Linear-by-Linear Association: what it means and how to read it
In the report: 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.
How to read it
Makes sense for ordered categories (low, medium, high): do higher codes of one column go with higher codes of the other? For names of groups with no order, ignore it.
In plain words
A teacher asked 60 students how much they like math and how much they like science, each as low, medium or high. She could not tell whether higher liking for one goes together with higher liking for the other. She looked at the Linear-by-Linear Association and got 8.4. Now she can say that students who chose a higher answer for math also tended to choose a higher answer for science, and that this is hard to put down to chance alone. A number near 0 would mean the answers do not rise together. It only makes sense when the answers have an order, not for names of clubs or towns.
How it is computed
(N − 1) · r², r — the Pearson correlation of the codes of the rowsExample
The cell with Linear-by-Linear Association 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.
Related values
- 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.
- Degrees of freedom 1 — The first (numerator) degrees of freedom of the F statistic next to it.
- Degrees of freedom 2 — The second (denominator) degrees of freedom of the F statistic next to it.
Get it in your sheet
One formula in a cell gives the whole report, Linear-by-Linear Association included. ALS Stats is a free add-on for Google Sheets™.
Install ALS Stats from Google Workspace Marketplace (opens in a new tab)