6. The 2x2 Table: Risk Ratio and Risk Difference Explained Simply
After this lesson you can
- Build a two-by-two table in the course's fixed layout and fill in its margins
- Compute risk in each row by reading across, never down
- Compute and interpret the risk ratio at, above and below one, including the percent lower for a protective exposure
- Compute and interpret the risk difference as excess cases per 100 exposed over a stated window
- Build a rate table from person-time and compute the rate ratio and rate difference
- Report every comparison in two sentences, one relative and one absolute
This lesson makes the first comparison between groups. It builds the two-by-two table in one fixed layout, exposure in rows and outcome in columns, and uses an invented factory cohort to compute risks, the risk ratio and the risk difference, then the rate ratio and rate difference from person-time. It shows why a ratio and a difference answer different questions and why a careful report gives both.
Questions and answers
Questions a learner would ask about this lesson. Think through your own answer before you open each one.
- How is the two-by-two table laid out in this course?
Show answer
Exposure goes in the rows with the exposed on top, and the outcome goes in the columns with the outcome on the left. The cells read a, b, c, d from left to right and top to bottom, and the margins hold the row totals, column totals and grand total. The layout never rotates, so one set of formulas always works.
- Why do I read across the rows and not down the columns?
Show answer
A risk needs the exposure group as its denominator, so you divide the cases in each row by that row's total. In the factory, 100 of 400 exposed workers and 75 of 600 unexposed workers became ill, giving risks of 25 percent and 12.5 percent. Reading down a column gives the share of cases who were exposed, which answers a different question.
- If the risk ratio is 2.0, why do I also need the risk difference?
Show answer
The two measures answer different questions. The risk ratio of 2.0 says how strong the association is: exposed workers had twice the risk. The risk difference of 12.5 per 100 says how many extra cases the exposure adds: 12.5 excess cases per 100 exposed workers over one year. A careful report gives both, one relative sentence and one absolute sentence.
- How do I read a risk ratio below one?
Show answer
A risk ratio below one means lower risk among the exposed, possibly a protective exposure. The percent lower is one minus the ratio, so a risk ratio of 0.25 means 75 percent lower risk, not 25 percent lower. In the lesson's vaccine example, attack rates of 2 percent and 10 percent give a risk ratio of 0.2, which is one fifth the risk, or 80 percent lower.
- When do I build a rate table instead of a risk table?
Show answer
When workers enter late and leave early, the denominator becomes person-time and you build a rate table. Its columns are cases, person-years and rate, with no column for people without the outcome. In the factory's person-time version, 60 cases in 2,000 person-years against 30 cases in 2,000 person-years gives a rate ratio of 2.0 and a rate difference of 1.5 per 100 person-years.
Practice quiz
- Question 1In the two-by-two table, what does cell b hold?
- Question 2A cohort has 400 exposed workers with 100 cases and 600 unexposed workers with 75 cases. What is the risk ratio?
- Question 3Using the same cohort, what is the risk difference over the one year?
- Question 4Exposed workers had 60 cases in 2,000 person-years and unexposed workers had 30 cases in 2,000 person-years. What is the rate difference?
- Question 5The vaccinated attack rate is 2 percent and the unvaccinated attack rate is 10 percent. Which statement is correct?
- Question 6What is the null value for a risk difference?
- Question 7Which column does a rate table not have?
- Question 8A rare outcome occurs in 2 per 10,000 exposed and 1 per 10,000 unexposed people. What are the risk ratio and the risk difference?
- Question 9A planner asks how many cases would be removed if an exposure were eliminated. Which measure answers that question?
- Question 10Someone divides the case counts directly, 100 over 75, and calls the result a risk ratio. What is wrong?
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Principles of Epidemiology is education in epidemiologic reasoning, not clinical, screening, or policy guidance. Every example is set in the fictional Oakhaven Health District, and every number is invented for teaching.