Chi-square test (r × c table)

Compares a category or yes/no outcome across three or more independent groups.

Clinical example

Whether the proportion of patients with a wound infection differs between three hospitals.

When to use it

The outcome is a category or yes/no, one per patient.
You compare three or more independent groups.
You don't need to adjust for other variables.

Assumptions to check

Independent observations

Each patient appears in the table once.

Expected counts are not too small

Look at the expected counts per cell. With many small counts, use an exact test (Fisher–Freeman–Halton).

Use the order of ordered groups

If the groups have a natural order, a chi-square test for trend has more power than the general test.

What to report

n (%) per group

Common mistakes

Ignoring the order of ordered groups, which costs power

A chi-square test on a large table with many small expected counts

Alternatives

If your situation is…	Use
Only two independent groups	Chi-square test

In your software

# R
tab <- table(d$hospital, d$infection)
chisq.test(tab)

# Small expected counts: exact test
fisher.test(tab)            # add simulate.p.value = TRUE for large tables

# Ordered groups: test for trend (events and totals per group)
prop.trend.test(x = c(5, 12, 20), n = c(100, 100, 100))

SPSS

CROSSTABS
  /TABLES=hospital BY infection
  /STATISTICS=CHISQ
  /CELLS=COUNT EXPECTED ROW.