Odds ratio: what it means and how to read it

In the report: Exp(B) — 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.

How to read it

The number to report. 1.65 means every extra unit multiplies the odds of the event by 1.65 (+65%); 0.80 means the odds fall by 20%; 1 means no effect.

Odds are not a probability: odds of 1 are a 50% chance, odds of 3 a 75% chance.

In a paper: "Each additional hour of study raised the odds of passing (OR = 1.65, 95% CI 0.95–2.86, p = .077)."

In plain words

A teacher wanted to know how much an extra hour of study goes with passing. She counted the odds ratio and it came out 1.65. Now she can say that students who studied one hour more had odds of passing 65 percent larger. A number below 1 would mean lower odds, and exactly 1 would mean no link. Odds are not the same as a chance: odds of 1 mean 50 chances out of 100, as with a coin, and odds of 3 mean 75 out of 100, three passes for every fail. In her report she writes it as OR, with its range.

How it is computed

Exp(B) = e^B

Example

The cell with Exp(B) 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).

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.
R² change — What this step adds to the share of explained variance: its R² minus the R² of the step before (at the first step, its own R²). Shown when the model has two or more steps, as SPSS "Change Statistics".
Adjusted R² — R² corrected for the number of predictors: it goes down when a predictor adds less than chance would.
Standardized coefficient β — B in standard deviations: how many standard deviations Y changes for one standard deviation more of the predictor. The intercept has none.

Get it in your sheet

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

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