Cox & Snell pseudo R²: what it means and how to read it
In the report: Cox & Snell R Square — A pseudo R² from the likelihood ratio; even a perfect model stays below 1.
How to read it
Mostly reported next to Nagelkerke R², because SPSS prints both; Nagelkerke is the easier one to read.
In plain words
A teacher guessed who passes and got two numbers for how good the guesses are: Cox and Snell R Square, 0.28, and Nagelkerke R Square, which came out higher. She did not know which one to trust. Now she knows that Cox and Snell can never reach 1, even if every guess were right, which is why her number looks lower than it is. Nagelkerke stretches it so that perfect guesses would reach 1. SPSS prints both, and so does the add-on. In her report she writes the Nagelkerke one, which is easier to read, and keeps Cox and Snell for people who compare with SPSS.
How it is computed
1 − exp(2 (LL₀ − LL) / n)Example
The cell with Cox & Snell R 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).
Related values
- Nagelkerke pseudo R² — Cox & Snell R² rescaled so that a perfect model reaches 1.
- Classification accuracy — The share of rows classified correctly when a predicted probability of 0.5 or more is read as 1.
- Odds ratio — The odds ratio: how many times the odds of Y = 1 multiply for one unit more of the predictor. In the Intercept column it is the odds of Y = 1 when every predictor is 0, not a ratio. Empty when lambda is above 0.
- Multiple correlation R — The square root of R Square. For ordinary least squares it equals the correlation between the observed and the predicted Y; with lambda above 0 it does not.
- R² — The share of the variance of Y explained by the predictors.
Get it in your sheet
One formula in a cell gives the whole report, Cox & Snell pseudo R² included. ALS Stats is a free add-on for Google Sheets™.
Install ALS Stats from Google Workspace Marketplace (opens in a new tab)