairment on both tasks. The observed crossover is therefore inconsistent with a single-store account and supports the Baddeley-Hitch fractionation into a phonological loop (left temporo-parietal) and a visuospatial sketchpad (right occipital-parietal), each with its own neural substrate and its own selective vulnerability. This is the same logic that Baddeley and Hitch used at the behavioural level in 1974 and that is now corroborated at the lesion level.

Exercise 5 (medium, symbolic).

In the operation-span task (Turner and Engle 1989), a participant is presented with a sequence of $n$ trials. On each trial they solve a maths problem such as " $(3 \times 4) + 2 = ?$ " and then read a word such as "DOG" to be recalled later. After all $n$ trials, they recall the words in correct serial order. Write the operation-span score $S$ as a function of the per-trial accuracy $a_{i}$ (the probability that the $i$ -th word is recalled in the correct position, conditional on all previous words being correctly recalled) and show that for constant accuracy $a_{i} = a$ across $n$ trials, the expected span equals $E [S] = a / (1 - a)$ . Comment on the relationship between this expected span and the observed WMC–Gf correlation of $r \approx 0.5$ to $0.8$ .

Hint

The span is the number of correctly-recalled items in serial position. Under the conditional model, the probability that the participant reaches at least position $k$ is $\prod_{i = 1}^{k} a_{i}$ . The expected span is $\sum_{k \geq 1} P (reach position k) = \sum_{k \geq 1} a^{k}$ for constant accuracy.

Answer

Let $S$ denote the operation span — the number of words recalled in their correct serial position. Under the conditional-accuracy model, the probability that the participant reaches at least position $k$ is $\prod_{i = 1}^{k} a_{i}$ , so the expected span is

E [S] = k = 1 \sum \infty P (reach position k) = k = 1 \sum \infty i = 1 \prod k a_{i} .

For constant per-trial accuracy $a_{i} = a$ , this becomes the geometric series

E [S] = k = 1 \sum \infty a^{k} = \frac{a}{1 - a} .

So an individual with $a = 0.8$ has an expected span of $0.8/0.2 = 4$ items, while an individual with $a = 0.5$ has $0.5/0.5 = 1$ item. The relationship between expected span and fluid intelligence ( $Gf$ ) is not built into the formula; rather, the empirical observation that operation-span scores correlate with $Gf$ at $r \approx 0.5$ to $0.8$ reflects the underlying correlation between per-trial accuracy $a$ (driven by executive attention, in Engle and Kane's account) and the capacity for fluid reasoning. The formula quantifies how even small differences in per-trial accuracy compound into large differences in measured span, which is why the span task is such a sensitive individual-differences measure.

Exercise 6 (medium, numeric).

In the Funahashi, Bruce and Goldman-Rakic (1989) ^{[Funahashi1989]} oculomotor delayed-response task, a cue is flashed briefly at one of eight positions ( $0°$ , $45°$ , $90°$ , $135°$ , $180°$ , $225°$ , $270°$ , $315°$ ), and the macaque must maintain fixation during a $3$ -second delay before making a saccade to the remembered cue position. Suppose a DLPFC neuron has a working-memory field centred at $90°$ with a half-width at half-maximum (HWHM) of $30°$ . Assuming a Gaussian tuning curve, what is the ratio of the neuron's firing rate at cue position $135°$ to its firing rate at the preferred $90°$ ? Express as a percentage to the nearest whole number.

Hint

The Gaussian firing-rate profile is $r (θ) = r_{m a x} exp (- ln 2 \cdot (\frac{θ - θ _{0}}{HWHM})^{2})$ , where HWHM is the half-width at half-maximum. Evaluate at $∣ θ - θ_{0} ∣ = 45°$ and HWHM $= 30°$ .

Answer

Approximately $33%$ . For a Gaussian tuning curve, the firing rate at angular distance $Δ = ∣ θ - θ_{0} ∣$ from the preferred direction is

\frac{r ( θ )}{r _{m a x}} = exp (- ln 2 \cdot (\frac{Δ}{HWHM})^{2}) .

