Likelihood-ratio chi-square: what it means and how to read it

In the report: Chi-square — How much −2 Log Likelihood dropped compared with the model with the intercept only.

How to read it

The larger, the more the predictors together improve the prediction. Read its Sig.; in a report: χ²(2) = 4.08, p = .130.

In plain words

A clinic scored how far its guesses about who would recover were from what really happened. With no information about the patients the score was 120, and with age and weight it was 104. The chi-square is simply the drop: 16. The bigger the drop, the more age and weight together brought the guesses closer to reality. A drop of 16 looks like a lot, but the clinic does not stop there. It looks at the chance column next to it, which says whether such a drop could easily be luck, and only then writes it in the report.

How it is computed

χ² = −2LL₀ − (−2LL), compared with the chi-square distribution with df = k − 1

Example

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

— the sample data (50 rows) the examples use
— two steps; pass is coded 0 and 1 =STATS_LOGISTIC(Data!A1:T51, "pass", "x1,x2|x", 0, 50, 1e-8)

Where you see it

STATS_LOGISTIC — Binary logistic regression with optional ridge regularization (lambda >= 0).

Wald statistic — The Wald statistic of the coefficient: (B / StdError)². Empty when lambda is above 0.
F change — The F test of R Square Change: whether the predictors added at this step explain more than chance. At the first step it equals the F of the model. Empty when the step entered no predictor (df1 = 0).
z statistic — The test statistic on the normal scale.
Mann–Whitney U — How often a value of one group comes before a value of the other when all values are sorted (ties count half) — the smaller of the two counts, as SPSS.
Wilcoxon W — The rank sum of the group whose U is the smaller one — Wilcoxon's rank-sum form of the same test, as SPSS.

Get it in your sheet

One formula in a cell gives the whole report, Likelihood-ratio 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)