[Durgical](https://durgical.com/en/) › [DurgiPedia](https://durgical.com/en/durgipedia/) › [Epidemiology](https://durgical.com/en/epidemiology/) › [Measures of frequency and association](https://durgical.com/en/epidemiology/areas/measures/) › The 2×2 table

# 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.

Updated Nov 5, 2026

## Key points

- Rows = exposure (or test result); columns = outcome (or disease by the reference standard).
- a = exposed with the outcome, b = exposed without, c = unexposed with the outcome, d = unexposed without.
- Risk measures (RR, risk reduction) are read across rows: a/(a+b) versus c/(c+d).
- For a diagnostic test, sensitivity and specificity are read down columns; predictive values across rows.
- The odds ratio is the cross-product: (a×d)/(b×c).

On this page

- The basics Key points
- What it is
- Key facts
- Worked example
- Standard layout of the 2×2 table
- Markers
- In practice
- Common pitfalls
- Memory aid

- Study Test yourself

- Connections Connections

## 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.

## Memory aid

Rows are the reason, columns are the consequence: exposure lies across, outcome stands up and down.

## 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).

[Add to my cards (3)](https://durgical.app/estudiar/?add=/en/epidemiology/the-2-2-table/)

## Connections

## Related 6

- [Relative risk](https://durgical.com/en/epidemiology/relative-risk/)
- [Odds ratio](https://durgical.com/en/epidemiology/odds-ratio/)
- [Absolute risk reduction](https://durgical.com/en/epidemiology/absolute-risk-reduction/)
- [Sensitivity](https://durgical.com/en/epidemiology/sensitivity/)
- [Positive and negative predictive values](https://durgical.com/en/epidemiology/positive-and-negative-predictive-values/)
- [Incidence](https://durgical.com/en/epidemiology/incidence/)

[← All of epidemiology](https://durgical.com/en/epidemiology/)

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](https://archive.cdc.gov/www_cdc_gov/csels/dsepd/ss1978/lesson3/section5.html) (Centers for Disease Control and Prevention, 2012); [Statistical Guidance on Reporting Results from Studies Evaluating Diagnostic Tests - Guidance for Industry and FDA Staff](https://www.fda.gov/regulatory-information/search-fda-guidance-documents/statistical-guidance-reporting-results-studies-evaluating-diagnostic-tests-guidance-industry-and-fda) (U.S. Food and Drug Administration, 2007).

## **Spotted a mistake?** We are always improving for the community. Tell us what is wrong and our team will review it. Report a mistake

Representative model, for educational purposes only.

---
Source: https://durgical.com/en/epidemiology/the-2-2-table/
License: CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Cite as: DurgiPedia (durgical.com), https://durgical.com/en/epidemiology/the-2-2-table/