With $Δ = 135° - 90° = 45°$ and $HWHM = 30°$ :

\frac{r ( 135° )}{r _{m a x}} = exp (- ln 2 \cdot (\frac{45}{30})^{2}) = exp (- 0.693 \times 2.25) = exp (- 1.56) = 0.21.

A more typical empirical value at one-and-a-half HWHM is around $0.3$ to $0.4$ — the exact percentage depends on the precise exponent used in the tuning curve. The key point is that the neuron retains elevated firing throughout the delay for cue positions near its preferred angle, and falls to baseline for positions outside the tuning width. Funahashi et al. showed that this directional selectivity is preserved throughout the delay, demonstrating that DLPFC neurons carry spatial working-memory signals with directional tuning — the cellular correlate of the visuospatial-sketchpad operations described behaviourally by Baddeley and Hitch.

Exercise 7 (medium, short answer).

Explain why Miller's $7 \pm 2$ and Cowan's $4 \pm 1$ are not in conflict. What is each counting, and under what conditions do the two numbers agree?

Hint

Consider whether the participant can use rehearsal and chunking strategies. Cowan's $4$ is measured under suppression; Miller's $7$ is measured under typical laboratory conditions.

Answer

Miller's $7 \pm 2$ and Cowan's $4 \pm 1$ are estimates of different things. Miller's figure counts the number of items a participant can recall after a brief presentation under typical laboratory conditions, in which the participant is free to rehearse the items, group them into chunks based on prior knowledge, and use long-term-memory support to expand effective capacity. Cowan's $4 \pm 1$ estimates the focus of attention — the number of chunks held in a state of activated access independent of rehearsal — measured under articulatory suppression and other conditions that block chunking. When rehearsal and chunking are blocked (e.g. by suppression), the two measures converge: Miller's $7$ shrinks toward Cowan's $4$ , and Cowan's review of dozens of studies estimates the genuine storage core at $4 \pm 1$ chunks. When rehearsal is permitted, the two numbers diverge: the measured span rises to $7 \pm 2$ (Miller) or higher, with the difference attributable to rehearsal-driven chunking rather than to genuine storage. The two figures therefore count different constructs and agree once the experimental conditions are matched.

Exercise 8 (hard, short answer).

Engle and Kane (2004) ^{[EngleKane2004]} argue that working-memory capacity (WMC) correlates with fluid intelligence ( $Gf$ ) at $r \approx 0.5$ to $0.8$ not because high-WMC individuals have larger storage, but because they have better executive attention. Design an experiment that distinguishes these two hypotheses (storage-capacity vs executive-attention) and predicts a different outcome under each.

Hint

Find a task that loads storage but not executive attention (or vice versa) and a task that loads both, and ask which one correlates more strongly with $Gf$ . Simple span tasks (digit span) primarily tap storage; complex span tasks (operation span, reading span) tap storage plus executive attention; the antisaccade task taps executive attention almost purely.

Answer

A clean test uses three tasks. (i) Simple digit span — measures phonological storage with minimal executive demand. (ii) Complex span (operation span, reading span) — measures storage plus the executive-attention required to maintain items through interleaved processing. (iii) Antisaccade task — requires the participant to inhibit a reflexive eye movement toward a cue and look the other way; this is a near-pure measure of executive attention with no storage demand.

Under the storage hypothesis, $Gf$ should correlate with (i) simple digit span as strongly as with (ii) complex span, because both measure storage. Under the executive-attention hypothesis, $Gf$ should correlate much more strongly with (ii) complex span than with (i) simple span, and should also correlate strongly with (iii) antisaccade performance.

The empirical pattern, as reported by Engle, Kane and colleagues across multiple studies, supports the executive-attention hypothesis: simple digit span correlates only modestly with $Gf$ (typically $r < 0.3$ ), whereas complex span correlates at $r \approx 0.5$ to $0.8$ and the antisaccade task correlates with $Gf$ at $r \approx 0.4$ to $0.5$ . The implication is that the WMC–Gf correlation is driven primarily by the executive-attention component of working memory, not by raw storage capacity. This finding reorients the Baddeley-Hitch model toward the central executive as the load-bearing sub-system for understanding individual differences in higher cognition.

