Classification accuracy: what it means and how to read it

In the report: Accuracy — The share of rows classified correctly when a predicted probability of 0.5 or more is read as 1.

How to read it

Easy to explain: 0.75 means the model gets 3 cases of 4 right. Compare it with the share of the more common outcome: if 70% of the rows are 1, always guessing 1 already gives 0.70.

It is the Overall Percentage of the SPSS Classification Table at the cut-off 0.5; the table itself (right and wrong answers for 0 and for 1) is not reported.

In plain words

A teacher guessed who would pass among 40 students, and the add-on got 30 of them right. She counted the accuracy and it came out 0.75: right in 75 guesses out of 100, three out of four. That is easy to say, but is it good? Of the 40 students, 28 passed, so simply guessing pass for everyone would already be right 70 times out of 100. Now she can say her guesses are only 2 students better than that. The add-on counts a student as pass when the guessed chance of passing is one half or more, the same way SPSS does in its table.

How it is computed

(rows where ŷ = y) / n, ŷ = 1 when p ≥ 0.5

Example

The cell with Accuracy 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).

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.
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.

Get it in your sheet

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

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