Contingency table example: a 2 × 2 with marginal totals

What it shows

A 2 × 2 contingency table of sex against handedness for 100 individuals, a standard textbook example.

The marginal totals are tinted and the grand total more strongly, each cell carries its row percentage, and a panel underneath works out the odds ratio and its 95% confidence interval.

How to read it

1. 1

   The four inner cells are counts: 43 right-handed and 9 left-handed males, 44 right-handed and 4 left-handed females.

2. 2

   The marginal totals add across and down: 52 males and 48 females, 87 right-handed and 13 left-handed, 100 in all.

3. 3

   Row percentages compare the groups fairly when they differ in size: 82.7% of males and 91.7% of females are right-handed.

4. 4

   The proportions are about the same. The odds ratio is 2.30, but its 95% confidence interval, 0.66 to 8.04, includes 1, so this sample gives no clear evidence of a difference; judging one needs a test or an interval, not the ratio alone.

The numbers

• Male: 43 right-handed (82.7%), 9 left-handed (17.3%), total 52.
• Female: 44 right-handed (91.7%), 4 left-handed (8.3%), total 48.
• Total: 87 right-handed (87.0%), 13 left-handed (13.0%), grand total 100.
• Odds ratio (left-handed, males vs females): (9 / 43) / (4 / 44) = (9 × 44) / (43 × 4) = 396 / 172 = 2.30, with a 95% confidence interval of 0.66 to 8.04 (Woolf’s method).

Ways to use it in teaching

• Hide the totals and have students fill them in, then compute the row percentages.

• Ask whether 82.7% against 91.7% is a meaningful difference with only 13 left-handed people in the sample; it leads into a chi-squared or Fisher’s exact test.

• Recompute the odds ratio for being right-handed and show that it is the reciprocal, 0.43.

For the chi-square test of a table like this, and what its result does and does not show, see our guide to inferential statistics.

Sources

• Contingency table. (n.d.). In Wikipedia. Retrieved October 19, 2026, from https://en.wikipedia.org/wiki/Contingency_table
• StataCorp. (2013). Stata survival analysis and epidemiological tables reference manual: Release 13. Stata Press. https://www.stata.com/manuals13/stepitab.pdf

The 95% confidence interval for the odds ratio uses Woolf’s method (Woolf, 1955, as cited in StataCorp, 2013), computed by us.