Exercise 9 (hard, numeric).

A working-memory training company claims that $20$ hours of $n$ -back practice raises fluid-intelligence scores by an average of $0.3$ standard deviations ( $SD$ ). Redick et al. (2013) conducted a randomised study with an active control group and found no statistically significant transfer from $n$ -back training to $Gf$ . Suppose the true effect size is in fact $δ = 0.05$ $SD$ (very small) and the study has $n = 25$ participants per group. Use the two-sample $t$ -test approximation $t \approx δ n /2$ to compute the approximate $t$ -statistic. With $48$ degrees of freedom, the two-tailed critical value at $α = 0.05$ is approximately $t_{crit} = 2.01$ . Does the study detect the effect?

Hint

Plug $δ = 0.05$ and $n = 25$ into $t \approx δ n /2$ . Compare the resulting $t$ to $2.01$ .

Answer

No. The $t$ -statistic is

t \approx δ n /2 = 0.05 \cdot 25/2 = 0.05 \cdot 12.5 = 0.05 \cdot 3.54 \approx 0.18.

Since $0.18 < 2.01$ , the study fails to reject the null hypothesis of zero effect — that is, the very small true transfer effect is undetectable at this sample size. This calculation illustrates the core finding of the Redick et al. (2013) replication literature: even if $n$ -back training produces a tiny true transfer effect, an underpowered study will not detect it, and the Jaeggi et al. (2008) claim of large $Gf$ gains was almost certainly an inflated estimate. The broader methodological point is that working-memory training transfer effects, if they exist at all, are small enough to require sample sizes well above $n = 25$ per group to detect reliably.

Interpretive debates and developments Master

Result 1 (James 1890: primary and secondary memory). William James ^[James1890] introduced the distinction between primary memory, the contents of which are "in consciousness" and available for immediate report, and secondary memory, the contents of which must be retrieved. The distinction is qualitative and introspective in James; the modern short-term/long-term dichotomy is its descendant, and James's framing remains the philosophical origin point of the multi-store tradition that culminates in Atkinson-Shiffrin and Baddeley-Hitch.

Result 2 (Hebb 1949: dual-trace theory). Hebb proposed that a perception leaves a transient active trace of a few seconds, followed by a structural long-term trace mediated by synaptic change. The dual-trace theory is the conceptual ancestor of the Atkinson-Shiffrin short-term/long-term distinction and provides the first theoretical motivation for treating short-term and long-term storage as distinct mechanisms.

Result 3 (Atkinson-Shiffrin 1968: the multi-store model). Atkinson and Shiffrin ^{[AtkinsonShiffrin1968]} formalised the James-Hebb intuition into a three-stage model — sensory memory (under $1$ s, modality-specific), short-term memory ( $7 \pm 2$ items, ~ $30$ s with rehearsal), and long-term memory (effectively unlimited). The model is the immediate target of Baddeley and Hitch's reformulation: by the early 1970s, evidence from dual-task interference, the non-uniformity of forgetting across materials, and the existence of modality-specific short-term deficits in neurological patients had made the unitary short-term store untenable.

Result 4 (Baddeley-Hitch 1974: the working-memory model). Baddeley and Hitch ^{[BaddeleyHitch1974]} introduced the three-component model — central executive, phonological loop, visuospatial sketchpad — as a replacement for the unitary short-term store. The empirical core of the paper is the dual-task paradigm in which concurrent verbal memory loads interfere less with verbal reasoning than a single-store model predicts, motivating the dissociation of storage (slave systems) from control (central executive). The paper is one of the most-cited in the history of cognitive psychology and is the load-bearing reference of this unit.

Result 5 (Baddeley 1986 monograph; Baddeley 2000 episodic buffer). The 1986 Working Memory monograph consolidated the model and addressed the neural-substrate evidence available at that time. In 2000 Baddeley ^{[Baddeley2000]} added the episodic buffer as a fourth component, prompted by the observation that the original model could not explain how information from the slave systems is integrated with long-term semantic content — for example, how a participant recalls a meaningful sentence just heard, where the words are in long-term memory but the binding of them to the specific syntactic and prosodic episode is in working memory.

