Test of equal variances: what it means and how to read it
In the report: Levene (based on median) — 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.
In plain words
A coach compared the sprint times of two teams. Before comparing the averages, she wanted to know whether both teams were equally scattered: one team all ran close to 14 seconds, the other anywhere from 12 to 17. The test of equal variances said the two teams did not look equally scattered, and that gap was hard to put down to chance alone. Now she knows the usual comparison, which counts on equal scatter, could mislead her, so she uses the version that does not. By default the check uses the middle time of each team, so a few odd runs do not throw it off. To match SPSS, she can switch it to the average instead.
Example
The cell with Levene (based on median) 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.
Related values
- 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).
- Mean of the group — The mean of the values of the group.
Get it in your sheet
One formula in a cell gives the whole report, Test of equal variances included. ALS Stats is a free add-on for Google Sheets™.
Install ALS Stats from Google Workspace Marketplace (opens in a new tab)