Analysis Workshop: How Many Digits Can You Hold?

Part 1 — The Big Picture

This week you learned that short-term memory holds only a handful of items for a short time: Miller (1956) put the span at about 7 ± 2 items, and Cowan (2010) revised working memory to about 4 ± 1 chunks. Psychology counts that as knowledge only once it is measured. In this workshop you turn short-term memory into an operational definition, measure your own span with eight digit strings, put one number on the pattern with the correlation coefficient r, and design the experiment that could test whether chunking helps. A chatbot then answers questions about your work, and you catch where it goes wrong.

Time budget: Plan for about 90 minutes.

Part 2 — The Task

Guiding question: How long a string of digits can you hold in short-term memory, how would you measure that honestly, and what would it take to show that chunking causes better recall?

Before you begin — hypothesis: Before you start, write one sentence in this form: If I try to recall digit strings that get longer from 4 to 11 digits, then the share of digits I recall correctly will ___ because ___.

Workshop data: your-digit-span-run

Source: Your own recall of eight digit strings printed in this workshop, from 4 to 11 digits long, recorded in your second table; no outside file is needed.

• Rows: 8 recall trials, one per printed digit string from 4 to 11 digits; the definition table has 4 rows, and the recall table has 9 rows, the 8 trials plus one row for r
• Columns: String length in digits, digits recalled in the right position, and proportion correct

Part 3 — Materials & Procedure

Tools and materials

• Google Sheets (free) or Excel
• A sheet of paper or a card to cover each string
• A timer, such as a phone or a clock with a second hand
• A document or notebook for your written answers

Ways of working

• operationalize-a-construct
• design-a-correlational-or-experimental-check
• compute-and-interpret-r

Procedure

1. Fill in the first scaffold table, your operational definition, before you look at any string: what you are measuring, exactly how long you look at each string, how you cover it, when you write, and how you score one string. Tool: A document or notebook for your written answers. Check: The first table is complete before the first string is uncovered.
2. Cover the second scaffold table's digit strings with a sheet of paper. Uncover string 1 only, read it for 5 seconds, cover it again, and write the digits from memory in your notebook. Then do the same for strings 2 through 8, in order, one at a time. Tool: A sheet of paper or a card to cover each string. Check: Eight written attempts, one per string.
3. Use the timer to keep each look to 5 seconds, and do not say the digits aloud or group them on purpose; this run measures your span with the strings as printed. Tool: A timer, such as a phone or a clock with a second hand. Check: Every string was seen for the same 5 seconds.
4. Score each attempt by counting the digits you wrote in the right position, and fill in the recall table. Proportion correct is that count divided by the string's length. Check: Eight counts and eight proportions between 0 and 1.
5. Open a blank sheet. Type Length in cell A1, Correct in B1, and Proportion in C1. Enter the eight lengths in A2 through A9 and your eight counts in B2 through B9, type =B2/A2 in C2, and copy it down to C9. In an empty cell, type =CORREL(A2:A9,C2:C9) and record the result to two decimals in the last row of the recall table. If every proportion is the same, the formula shows an error because r cannot be computed when one variable never changes; record that and explain it in your first analysis answer. Tool: Google Sheets (free) or Excel. Check: A value between negative 1 and positive 1, or an error message if all eight proportions match.
6. Select A1 through A9 and C1 through C9 and insert a scatter chart with string length across the bottom and proportion correct up the side. Title both axes. Tool: Google Sheets (free) or Excel. Check: Eight dots, one per string, that you can describe in words.
7. Fill in the third scaffold table, your experiment design, then answer the analysis questions and run the critique step in Part 6. Tool: A document or notebook for your written answers. Check: Three completed tables, five written answers, and a critique.

Fallback route

When to use it: Use this route if you cannot run the eight-string recall, for example if no spreadsheet is available, or if a vision, attention, or other access reason makes the timed reading unsuitable for you.

Write the operational definition in the first table as if you were going to run the test. Then use the model data below in place of your own recall: compute r for the ten pairs with the same =CORREL formula, make the scatter chart, and answer the first analysis question about these data. For questions 2 and 3, describe the pattern you would predict for a digit-span run and explain it with short-term memory, Miller's 7 ± 2, and chunking. Complete the design table, the remaining questions, and the critique step. Submit the same items for equal credit.

This route earns the same credit as the primary route.

An illustrative paired dataset this course uses for practicing r, constructed for teaching rather than collected from real students.

