Group size ratio: what it means and how to read it

In the report: balance — The size of the largest group divided by the size of the smallest. 1 — all groups have the same number of values.

How to read it

How unequal the group sizes are: 2 means the largest group is twice the smallest.

Unequal groups together with unequal scatter make the classic test unreliable, so above 1.5 the add-on prefers Welch.

Above 1.5 the automatic choice takes Welch: unequal groups make the classic test sensitive to unequal variances.

In plain words

A shop owner wanted to compare what customers spend on weekdays and at weekends. She had 30 weekday customers and 60 weekend customers and wondered whether such uneven groups matter. She looked at the group size ratio and it came out 2: the weekend group is twice as big as the weekday group. A ratio of 1 would mean both groups are the same size. When groups are uneven and also spread out differently, the old test can mislead, so above 1.5 the add-on prefers Welch's test. Now she can see at once why the add-on picked that test for her.

How it is computed

balance = max nᵢ / min nᵢ

Example

The cell with balance 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.

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.
Standard deviation of the differences — The sample standard deviation of the row-by-row differences (n − 1).

Get it in your sheet

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

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