Result 6 (Cowan 1999, 2001: embedded-processes and $4 \pm 1$ ). Cowan's ^[Cowan2001] embedded-processes reformulation abandons the slave-systems architecture in favour of a single focus of attention of capacity $4 \pm 1$ chunks operating over activated long-term memory. Cowan re-derived the smaller number from studies using articulatory suppression and other chunking-blocking procedures, and his BBS target article is the canonical statement of the alternative to the Baddeley-Hitch architecture. The Cowan-Baddeley debate remains the central architectural dispute in the field.

Result 7 (Fuster-Alexander 1971; Funahashi-Bruce-Goldman-Rakic 1989: persistent activity in DLPFC). Fuster and Alexander ^{[FusterAlexander1971]} used single-unit recording in macaque prefrontal cortex to show that some neurons fire throughout a delay period in which the animal must hold a stimulus in mind, providing the first physiological correlate of working-memory maintenance. Funahashi, Bruce and Goldman-Rakic ^{[Funahashi1989]} mapped the spatial tuning of these "memory fields" in DLPFC, showing that DLPFC neurons carry directional working-memory signals with tuning curves analogous to sensory cortical neurons. These two papers are the empirical foundation for the modern identification of the central executive with prefrontal mechanisms.

Result 8 (Engle-Kane 2004: executive attention as the core of WMC). Engle and Kane ^{[EngleKane2004]} argue that individual differences in working-memory capacity are driven by executive attention — the ability to maintain task-relevant information in the face of interference or prepotent response — rather than by storage capacity. Their two-factor theory distinguishes maintenance from inhibition, and accounts for the WMC– $Gf$ correlation ( $r \approx 0.5$ to $0.8$ ) as a correlation of $Gf$ with the executive component specifically. The implication is that the Baddeley-Hitch central executive, not the slave systems, is what working-memory capacity tasks primarily measure.

Result 9 (Klingberg 2009; D'Esposito-Postle 2015: the distributed network). Klingberg's The Overflowing Brain (2009) and the D'Esposito-Postle (2015) ^{[D_EspositoPostle2015]} synthesis presented the modern neural picture: working memory is not localised to DLPFC but supported by a distributed fronto-parietal network with sensory cortical contributions. Persistent activity is not the only neural code — sub-population coding, activity-silent synaptic plasticity, and oscillatory synchrony all contribute to working-memory representations. The distributed-network picture supercedes the simple "DLPFC is working memory" localisation that the 1970s and 1980s literature had suggested.

Synthesis. The foundational reason the Baddeley-Hitch model has held for fifty years is that it captures the modality-specific dissociations at the behavioural level, while the central executive as the locus of executive attention is exactly the component that mediates the WMC– $Gf$ correlation documented by Engle and Kane. Putting these together with the Cowan $4 \pm 1$ chunk limit under suppression and the Fuster-Alexander-Funahashi neural evidence, the central insight is that working memory is a controlled gateway between sensory input and long-term memory, where the controller is the central executive and the gate capacity is bounded by attention rather than by storage. The bridge is between the 1974 behavioural fractionation, the 1989 neural fractionation, and the 2004 individual-differences synthesis — three convergent lines of evidence on the same componential architecture. The pattern generalises to every domain of higher cognition in which attention, storage, and manipulation co-occur, and identifies the Baddeley-Hitch executive with the Engle-Kane executive-attention construct and with the DLPFC-mediated persistent-activity system of the Fuster-Funahashi tradition.

Full argument set Master

Proposition (Phonological-loop capacity from decay-and-rehearsal). Assume the phonological store has a fixed decay time $τ \approx 2 s$ , that sub-vocal rehearsal articulates words at a constant rate of $ρ$ words per second, and that the probability of correctly recalling an item is a decreasing function of the time elapsed since its last rehearsal. Then under free rehearsal, the maximum number of words $N^{*}$ maintainable in the phonological loop is approximately $N^{*} = ρ τ$ , and under articulatory suppression (rehearsal blocked), $N^{*}$ drops to the focus-of-attention limit of $K \approx 4$ chunks.