Fallback model data

Hours of sleep	Quiz score (of 20)
5	11
6	14
6.5	12
7	15
7	13
7.5	16
8	17
8	14
8.5	18
9	17

Part 4 — The Scaffold

Write the operational definition first, because a construct you have not defined as a procedure is not yet measurable.

Student scaffold table 1

Part of the definition	Your entry
The construct I am measuring	Short-term memory span for digits
How long I look, how I cover the string, and when I write
How I score one string
What one score measures, in one sentence

Record each attempt as you go, because r pairs each string's length with the share of it you recalled.

Student scaffold table 2

String	Digits to read for 5 seconds	Length (digits)	Digits recalled in the right position	Proportion correct
1	0 9 5 8	4
2	8 7 0 8 8	5
3	8 4 1 7 7 0	6
4	1 4 6 1 9 4 7	7
5	4 7 7 3 8 6 5 9	8
6	4 7 7 1 6 9 7 1 7	9
7	7 6 9 8 2 0 7 5 4 9	10
8	4 0 5 8 4 7 6 0 6 4 2	11
Correlation r (two decimals)

Plan the experiment that could test a cause, because your eight-string run can only show an association.

Student scaffold table 3

Design element	Your plan
The claim being tested	Showing digits in groups of three makes long strings easier to recall
Independent variable (IV) and its two conditions
Dependent variable (DV) and how it is measured
How participants are assigned to conditions
How participants are chosen, and who the results could apply to
One third variable you would hold the same in both conditions
What the result would be allowed to claim

Part 5 — Analysis Questions

1. Report your r to two decimals. Describe its direction and strength in words, and write one sentence that uses the phrase associated with. If r could not be computed, explain why in terms of your proportions.
2. Name the longest string you recalled perfectly, and describe where your recall began to break down. Compare that length with Miller's span of 7 ± 2 items, which runs from 5 to 9.
3. Explain your result with short-term memory and working memory. Did you find yourself grouping digits without meaning to? Use chunking and Cowan's estimate of about 4 ± 1 chunks to explain how someone could hold more digits than four.
4. Your run is correlational in form: the strings got longer as you went, and you manipulated nothing between groups. Name one third variable, such as growing tiredness, boredom, or practice, that could change your recall along with length, and explain how the experiment in your third table would rule it out.
5. Choose one and answer it in 3–4 sentences. (a) If you took the same eight strings again tomorrow, would you expect the same scores? Say what that tells you about the reliability of your measure, and whether a reliable measure is automatically valid. (b) Could your score capture reading speed, attention, or having seen the strings before instead of short-term memory? Explain the validity problem and suggest one change that would make the measure more valid.

Part 6 — AI-Critique Moment

Choose one equal-credit critique route. Route A: ask an approved AI tool to critique your completed work, then check its response against your own evidence. Route B is the no-AI equivalent printed below.

Approved tools: Claude, Gemini, ChatGPT, Grok, Microsoft Copilot.

Prompt to paste:

I measured my own short-term memory with eight digit strings from 4 to 11 digits long, and I've pasted my completed tables above, including the proportion of digits I recalled on each string, my correlation r between string length and proportion correct, and my plan for an experiment on chunking. Please answer five things in short sentences. First, does my correlation prove that longer strings cause forgetting? Second, in my planned experiment, which is the independent variable and which is the dependent variable? Third, if I want my results to apply to all adults, should I use random assignment or random sampling? Fourth, my scores came out almost the same when I took the test twice, so is my digit test valid? Fifth, is the general idea that short-term memory holds only a few items a theory or a hypothesis, and is my prediction that I will recall fewer digits on longer strings a theory or a hypothesis?

Test the response for these likely failures:

• Chatbots often say a negative r proves that string length caused the drop in recall.
• Chatbots often call the number of digits recalled the independent variable because it is the main measure.
• Chatbots often say random assignment is what lets the results apply to all adults.
• Chatbots often say a test that gives the same score twice is therefore valid.
• Chatbots often call the student's specific prediction a theory, or treat theory and hypothesis as the same thing.

In 3–4 sentences, quote at least two of the chatbot's answers, say which one it got right, and correct at least one error using evidence from your tables or the course definitions.

