Pearson Chi-Square: what it means and how to read it

In the report: 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.

How to read it

The main test of the table. Below 0.05 in the p column — the two variables are related. Use it when the expected counts are not small (Warnings is empty).

In plain words

A shop owner counted 100 customers by age group and by drink, and wanted to know whether the two go together. The Pearson Chi-Square row is the main test of this table, and its number came out 9.5, the same as chi2 at the top of the report. Next to it is the chance column. When it says less than 5 times in 100, the link is hard to put down to luck. Hers did, so she can say age and drink go together. She trusts this row only when the table has no very small counts; if Warnings is not empty, she looks at the other rows too.

How it is computed

χ² = Σ (O − E)² / E

Example

The cell with Pearson Chi-Square is selected in each report; point at a label to see its note.

— the sample data (50 rows) the examples use
— with the Chi-Square Tests and Symmetric Measures tables at the end =STATS_CHI2(Data!A1:T51, "gender", "group", TRUE)

Where you see it

STATS_CHI2 — Pearson chi-square test for association between two categorical columns.

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.
F statistic — A ratio of two variance estimates. The larger F, the stronger the evidence against the null hypothesis; its p comes from the F distribution with the two degrees of freedom next to it.

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)