Digit Span Task

Version: v1 (current)

The Digit Span task is a classic measure of short-term memory capacity and working memory function. Participants view sequences of digits presented one at a time, then must recall them in either forward or backward order, providing a simple yet powerful assessment of memory span.

Overview

Short-term memory capacity is fundamental to cognition. It determines how much information we can hold in mind while performing mental operations. The Digit Span task, part of many standardized assessments (e.g., Wechsler scales), measures this capacity by presenting increasingly long sequences of digits for immediate recall.

The task comes in two variants: Forward Span (recall in presentation order) assesses passive short-term storage, while Backward Span (recall in reverse order) requires active manipulation and thus taps working memory's executive component. The difference between forward and backward spans reveals the cost of mentally transforming information.

Digit Span is widely used in clinical neuropsychology, cognitive aging research, and studies of attention and working memory. Its brevity, simplicity, and sensitivity to individual differences make it an ideal screening tool for memory impairment and a standard component of cognitive batteries.

Scientific Background

Key Findings:

• Capacity Limits: Average forward span is 7±2 items (Miller, 1956), though modern estimates suggest ~4 chunks in working memory (Cowan, 2001)
• Forward vs. Backward: Backward span is typically 1–2 digits shorter than forward span, reflecting the added executive demand
• Neural Basis: Forward span engages phonological loop (left temporoparietal cortex), while backward span additionally recruits prefrontal executive regions (Hoshi et al., 2000)
• Aging Effects: Backward span shows steeper decline with age than forward span, consistent with executive function vulnerability

Theoretical Framework: According to Baddeley's working memory model, forward digit span primarily reflects the capacity of the phonological loop (articulatory rehearsal + phonological storage), while backward span requires the central executive to manipulate stored information.

Seminal References:

• Miller (1956): "The Magical Number Seven, Plus or Minus Two"
• Wechsler (1939): Introduced Digit Span as part of intelligence assessment
• Baddeley & Hitch (1974): Working memory model distinguishing storage from executive processes

Why Researchers Use This Task

Researchers choose the Digit Span task to:

• Assess working memory capacity in clinical and healthy populations
• Screen for memory impairment in dementia, MCI, ADHD, and learning disabilities
• Study aging effects on storage vs. executive memory processes
• Examine load effects by varying sequence length
• Compare forward vs. backward span to dissociate storage from manipulation
• Predict performance on complex cognitive tasks (reading comprehension, reasoning)

Configuration Options

Visual Parameters

Parameter	Type	Default	Description
Font size (px)	number	96	Size of digit display in pixels (range: 8–400).
Forward prompt	string	"Type the digits in the same order:"	Prompt shown before forward recall trials.
Backward prompt	string	"Type the digits in reverse order:"	Prompt shown before backward recall trials.

Timing Parameters

Timing parameters are defined per-trial in the trial configuration:

Parameter	Type	Default	Description
Digit duration (ms)	number	1000	How long each digit is displayed (100+ms).
ISI (ms)	number	500	Inter-stimulus interval (blank screen between digits, 0+ms).
Response timeout (ms)	number	10000	Maximum time to wait for response (1000-30000ms, 0 = unlimited).

Practice Trials

Parameter	Type	Default	Description
Enable practice	boolean	False	Enable practice trials with visual feedback (green checkmark for correct, red X for incorrect).
Practice trials	array	[]	Array of practice trial configurations (same structure as main trials).

Keyboard Shortcuts

Researchers can customize the keyboard bindings used during the task:

Parameter	Type	Default	Description
Show keyboard hint	boolean	True	Display an on-screen hint showing the configured keys
Number key	key	Any number (0-9)	Key accepted for digit input
Number action label	text	"to type digits"	Label shown in the keyboard hint
Submit key	key	Enter	Key to submit the response
Submit action label	text	"to submit"	Label shown in the keyboard hint

The default "Any number" setting accepts any digit key 0-9.

Instructions

Four instruction types are available:

Instruction Type	Description
Main instructions	Shown before task starts on a dedicated page with camera/screenshare preview.
Hint instructions	Quick reference shown via "?" button during task execution.
Practice instructions	Shown before practice trials begin (if practice enabled).
Trials instructions	Shown after practice, before main trials (if practice enabled).

Trial Configuration

Each trial in the trials spreadsheet is defined by:

Column	Type	Required	Description
digits	array or comma-separated	Yes	Sequence to present (e.g., 3,7,2,9 or [3,7,2,9]).
direction	Forward or Backward	Yes	Recall order: forward (as presented) or backward (reversed).
digit_duration_ms	number	No	Override display duration for this trial (default: 1000ms).
isi_ms	number	No	Override ISI for this trial (default: 500ms).
response_timeout_ms	number	No	Override response timeout for this trial (default: 10000ms).
block	string	No	Optional block label for grouping trials in analysis.