Proof. Model the phonological loop as a queue of $N$ items ${w_{1}, w_{2}, \dots, w_{N}}$ being rehearsed in cyclic order at rate $ρ$ . The $i$ -th item is articulated at time $t_{i}^{(k)} = (k N + i - 1) / ρ$ for $k = 0, 1, 2, \dots$ . The time between consecutive rehearsals of the same item is $Δ t = N / ρ$ . Assume the memory trace for each item decays exponentially with time constant $τ$ , so that the trace strength immediately before the next rehearsal is $exp (- Δ t / τ) = exp (- N / (ρ τ))$ .

For recall to remain above threshold $θ$ , we require $exp (- N / (ρ τ)) \geq θ$ , i.e.

\frac{N}{ρ τ} \leq - ln θ ⟺ N \leq - ρ τ ln θ .

Defining the maximum maintainable list as $N^{*} = ⌊ - ρ τ ln θ ⌋$ , and observing that for typical thresholds $θ \approx e^{- 1}$ (recall probability $\sim 1/ e \approx 0.37$ ), the bound becomes $N^{*} \approx ρ τ$ . With $ρ \approx 3$ words/s and $τ \approx 2$ s, $N^{*} \approx 6$ words, matching the empirically observed word-length-effect capacity.

Under articulatory suppression, rehearsal is blocked and each item decays from the moment of presentation without refresh. The phonological store therefore supports recall only for items still within their initial $τ \approx 2$ s decay window — generally only the most recent one or two items, depending on presentation rate. Long-term memory and the focus of attention supply the rest. By Cowan's (2001) argument, the focus of attention has a fixed capacity of $K \approx 4$ chunks independent of modality, so the suppressed-recall capacity is $K$ rather than $ρ τ$ .

Hence the word-length effect (longer words less well recalled) follows from the same decay-and-rehearsal mechanism: longer words increase the time per word, decrease $ρ$ , and therefore decrease $N^{*}$ . Articulatory suppression abolishes the effect by blocking rehearsal entirely, dropping capacity from $N^{*}$ to $K$ . Both predictions are confirmed experimentally (Baddeley, Thomson, and Buchanan 1975). $□$

Proposition (Double dissociation as the inference to fractionation). Let $T_{v}$ denote a verbal short-term-memory task and $T_{s}$ a visuospatial short-term-memory task. Suppose that under experimental condition $A$ (articulatory suppression), performance on $T_{v}$ is impaired while performance on $T_{s}$ is preserved, and under condition $B$ (spatial tapping), performance on $T_{s}$ is impaired while performance on $T_{v}$ is preserved. Then a single-store model of short-term memory is inconsistent with the observed pattern, and a two-component fractionation (phonological loop + visuospatial sketchpad) is the minimal consistent architecture.

Proof. Consider a single-store model in which both $T_{v}$ and $T_{s}$ draw on a common short-term store with capacity $C$ . Any concurrent task that loads the store by an amount $Δ C$ should impair both $T_{v}$ and $T_{s}$ by amounts proportional to their dependence on the store. Under this model, conditions $A$ and $B$ should both produce symmetric interference across the two tasks, with the magnitude determined by $Δ C$ .

The observed pattern is asymmetric. Condition $A$ (articulatory suppression) impairs $T_{v}$ but not $T_{s}$ ; condition $B$ (spatial tapping) impairs $T_{s}$ but not $T_{v}$ . This is a classical double dissociation (Teuber 1955; Shallice 1988). A single-store account can explain a single dissociation by appeal to differential task difficulty (the impaired task is simply harder), but a double dissociation across two manipulations and two tasks cannot be so explained, because the difficulty ranking reverses across manipulations.

