F statistic: what it means and how to read it
In the report: F — 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.
How to read it
F compares how much the groups differ with how much individuals differ inside each group. F near 1 — the groups differ no more than people do anyway; the larger F, the more the group matters.
F on its own is hard to read — look at the p next to it. In a report F goes with its two degrees of freedom: F(2, 147) = 4.12.
In plain words
A teacher tried three ways of teaching, one in each group. Scores inside every group were all over the place, from 50 to 90, so she could not tell whether the groups differed more than pupils always differ from each other. She counted F and it came out 6. Now she can say the three group averages are much farther apart than pupils usually are inside one group. An F near 1 would have meant the groups differ no more than pupils do anyway. F alone does not say whether the gap could be luck, so she also looks at the chance column next to it.
Example
The cell with F is selected in each report; point at a label to see its note.
- — the sample data (50 rows) the examples use
- —
=STATS_LINEAR(Data!A1:T51, "y", "x1,x2", 0) - —
=STATS_INDEPENDENT(Data!A1:T51, "y,x1", "welch",0.95) - — classic one-way ANOVA
=STATS_ANOVA(Data!A1:T51, "x1,x2")
Where you see it
STATS_LINEAR— Multiple linear regression (OLS) with hierarchical steps separated by | and interactions a*b.STATS_INDEPENDENT— Independent-samples t-test for two groups: the two selected columns are the groups.STATS_ANOVA— One-way ANOVA: each selected column is a group. Classic (Student) or Welch ANOVA, chosen by welch (auto by default), with homogeneity of variances and post-hoc comparisons.STATS_ANALYZE— Runs several analyses on one range and returns one report.
Related values
- 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.
- Degrees of freedom — The degrees of freedom of the statistic next to it: how much independent information the estimate rests on.
Get it in your sheet
One formula in a cell gives the whole report, F statistic included. ALS Stats is a free add-on for Google Sheets™.
Install ALS Stats from Google Workspace Marketplace (opens in a new tab)