Likelihood Ratio: what it means and how to read it

In the report: Likelihood Ratio — The likelihood-ratio chi-square (G²) of the table with the same df as Pearson's; p from the chi-square distribution.

How to read it

Another test of the same question, close to Pearson's with enough rows. Report Pearson unless your course asks for this one.

In plain words

A school nurse wanted to know whether the kind of lunch children bring, hot, packed or none, goes with their grade. She put 50 children in a table and wanted a second way to check the same question. She looked at the Likelihood Ratio, and it came out 0.35. A number that low means her table looks almost like one where lunch and grade have nothing to do with each other. In another school the number came out many times bigger, far from such a picture and hard to put down to chance alone. With enough children it agrees with Pearson Chi-Square, so she reports Pearson unless her course asks for this one.

How it is computed

G² = 2 · Σ O · ln(O / E), cells with O = 0 add nothing

Example

The cell with Likelihood Ratio 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.

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.
Degrees of freedom between groups — The first degrees of freedom of F: the number of groups minus 1.
Degrees of freedom within groups — The second degrees of freedom of F. For the classic test — all values minus the number of groups; for Welch it is smaller and usually fractional.

Get it in your sheet

One formula in a cell gives the whole report, Likelihood Ratio included. ALS Stats is a free add-on for Google Sheets™.

Install ALS Stats from Google Workspace Marketplace (opens in a new tab)