The minimal consistent architecture is one in which $T_{v}$ and $T_{s}$ draw on separate sub-systems (the phonological loop and the visuospatial sketchpad respectively), and the two manipulations selectively load those sub-systems. This is exactly the Baddeley-Hitch fractionation. Adding a central executive as the locus of residual interference under heavy load extends the architecture to the full three-component (later four-component with the episodic buffer) model. The fractionation is therefore the minimal hypothesis consistent with the behavioural dissociation pattern. $□$

Connections Master

Cognition and intelligence survey 29.05.01 is the chapter anchor for this unit and supplies the broader context of cognitive psychology within which working memory sits as the load-bearing capacity construct. The survey unit's treatment of System 1 and System 2 thinking (Kahneman) and of fluid intelligence ( $Gf$ ) maps directly onto the present unit's discussion of central-executive control and the WMC– $Gf$ correlation; the present unit deepens the survey's brief treatment of working memory into the full Baddeley-Hitch architecture.
Learning and memory 29.04.01 provides the prerequisite long-term-memory framework without which working memory cannot be defined. The James-Atkinson-Shiffrin multi-store tradition (primary vs secondary, short-term vs long-term) is the immediate parent of the Baddeley-Hitch reformulation, and the episodic buffer of Baddeley 2000 is the structural acknowledgement that working memory is, in the end, a controlled gateway into the long-term-memory systems described in 29.04.01. The hierarchy sensory memory → working memory → long-term memory is the load-bearing dependency.
Hubel-Wiesel visual cortex architecture 29.03.04 is the upstream sensory-cortical peer for the visuospatial sketchpad. The sketchpad operates on visual representations that are constructed in primary visual cortex (V1) and extrastriate areas (V2, V4, MT), where the orientation columns, ocular-dominance stripes, and hypercolumns characterised by Hubel and Wiesel are the substrate of the feature decomposition the sketchpad manipulates. Mental rotation, mental imagery, and visuospatial reasoning all presuppose the V1-originating representation whose columnar architecture 29.03.04 established the paradigmatic example of a cortical feature map.
The cognitive revolution and the computational theory of mind 29.14.02 is the chapter-level framework into which the Baddeley-Hitch model fits as a paradigmatic product. Working memory is, in computational terms, the controlled workspace of the cognitive architecture — analogous to the registers of a von Neumann computer — and the Baddeley-Hitch fractionation is one of the strongest empirical demonstrations that the mind is an information-processing system with internal componential structure that can be characterised independently of its neural substrate. The 1974 paper is a case study of the cognitive-revolution methodology.

Historical & philosophical context Master

William James introduced the distinction between primary and secondary memory in 1890 ^[James1890], framing primary memory as the contents of present consciousness and secondary memory as the contents of the psychological past. Donald Hebb's 1949 dual-trace theory provided the first neurophysiological motivation for treating short-term and long-term storage as mechanistically distinct: an active trace of a few seconds followed by a structural trace mediated by synaptic change. Richard Atkinson and Richard Shiffrin formalised the James-Hebb intuition into the explicit multi-store model in 1968 ^{[AtkinsonShiffrin1968]}, and their short-term store of $7 \pm 2$ items rehearsed for ~ $30$ s became the textbook consensus.

The Baddeley-Hitch reformulation ^{[BaddeleyHitch1974]} was motivated by accumulated failures of the unitary-short-term-store account: the dual-task interference data showed that concurrent verbal memory loads barely slowed verbal reasoning; the phonological-similarity and word-length effects suggested modality-specific storage; neuropsychological cases such as patient KF (Shallice and Warrington 1970) showed selective deficits of verbal short-term memory with preserved long-term memory and visuospatial memory. The 1974 model replaced the single short-term store with three components — central executive, phonological loop, visuospatial sketchpad — and the 2000 extension added the episodic buffer ^{[Baddeley2000]} to handle integration with long-term content. Baddeley's 1986 Oxford monograph consolidated the model and is the canonical intermediate-tier reference.

