If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

# Miller’s law, chunking, and the capacity of working memory

## Problem

In 1956, George Miller asserted that the span of immediate memory and absolute judgment were both limited to around $7$ pieces of information. The main unit of information is the bit, the amount of data necessary to make a choice between two equally likely alternatives. Likewise, $4$ bits of information is a decision between $16$ binary alternatives ($4$ successive binary decisions). The point where confusion creates an incorrect judgment is the channel capacity. In other words, the quantity of bits which can be transmitted reliably through a channel, within a certain amount of time.
Chunking, or clustering, is the function of grouping information together related by perceptual features. This is a form of semantic relation, such as types of fruit, parts of speech, or 1980s fashion. Chunking allows the brain to increase the channel capacity of the short term memory; however, each chunk must be meaningful to the individual. There are many other memory consolidation techniques. The peg memory system creates a mental peg from an association, such as a rhyme, letter, or shape. Another memory technique is the link system, where images are creating links, stories, or associations between elements in a list to be memorized.
A researcher wanted to challenge the limits imposed by Miller’s Law ($7$ plus/minus $2$). In the study ($n$ = $20$, ${\text{H}}_{0}$ = $7$ plus/minus $2$), subjects completed a backward digit span test and other memory tests administered during each of five sessions over the course of a year. The backward digit span test consisted of five trials during each session. Each trial began with instructions and a statement of understanding from the subject. Each backward digit span test began with two digits and was read at a rate of one digit per second. The digit span length increased until there were three incorrect attempts. The digits must be repeated in reverse order by the subject (researcher – “$3,5,6,2,3,1$” subject – “$1,3,2,6,5,3$”). The results for the average longest correctly repeated string of digits over all sessions by each subject are shown in Table 1 below.
Table 1: The averaged results of the backward digit span test throughout all $25$ trials ($5$ trials, $5$ sessions) for each subject ($n$ = $20$). Mean (μ) = $4.73$, Confidence interval at $95\mathrm{%}$ [$4.02,5.45$], Standard deviation (σ) = $1.48$, p-value $2.32×$ ${10}^{-5}$, and the significance criterion (α) was $5\mathrm{%}$.
SubjectAverage resultsSubjectAverage results
$1$$4.63$$11$$4.18$
$2$$4.53$$12$$4.81$
$3$$5.12$$13$$9.32$
$4$$3.81$$14$$3.79$
$5$$3.27$$15$$2.67$
$6$$5.38$$16$$4.65$
$7$$7.75$$17$$3.82$
$8$$5.46$$18$$3.75$
$9$$5.41$$19$$4.19$
$10$$4.41$$20$$4.37$
Adapted from: 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.
Which system of the working memory model was the researcher testing by utilizing the backwards digit span test?