Equivalent route (no AI required)

No AI account is required for this workshop. Instead of the chatbot, critique this flawed analysis, printed here in full: "My proportion correct fell as the strings got longer and my r was strongly negative, which proves that string length causes forgetting. In my chunking experiment, the number of digits recalled is the independent variable and the chunked or unchunked display is the dependent variable. I will randomly assign students to the chunked and unchunked groups so that my results apply to every adult. When I took the test twice, I got almost the same scores, so my digit test is a valid measure of short-term memory. That short-term memory holds only a few items is my hypothesis, and my prediction that I will recall fewer digits on longer strings is a theory." Mark it up: quote each flawed sentence, name what is wrong (cause read from a correlation, the IV and DV swapped, random assignment confused with random sampling, reliability confused with validity, or theory confused with hypothesis), cite the evidence from your tables or the course definitions, and write a corrected sentence beneath it. This route assesses the same objective (Objective 5 — compare the major models of learning and memory and apply them to everyday behavior, including why memory is reconstructive) as the chatbot critique, takes comparable effort (about 30 minutes and 200–300 words), is scored by the same scoring criteria for the same credit, and its own submission artifact is the marked-up flawed analysis, posted in place of the chatbot share link and report.

Part 7 — What to Submit

• All three completed scaffold tables
• Your scatter chart with titled axes, or a labelled sketch of it
• Your hypothesis sentence and written answers to all five analysis questions
• The chatbot critique report with its share link, or the equivalent route's marked-up flawed analysis

Deliverable:

A short Analysis Workshop report: three completed tables (your operational definition of short-term memory span, your eight recall scores with r, and an experiment design), a scatter chart with titled axes or a labelled sketch, a hypothesis sentence and written answers to five analysis questions, and a critique of a chatbot's answers about your work, or, on the equivalent route, a marked-up correction of the printed flawed analysis. Submit in any accessible file type or as a link; a recorded response may be submitted as audio or video with a transcript, or as text. Choose a written, recorded, or visual form for your answers; every form is graded by the same scoring criteria.

Rubric

The rubric below shows how each submitted part is evaluated; bands are full, partial, or none.

Workshop evaluation criteria

Criterion	Full	Partial	None
Operational definition of short-term memory span	The first table states the look time, how the string is covered, when the digits are written, and how one string is scored, and its one-sentence statement says what a single score measures.	A definition is given, but the look time, the covering step, or the scoring rule is missing or vague.	No operational definition is written.
Data, r, and its interpretation	Eight scored attempts or the fallback data are recorded, r is computed and reported to two decimals or its error is explained, the scatter chart or sketch has titled axes, and the interpretation says associated with, gives direction and strength, and names a third variable.	The data and r are present, but the chart, the direction and strength, or the third variable is missing, or the sentence slips into cause.	No scores or correlation are recorded, or the values are invented.
Experimental design check	The design table puts the manipulated display (chunked or unchunked) as the IV and the digits recalled as the DV, uses random assignment for the conditions and random sampling for who could be studied, holds a third variable constant, and states what the result could claim.	The design is attempted, but the IV and DV are swapped, or assignment and sampling are confused, or the claim goes beyond the design.	No experiment design is submitted.
Memory reasoning and the limitation	Questions 2 to 5 compare the result with Miller's 7 ± 2, explain it with working memory and chunking, connect the third variable to the experiment, and answer the chosen limitation question with an accurate account of reliability or validity.	Most questions are answered, but capacity is misstated, chunking is confused with rehearsal, or reliability and validity are blurred, or a reason is missing.	The analysis questions are missing or do not address the measurement.
Critique of the chatbot or of the printed flawed analysis	On either route, at least two errors are quoted and corrected with evidence from the student's own tables or the course definitions, and one correct point is acknowledged; both routes earn this band equally.	On either route, errors are named but corrected without evidence, or only one error is caught.	No critique appears, or pasted output is submitted without any checking.

Quality Gate

• The operational definition is written before any string is uncovered, and it names the look time, the covering method, the writing step, and the scoring rule.
• Every count, proportion, and the correlation come from your own run and formula, or from the fallback model data, never from memory or a chatbot.
• The scatter chart puts string length across and proportion correct up, with both axes titled.
• Every sentence about r says associated with and names a third variable; no sentence claims that length causes the drop in recall.
• The design table names the IV, the DV, random assignment, and random sampling, each in its correct role.
• No statistic, score, or source is invented anywhere in the submission.
• The critique quotes the chatbot or the flawed analysis and corrects at least two errors with evidence from your tables or the course definitions.