Digit Span

Abstract

The philosophical construct of a finite span of memory dates back to Leibniz; he suggested that individuals have a finite capacity to process or hold information. He termed this capacity the span of apperception [1]. Digit Span is a psychological test to assess working memory and/or the ability to cache a circumscribed amount of information for a short period of time.

The classical methodology accrues to Wechsler [2], when he included Digit Span in the Wechsler Adult Intelligence Scale (WAIS) – an IQ test designed to measure intelligence and cognitive ability in adults. The Digit Span test has been shown to load on verbal comprehension, working memory, attention & information processing [3, 4, 5].

Experiment

Methodology

I’ve followed the experimental design of this paper, which improves upon the original Wechsler test.

The subject is shown an increasing length of list of digits (e.g. {1, 4}, {5, 1, 3}). For each list, the digits are flashed sequentially with a delay of one second b/w each digit. The experiment follows a 1:2 staircase approach; a single correct response increases the length of the subsequent list by one digit, while two consecutive incorrect responses decrease the subsequent list length by one.

In Forward Span (FS), the participant responds with the recalled order of the digit list. In Backward Span (BS), the participant responds in reverse order of the original list.

I used a Python script to emulate the experiment. The script displays the digits on the terminal and records the response.

1import sys
2import time
3import random
4
5FS = '-f'
6BS = '-b'
7
8mode = sys.argv[1]
9n_digits = int(sys.argv[2])
10if mode not in [FS, BS]:
11    raise Exception(f'usage: python digit_span.py [{FS} | {BS}] n_digits')
12print(f'Playing {"FS" if mode == FS else "BS"} for {n_digits} digits.')
13
14def digit_span(n: int, sleep=1):
15    l = []
16    time.sleep(1)
17    for _ in range(n):
18        k = random.randint(0, 9)
19        print(k, end='\r')
20        l.append(str(k))
21        time.sleep(sleep)
22    print('', end='\r')
23    return l
24
25l = digit_span(n_digits)
26actual = ' '.join(l)
27
28ip = str(input(f'Enter the sequence of digits{" in reverse" if mode == BS else ""}: '))
29guess = ' '.join(ip)
30
31if mode == BS:
32    guess = guess[::-1]
33
34if guess == actual:
35    _repr = f'Congrats!'
36    if n_digits > 7:
37        _repr += f' Your short term memory is *probably* top-notch.'
38else:
39    _repr = f'Uh oh!'
40    if n_digits < 7:
41        _repr += f' You might wanna see a doc?'
42    if len(ip) != n_digits:
43        _repr += f' That\'s not even {n_digits} digits smh!'
44print(_repr)
45print(f'Actual: {actual}')
46print(f' Guess: {guess}')

Each test (FS & BS) carries till 15 trials. The entire experiment is repeated after a random period (b/w 15-20 days). A total of three experiments are carried out to minimise any dispositional errors such as fatigue, distraction, etc.

Experiment log

Scoring

Four measures were tracked for each experiment. Two of these (TE-TL & TE-ML) can be used for baseline comparison with the original test per WMS-III. MS is shown to be the most effective measure [6].

Table 1: a sample of one experiment (BS).

Two error maximum list length (TE-ML)
Measures the maximum list length prior to the first two consecutive misses. In Table 1, the TE-ML score is 10 (reached length 10, prior to two consecutive misses at length 11).

Two error total trials (TE-TL)
Measures the total number of trials prior to the first two consecutive misses. In Table 1, the TE-TL score is 9 (reached trial 9, prior to two consecutive misses at length 11).

Maximum length (ML)
Measures the maximum successful length. In Table 1, the ML is 10.

Mean span (MS)
Measures the outcome-weighted average of all lengths (plus a baseline offset). In Table 1, the MS score is 9.0;

$$\small {(3=1, 4=1, 5=0.5, 6=1, 7=1, 8=1, 9=1, 10=1, 11=0, sum = 7.5)} \ \text{\small{{MS = 7.5(sum) + 1.5(baseline) = 9.0}}}$$.

$$\text{MS} = \sum_{l=3}^{n}{{(\sum_{t; i=l}\text{outcome}}})/\text t + \text{baseline value}\text{ (l = lengths, t = trials)} \ \text{Baseline: FS = 2.5, BS = 1.5}$$

Results

Following is the result log & comparison with the touchstone study by Woods (2011, Exp - II) [7]:

References

1. https://plato.stanford.edu/entries/leibniz-mind/
2. Ryan, J.J., Lopez, S.J. (2001). Wechsler Adult Intelligence Scale-III. In: Dorfman, W.I., Hersen, M. (eds) Understanding Psychological Assessment. Perspectives on Individual Differences.
3. Tulsky, D. S., & Price, L. R. (2003)
4. John T.E. Richardson (2007). Measures of Short-Term Memory: A Historical Review.
5. Richardson JT. Measures of short-term memory: a historical review. Cortex. 2007 Jul
6. Woods DL, Kishiyamaa MM, Lund EW, Herron TJ, Edwards B, Poliva O, Hink RF, Reed B. Improving digit span assessment of short-term verbal memory. J Clin Exp Neuropsychol. 2011 Jan
7. Woods DL, Kishiyamaa MM, Lund EW, Herron TJ, Edwards B, Poliva O, Hink RF, Reed B. Improving digit span assessment of short-term verbal memory. J Clin Exp Neuropsychol. 2011 Jan