Example Trial Sheet

digits          | direction | digit_duration_ms | isi_ms | response_timeout_ms | block
----------------|-----------|------------------|---------|---------------------|----------
3,7,2           | forward   | 1000             | 500     | 10000               | forward
5,8,1,9         | forward   | 1000             | 500     | 10000               | forward
4,2,7,3,1       | forward   | 1000             | 500     | 10000               | forward
6,9,4           | backward  | 1000             | 500     | 10000               | backward
3,2,7,9         | backward  | 1000             | 500     | 10000               | backward

Design Tips:

• Gradual Difficulty: Start with short sequences (3 digits) and increase gradually (up to 7–9 digits)
• Forward First: Present forward trials before backward to establish the basic task before adding the reversal demand
• Multiple Trials per Length: Use 2–3 trials at each length to get reliable span estimates
• Stopping Rule: In adaptive testing, stop when participant fails 2 consecutive trials at a given length

Default Trials

If no trials are configured, the task provides 6 default trials (3 forward, 3 backward) with increasing span lengths from 3 to 5 digits.

Participant Experience

Unmoderated/Moderated Mode

1. Main Instructions: Participant reads task instructions and clicks "Start"
2. Practice Phase (if enabled):
   • Practice instructions appear
   • Practice trials with visual feedback (✓ or ✗)
   • Participant sees digits one at a time, then types the sequence
3. Trials Instructions (if practice was enabled): Brief reminder before main trials
4. Main Trials:
   • Digits appear sequentially (e.g., "3" → "7" → "2")
   • Blank screen during ISI between digits
   • After last digit, response input appears
   • Participant types the digits (forward or backward as instructed)
   • Press Enter to submit
5. Completion: Task ends after all trials

Strictly Moderated Mode

Same flow, but researcher controls advancement via moderator dashboard. Participant cannot advance trials independently. Input controls are hidden.

Response Input Methods

• Keyboard: Type digit keys (0-9) (default -- configurable by researcher), Backspace to delete, Enter to submit (default -- configurable by researcher)
• On-Screen Dial Pad: Click buttons to enter digits (touch-friendly alternative)
• Display: Current input shown on screen as digits are entered

Both methods are available simultaneously in non-strict mode. In strictly moderated mode, input controls are hidden and the moderator advances after observing the participant's verbal response or timeout.

All keyboard bindings are configurable by the researcher in the study configuration. The keys listed above are the defaults.

Data Output

Participation Log Events

The task logs high-resolution events for each trial:

Trial Start (digit_span_trial_start):

{
  "trial_index": 1,
  "stimulus_id": "digit_span_0_1",
  "direction": "forward",
  "sequence_length": 4,
  "digits": [5, 8, 1, 9],
  "block": "forward"
}

Stimulus Onset (digit_span_stimulus):

{
  "trial_index": 1,
  "stimulus_id": "digit_span_0_1",
  "direction": "forward",
  "sequence_length": 4,
  "digits": [5, 8, 1, 9],
  "block": "forward"
}

Response (digit_span_answer):

{
  "trial_index": 1,
  "stimulus_id": "digit_span_0_1",
  "source": "keyboard",
  "raw_key": "Enter",
  "direction": "forward",
  "sequence_length": 4,
  "digits_presented": [5, 8, 1, 9],
  "response": [5, 8, 1, 9],
  "response_correct": true,
  "latency_ms": 4523,
  "block": "forward"
}

Summary Artifact

At task completion, a JSON summary is generated (digit_span_summary_<taskIndex>.json):

{
  "task_kind": "digit_span",
  "task_index": 0,
  "total_trials": 12,
  "overall": {
    "total": 12,
    "valid_responses": 12,
    "correct": 8,
    "accuracy": 0.67,
    "mean_rt_ms": 5234,
    "mean_correct_rt_ms": 4821,
    "timeouts": 0
  },
  "by_direction": {
    "forward": {
      "total": 6,
      "correct": 5,
      "accuracy": 0.83,
      "max_span": 6,
      "mean_rt_ms": 4821
    },
    "backward": {
      "total": 6,
      "correct": 3,
      "accuracy": 0.50,
      "max_span": 4,
      "mean_rt_ms": 5647
    }
  },
  "trials": [...]
}

Key Metrics:

• Max Span: Longest sequence correctly recalled (primary measure)
• Accuracy by Length: Proportion correct at each sequence length
• Forward vs. Backward: Compare spans to assess executive demand
• Response Latency: Time from last digit to response submission

Design Recommendations

Trial Counts & Lengths

• Minimum: 6 trials (3–4, 4–5, 5–6 for forward; 3–4 for backward)
• Standard: 12–18 trials (2–3 trials each at lengths 3, 4, 5, 6, 7)
• Adaptive: Start at length 3, increase by 1 after success, decrease after failure

