Test variant: what it means and how to read it

In the report: welch — student — the classic test, which assumes equal variances in the groups; welch — Welch's test, which does not.

How to read it

Which version of the test was used. The classic test assumes that the groups scatter equally; when they do not, or when the groups are of very different sizes, its p can mislead, and Welch's version gives a fair one.

The add-on chooses for you. In a report say which one was used: "Because the variances differed, Welch's test was used."

In plain words

A teacher compared the marks of two classes, one with 12 pupils and one with 40, and the marks in the small class were far more spread out. With the setting student, the old version of the test that counts on both classes being spread out the same, the gap between the classes looked hard to put down to chance alone. When she switched to welch, the version that does not count on that, the gap could easily be luck. With classes so unequal in size and spread, the second answer is the fair one. The add-on picks one for you unless you tell it which, and in her report she writes which setting was used.

How it is computed

With welch = "auto" (the default) the classic test is taken only when all four hold: Levene p ≥ 0.05, varRatio ≤ 2, balance ≤ 1.5 and every group has at least 20 values; otherwise Welch. These are the defaults of ALS Stats, not a rule of SPSS.

The thresholds can be changed in Settings or in the formula ("varRatioMaxStudent=3"); TRUE or "welch" forces Welch, FALSE or "student" the classic test.

Example

The cell with welch 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.

Variance ratio — The largest group variance divided by the smallest. 1 — the variances are equal.
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.

Get it in your sheet

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

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