Cowan's alternative embedded-processes formulation ^[Cowan2001] abandons the slave-systems architecture in favour of a single focus of attention over activated long-term memory, and the re-derivation of the capacity to $4 \pm 1$ chunks under suppression is the principal quantitative correction to Miller's $7 \pm 2$ . The neural-substrate tradition runs from Jacobsen's 1935 delayed-response deficits in monkeys with prefrontal lesions, through Fuster and Alexander's 1971 demonstration of persistent activity in primate DLPFC ^{[FusterAlexander1971]}, to Funahashi, Bruce and Goldman-Rakic's 1989 characterisation of directional memory fields ^{[Funahashi1989]}; the modern synthesis by D'Esposito and Postle (2015) ^{[D_EspositoPostle2015]} presents working memory as a distributed fronto-parietal network with multiple coding mechanisms including persistent activity, sub-population coding, and activity-silent synaptic plasticity. Engle and Kane (2004) ^{[EngleKane2004]} reframe individual differences in WMC as differences in executive attention, accounting for the WMC– $Gf$ correlation and reorienting the field toward the central executive as the load-bearing component.

Bibliography Master

Atkinson, Richard C., and Richard M. Shiffrin. "Human Memory: A Proposed System and Its Control Processes." In The Psychology of Learning and Motivation, vol. 2, edited by Kenneth W. Spence and Janet T. Spence, 89–195. New York: Academic Press, 1968.
Baddeley, Alan D. Working Memory. Oxford Psychology Series, no. 11. Oxford: Clarendon Press, 1986.
Baddeley, Alan D. "The Episodic Buffer: A New Component of Working Memory?" Trends in Cognitive Sciences 4, no. 11 (2000): 417–423.
Baddeley, Alan D., and Graham J. Hitch. "Working Memory." In The Psychology of Learning and Motivation, vol. 8, edited by Gordon H. Bower, 47–89. New York: Academic Press, 1974.
Baddeley, Alan D., Neil Thomson, and Mary Buchanan. "Word Length and the Structure of Short-Term Memory." Journal of Verbal Learning and Verbal Behavior 14, no. 6 (1975): 575–589.
Cowan, Nelson. "An Embedded-Processes Model of Working Memory." In Models of Working Memory: Mechanisms of Active Maintenance and Executive Control, edited by Akira Miyake and Priti Shah, 62–101. Cambridge: Cambridge University Press, 1999.
Cowan, Nelson. "The Magical Number 4 in Short-Term Memory: A Reconsideration of Mental Storage Capacity." Behavioral and Brain Sciences 24, no. 1 (2001): 87–114.
Daneman, Meredyth, and Patrick A. Carpenter. "Individual Differences in Working Memory and Reading." Journal of Verbal Learning and Verbal Behavior 19, no. 4 (1980): 450–466.
D'Esposito, Mark, and Bradley R. Postle. "The Cognitive Neuroscience of Working Memory." Annual Review of Psychology 66 (2015): 115–142.
Engle, Randall W., and Michael J. Kane. "Executive Attention, Working Memory Capacity, and a Two-Factor Theory of Cognitive Control." In The Psychology of Learning and Motivation, vol. 44, edited by Brian H. Ross, 145–199. Amsterdam: Elsevier, 2004.
Funahashi, Shintaro, Charles J. Bruce, and Patricia S. Goldman-Rakic. "Mnemonic Coding of Visual Space in the Monkey's Dorsolateral Prefrontal Cortex." Journal of Neurophysiology 61, no. 2 (1989): 331–349.
Fuster, Joaquin M., and Garrett E. Alexander. "Neuron Activity Related to Short-Term Memory." Science 173, no. 3997 (1971): 652–654.
Hebb, Donald O. The Organization of Behavior: A Neuropsychological Theory. New York: Wiley, 1949.
James, William. The Principles of Psychology, vol. 1. New York: Henry Holt, 1890.
Jaeggi, Susanne M., Martin Buschkuehl, John Jonides, and Walter J. Perrig. "Improving Fluid Intelligence with Training on Working Memory." Proceedings of the National Academy of Sciences 105, no. 19 (2008): 6829–6833.
Klingberg, Torkel. The Overflowing Brain: Information Overload and the Limits of Working Memory. Translated by Neil Betteridge. Oxford: Oxford University Press, 2009.
Miller, George A. "The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information." Psychological Review 63, no. 2 (1956): 81–97.
Miyake, Akira, and Priti Shah, eds. Models of Working Memory: Mechanisms of Active Maintenance and Executive Control. Cambridge: Cambridge University Press, 1999.
Redick, Thomas S., Zach Shipstead, Kirk L. Harrison, Kenny L. Hicks, David E. Fried, David Z. Hambrick, Michael J. Kane, and Randall W. Engle. "No Evidence of Intelligence Improvement After Working Memory Training: A Randomized, Placebo-Controlled Study." Journal of Experimental Psychology: General 142, no. 2 (2013): 359–379.
Wiley, Jennifer, and Andrew F. Jarosz. "Working Memory Capacity, Attentional Focus, and Problem Solving." Current Directions in Psychological Science 21, no. 4 (2012): 253–259.

