The 2×2 table
- Concept
A four-cell table that crosses exposure (or a test result) with disease; almost every measure in this section comes out of it.
What it is
The 2×2 table sorts participants by two yes-or-no questions: were they exposed, and did they develop the outcome? By convention exposure goes in the rows and the outcome in the columns, and the cells are called a, b, c and d. Nearly every exam calculation (relative risk, odds ratio, risk reduction, sensitivity, predictive values) starts from this table, so building it correctly is the first step of any problem.
Key facts
- Risk in the exposed = a/(a+b); risk in the unexposed = c/(c+d).
- Total diseased = a+c; total healthy = b+d; grand total N = a+b+c+d.
- For a test: a = true positives, b = false positives, c = false negatives, d = true negatives.
- If a question puts exposure in the columns, redraw the table before calculating.
Worked example
- Data: in a factory, 150 workers use a solvent and 30 develop dermatitis; of 250 who do not use it, 20 develop it.
- Build the table: a = 30, b = 150 − 30 = 120, c = 20, d = 250 − 20 = 230; total N = 400.
- Check the margins: diseased a+c = 50, healthy b+d = 350; 50 + 350 = 400, it adds up.
- Risk in the exposed = 30/150 = 0.20 (20%); risk in the unexposed = 20/250 = 0.08 (8%).
- Relative risk = 0.20/0.08 = 2.5. Odds ratio = (30×230)/(120×20) = 6,900/2,400 ≈ 2.9.
- Reading: workers who use the solvent have 2.5 times the risk of dermatitis of those who do not.
Standard layout of the 2×2 table
| Group | Outcome present | Outcome absent | Total |
|---|---|---|---|
| Exposed (or test positive) | a | b | a+b |
| Unexposed (or test negative) | c | d | c+d |
| Total | a+c | b+d | N |
Markers
- a b c d
- N
- RR
- OR
In practice
- In a cohort or a trial the rows are fixed (exposed and unexposed are chosen) and outcomes are counted, so risks make sense.
- In a case-control study the columns are fixed (cases and controls are chosen), so risks cannot be calculated, only the odds ratio.
Common pitfalls
- Swapping b and c when copying the data, which inverts the result.
- Calculating sensitivity across rows or predictive values down columns.
- Forgetting to subtract the cases to get b and d when the question gives totals.
Test yourself
Think of the answer, then tap the question to see it.
In the usual layout, what does cell c represent?
Unexposed people who did develop the outcome.
Why is the relative risk not calculated in a case-control study?
Because the investigator fixes how many cases and controls are enrolled; the proportion with disease in each row does not reflect real risk.
In a diagnostic-test table, is sensitivity read across rows or down columns?
Down columns: true positives among all diseased people, a/(a+c).
Connections
Educational content on epidemiological and statistical methods; the examples use made-up numbers to teach the calculation. Not a clinical or legal guide: current Colombian rules are in the official sources.
Sources: Principles of Epidemiology | Lesson 3 - Section 5 (Centers for Disease Control and Prevention, 2012); Statistical Guidance on Reporting Results from Studies Evaluating Diagnostic Tests - Guidance for Industry and FDA Staff (U.S. Food and Drug Administration, 2007).
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Representative model, for educational purposes only.