Variance ratio: what it means and how to read it

In the report: varRatio — The largest group variance divided by the smallest. 1 — the variances are equal.

How to read it

How unequal the scatter of the groups is: 3 means that the values of one group vary three times as much as those of another.

Above 2 the add-on prefers Welch's test, which does not need equal scatter.

Above 2 the automatic choice takes Welch.

In plain words

A teacher wanted to know whether two classes were spread out the same way. In class A the scores stayed between 60 and 80. In class B they ran from 30 to 100. She looked at the variance ratio and it came out 3. Now she can say that the scores in class B jump around about three times as much as in class A. A ratio near 1 would mean both classes are spread out about equally. Above 2 the add-on prefers Welch's test, the version made for groups that are spread out differently, so now she knows why it picked that one.

How it is computed

varRatio = max s²ᵢ / min s²ᵢ, sample variances (n − 1). Infinity when a group has no spread.

Example

The cell with varRatio is selected in each report; point at a label to see its note.

— the sample data (50 rows) the examples use
— =STATS_INDEPENDENT(Data!A1:T51, "y,x1", "welch",0.95)
— classic one-way ANOVA =STATS_ANOVA(Data!A1:T51, "x1,x2")
— new syntax, 3 reports =STATS_ANALYZE(Data!A1:T51, "PAIRED('before,after', 0.99, 'greater') ANOVA('x1,x2,x') DESCRIPTIVE('mean,std,n', 'x1,x2')")

Where you see it

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.

Group size ratio — The size of the largest group divided by the size of the smallest. 1 — all groups have the same number of values.
Test of equal variances — Tests whether the groups have the same variance. By default it is based on the median — the Brown–Forsythe modification of Levene's test, robust to skewed data; "based on mean" is the original Levene test, the one SPSS T-TEST and ONEWAY print by default — set homogeneity to "levene" to match SPSS.
Posthoc comparisons — Posthoc (pairwise) comparisons: every pair of groups compared after the ANOVA, with p corrected for the number of comparisons. Shown only when the ANOVA is significant (p < 0.05) and there are at least three groups — unlike SPSS ONEWAY, which prints a requested posthoc table whatever the ANOVA shows.
Mean difference — The mean of the first group minus the mean of the second.
Standard error of the difference — How much the mean difference would vary from sample to sample.

Get it in your sheet

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

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