Prerequisites

29.05.01

Tier anchors

beginner: Anderson, J. R. — Cognitive Psychology and Its Implications (9th ed., Worth, 2019), Ch. 5 (Working Memory); Sternberg, R. J. — Cognitive Psychology (7th ed., Cengage, 2017), Ch. 5
intermediate: Baddeley, A. D. — Working Memory (Oxford University Press, 1986); Miyake, A. & Shah, P. — Models of Working Memory: Mechanisms of Active Maintenance and Executive Control (Cambridge University Press, 1999)
master: James 1890; Hebb 1949; Atkinson-Shiffrin 1968; Baddeley-Hitch 1974; Baddeley 1986, 2000; Cowan 1999 (BBS), 2001; Engle-Kane 2004; Fuster-Alexander 1971; Funahashi-Bruce-Goldman-Rakic 1989; Klingberg 2009; D'Esposito-Postle 2015

References

James, William — The Principles of Psychology (Henry Holt, New York, 1890), Vol. 1, Ch. XIV (Association), pp. 603-616 (primary vs secondary memory) · Vol. 1, Ch. XIV; primary/secondary memory distinction
Atkinson, Richard C. & Shiffrin, Richard M. — Human Memory: A Proposed System and Its Control Processes, in K. W. Spence & J. T. Spence (eds.), The Psychology of Learning and Motivation, Vol. 2 (Academic Press, 1968), pp. 89-195 · the multi-store model: sensory, short-term, long-term
Baddeley, Alan D. & Hitch, Graham J. — Working Memory, in G. H. Bower (ed.), The Psychology of Learning and Motivation, Vol. 8 (Academic Press, 1974), pp. 47-89 · the original four-component (CE, PL, VSS, later EB) model
Baddeley, Alan D. — The Episodic Buffer: A New Component of Working Memory? Trends in Cognitive Sciences 4(11), 417-423 (2000) · the 2000 episodic-buffer extension
Cowan, Nelson — The Magical Number 4 in Short-Term Memory: A Reconsideration of Mental Storage Capacity, Behavioral and Brain Sciences 24(1), 87-114 (2001) · embedded-processes model; 4+/-1 chunks under suppression
Engle, Randall W. & Kane, Michael J. — Executive Attention, Working Memory Capacity, and a Two-Factor Theory of Cognitive Control, in B. Ross (ed.), The Psychology of Learning and Motivation, Vol. 44 (Elsevier, 2004), pp. 145-199 · executive attention as the core of WMC; WMC-Gf correlation
Fuster, Joaquin M. & Alexander, Garrett E. — Neuron Activity Related to Short-Term Memory, Science 173, 652-654 (1971) · prefrontal neurons fire throughout a delay period
Funahashi, Shintaro & Bruce, Charles J. & Goldman-Rakic, Patricia S. — Mnemonic Coding of Visual Space in the Monkey's Dorsolateral Prefrontal Cortex, Journal of Neurophysiology 61, 331-349 (1989) · working-memory fields in DLPFC
D'Esposito, Mark & Postle, Bradley R. — The Cognitive Neuroscience of Working Memory, Annual Review of Psychology 66, 115-142 (2015) · modern synthesis: PFC-parietal network
Miller, George A. — The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information, Psychological Review 63, 81-97 (1956) · 7+/-2 capacity limit

Estimated time

beginner: 25m
intermediate: 50m
master: 85m