Quick answer: A chi-square test asks: are two categorical variables related, or is the observed pattern just chance? In jamovi: Frequencies → Contingency Tables → Independent Samples (chi-square test) — rows variable in, columns variable in, tick Chi-square, Expected counts and Contingency coefficient/Phi for effect size. Use it for infection × sex, treatment × outcome, smoking × diagnosis — any counts-in-cells question. The continuous-outcome counterparts live in our t-test walkthrough and ANOVA guide.
Worked example: treatment and outcome
120 patients: 60 given a new therapy, 60 standard care; outcome recovered/not. The data must arrive as one row per patient (Treatment, Outcome columns) — or as pre-counted weights (Frequency Counts option). jamovi builds the 2×2 table; suppose χ²(1) = 5.22, p = 0.022, phi = 0.21.
Reading it: expected counts assume treatment and outcome are unrelated; the test measures how far observed counts stray from that. p = 0.022 < .05 → recoveries aren’t independent of treatment (the inference logic: our hypothesis testing guide). Phi = 0.21 is a small-to-moderate association — real, but clinically modest. Report as: “Recovery differed by treatment, χ²(1) = 5.22, p = .022, φ = 0.21.”
The three conditions chi-square demands
- Expected count ≥ 5 in every cell (or ≥ 80% of cells with ≥5 and none <1). jamovi shows expected counts in the Cells menu; if violated with a 2×2, tick the Fisher’s exact option instead.
- Independent observations — each subject appears once. Repeated measures on the same people need McNemar’s test, not chi-square.
- Counts, not percentages — the test is defined on frequencies. If your data arrive as percentages, go back to the raw counts.
Goodness-of-fit: the one-variable variant
The same menu handles one categorical variable: Frequencies → N Outcomes (χ² goodness of fit). Classic use: are births evenly spread across weekdays, or is a coin actually fair? jamovi compares observed counts to the proportions you specify (equal by default) and returns χ² and p. For ratio-level data and means, remember the categorical machinery here is deliberately separate from the means machinery in the ANOVA workflow.
Where chi-square sits in the biostatistics toolkit — and when design, not the test, is the problem — is covered in hypothesis testing in biology. For one-to-one help choosing tests for your own categorical data, Ampersand Academy teaches biostatistics with jamovi one-to-one.
Frequently asked questions
When do I use a chi-square test?
When both variables are categorical and you have counts: infection by sex, treatment by outcome, grade by school. It tests whether the two variables are independent or associated.
What does an expected count below 5 mean for my test?
The chi-square approximation becomes unreliable. In a 2×2 table switch to Fisher’s exact test (one tick-box in jamovi); in larger tables combine sparse categories or collect more data.
How do I report a chi-square result in APA style?
Report the statistic, degrees of freedom, p and an effect size, for example: chi-square(1) = 5.22, p = .022, phi = .21. jamovi’s output contains every number you need.
What is the difference between chi-square and Fisher’s exact test?
Chi-square approximates the sampling distribution; Fisher’s computes exact probabilities from the hypergeometric distribution. Results are similar with large counts, but Fisher’s is the safe choice for small samples.
Can chi-square show how strong the relationship is?
Yes, via effect size statistics: phi or Cramer’s V for strength of association. A significant p with a tiny V means the relationship, while real, explains very little of the outcome.