Pearson chi-square: what it means and how to read it
In the report: chi2 — Pearson's chi-square: how far the observed counts are from those expected if the two variables were unrelated. No continuity correction.
How to read it
The larger, the stronger the evidence of a relation; read p. In a report: χ²(2, N = 50) = 0.31, p = .859.
In plain words
A shop owner wondered whether the drink a customer picks goes with the age group. She worked out how many customers would pick each drink if age and drink had nothing to do with each other: 20 young customers would pick tea. But 35 did. The chi-square put all such gaps into one number, and it came out 9.5. The bigger it is, the further the real counts are from those. If every count had matched, it would be 0. Now she can read the chance column next to it to see whether gaps this big could easily be luck.
How it is computed
χ² = Σ (O − E)² / E, E = row total · column total / N, over the non-empty categoriesExample
The cell with chi2 is selected in each report; point at a label to see its note.
- — the sample data (50 rows) the examples use
- —
=STATS_CHI2(Data!A1:T51, "gender", "group") - —
=STATS_CRAMER(Data!A1:T51, "gender", "group")
Where you see it
STATS_CHI2— Pearson chi-square test for association between two categorical columns.STATS_CRAMER— Cramer's V effect size for association between two categorical columns.
Related values
- Pearson Chi-Square — The same test as the chi2 at the top of the report, in the SPSS table: value, df and the asymptotic p from the chi-square distribution. No continuity correction.
- Continuity Correction (Yates) — Pearson's chi-square with the Yates correction, for a 2 × 2 table only; the row is absent for larger tables.
- Likelihood Ratio — The likelihood-ratio chi-square (G²) of the table with the same df as Pearson's; p from the chi-square distribution.
- Fisher's Exact Test — The exact p of a 2 × 2 table, in the two Exact Sig. columns; the value, df and asymptotic columns are empty. The row is absent for larger tables.
- Linear-by-Linear Association — The test of a linear trend between the codes of the two columns, df = 1. Shown only when both columns have codes: numbers, or labels with numbers; text without labels has no such row, as in SPSS.
Get it in your sheet
One formula in a cell gives the whole report, Pearson chi-square included. ALS Stats is a free add-on for Google Sheets™.
Install ALS Stats from Google Workspace Marketplace (opens in a new tab)