Recommended Sequence Lengths

Population	Forward Span	Backward Span
Children (7–10 yrs)	3–6 digits	2–4 digits
Adults (18–60 yrs)	4–8 digits	3–6 digits
Older Adults (60+)	3–7 digits	2–5 digits

Timing Guidelines

Parameter	Recommended	Notes
Digit duration	1000ms	Standard rate; 750ms for faster pace
ISI	500ms	Blank between digits; prevents grouping
Response timeout	10000–15000ms	Long enough for slower typists

Stopping Rules (Adaptive Testing)

1. Two-Failure Rule: Stop when participant fails 2 consecutive trials at a given length
2. Span Estimate: Max span = longest length with at least 1 correct trial
3. Ceiling: Stop at length 9 (very few people exceed this)

Common Issues and Solutions

Issue: Participants Make Transposition Errors

Symptoms: Correct digits but wrong order (e.g., [3, 7, 2] → [3, 2, 7])

Solutions:

• Emphasize order importance in instructions
• Slow down digit presentation rate (increase digit_duration_ms to 1200–1500ms)
• Provide practice trials focusing on maintaining serial order

Issue: High Error Rate on Backward Trials

Symptoms: Backward span much lower than expected (e.g., only 2 digits)

Possible Causes:

• Participants not understanding the reversal requirement
• Insufficient practice with backward direction

Solutions:

• Add more explicit backward instructions with examples
• Include 4–6 backward practice trials with feedback
• Use visual prompts (e.g., "Type in REVERSE order")

Issue: Task Too Easy or Too Hard

Solutions for Too Easy:

• Start at longer sequences (5–6 digits instead of 3–4)
• Use faster presentation rate (750ms per digit)
• Add backward-only trials

Solutions for Too Hard:

• Start at shorter sequences (2–3 digits)
• Slow down presentation (1500ms per digit)
• Use forward-only trials
• Increase ISI to reduce memory decay

Issue: Input Errors (Accidental Key Presses)

Symptoms: Many trials with 1 extra or missing digit

Solutions:

• Emphasize use of Backspace to correct mistakes before submitting
• Add confirmation prompt before submitting response
• Show current input clearly on screen as digits are typed
• Provide on-screen dial pad for mouse/touch input

Example Study Configurations

Configuration 1: Standard Clinical Assessment

Purpose: Estimate forward and backward span for clinical screening

Settings:

• Forward trials: Lengths 3, 4, 5, 6, 7 (2 trials each)
• Backward trials: Lengths 2, 3, 4, 5, 6 (2 trials each)
• Digit duration: 1000ms
• ISI: 500ms
• Practice: 2 forward, 2 backward trials

Expected Spans (adults):

• Forward: 5–7 digits
• Backward: 4–6 digits

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Configuration 2: Load Manipulation Study

Purpose: Examine how memory load affects recall accuracy

Settings:

• Set sizes: 3, 4, 5, 6, 7 digits
• 10 trials per set size (all forward)
• Plot accuracy as function of load
• Analyze RT increase with load

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Configuration 3: Developmental Study

Purpose: Assess span development in children

Settings:

• Ages 7–10: Forward lengths 3–6, Backward 2–4
• Ages 11–14: Forward lengths 4–7, Backward 3–5
• 3 trials per length for reliability
• Slower presentation (1200ms) for younger children

Expected Age Effects: ~0.5 digit increase per year in forward span

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Configuration 4: Working Memory Training Study

Purpose: Pre/post assessment for training intervention

Settings:

• Fixed set of 20 trials (balanced across lengths 4–8)
• Same trial order at pre and post
• Include both forward and backward
• Primary outcome: Backward span change

References

1. Baddeley, A. D., & Hitch, G. (1974). Working memory. In G. H. Bower (Ed.), The Psychology of Learning and Motivation (Vol. 8, pp. 47–89). Academic Press.

2. Cowan, N. (2001). The magical number 4 in short-term memory: A reconsideration of mental storage capacity. Behavioral and Brain Sciences, 24(1), 87–114.

3. Hoshi, Y., Oda, I., Wada, Y., Ito, Y., Yamashita, Y., Oda, M., ... & Tamura, M. (2000). Visuospatial imagery is a fruitful strategy for the digit span backward task: A study with near-infrared optical tomography. Cognitive Brain Research, 9(3), 339–342.

4. Miller, G. A. (1956). The magical number seven, plus or minus two: Some limits on our capacity for processing information. Psychological Review, 63(2), 81–97.

5. Wechsler, D. (1939). The measurement of adult intelligence. Williams & Wilkins.

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Related Tasks: N-Back Task, Operation Span Task, Visual Short-Term Memory