Gnumeric · Analysis and modeling · Intermediate
Run two-factor ANOVA with and without replication
Set rows per sample correctly for two-factor ANOVA, reconcile sums of squares, and avoid claiming an interaction test without replication.
Documentation-qualified exercise; native application verification pending · Editorial standards
Gnumeric uses one two-factor ANOVA dialog for both replicated and unreplicated designs. Rows per sample determines which analysis is performed. It is not a cosmetic grouping option: replication supplies the within-cell information needed to estimate interaction separately from error.
Scope and replicated fixture
Use the English GTK desktop controls documented in Gnumeric 1.12.62 source and the upstream 1.12 manual. This is not native execution evidence or a claim about an installed older build. Work in a disposable .gnumeric workbook with independent synthetic observations.
Enter this numeric block in B2:C5, leaving labels outside the selection for the first exercise:
| Row | B: Method A | C: Method B |
|---|---|---|
| 2 | 8 | 12 |
| 3 | 10 | 14 |
| 4 | 10 | 18 |
| 5 | 12 | 20 |
Rows 2–3 are two replicates under Condition 1; rows 4–5 are two replicates under Condition 2. Each column is one level of the method factor. The four cell means are 9, 13, 11 and 19; total 104 and grand mean 13.
Run the replicated analysis
- Choose Statistics > Multiple Sample Tests > ANOVA > Two Factor.
- Set Input range to B2:C5 and leave Labels off, because the selected block contains only numbers.
- Set Rows per sample to 2.
- On Options use Alpha 0.05. On Output choose a new sheet.
- Confirm and inspect the ANOVA report.
Independent checks are within-cell sum of squares 8 with 4 degrees of freedom, method sum of squares 72, condition sum of squares 32, interaction sum of squares 8, and total sum of squares 120. Each of the three effect terms has one degree of freedom. Error mean square is 2, so the corresponding F ratios are 36, 16 and 4.
Match terms by the factor arrangement, not an assumed label order. An interaction F ratio of 4 is not automatically “significant”; read its actual p-value or compare with the appropriate critical value using the chosen alpha and degrees of freedom. Statistical significance also does not establish practical importance or causation without an appropriate design.
Test the sensitivity of the interaction
Change C4:C5 from 18,20 to 14,16 and rerun to a separate output sheet. Cell means become 9,13,11,15. Method B now exceeds A by 4 under both conditions, so the interaction sum of squares should be zero. Within-cell sum of squares remains 8 because each pair still differs from its mean by ±1.
Expected method and condition sums of squares become 32 and 8; total becomes 48. This controlled change tests whether the grouping was understood correctly. Restore C4:C5 to 18,20 after comparing the reports.
Run a separate unreplicated design
In F2:G4 enter rows 8/12, 10/15 and 13/17. These are three condition levels and two method levels, with one observation in each combination. Select F2:G4 in the same dialog, Labels off, but set Rows per sample to 1.
The expected grand mean is 12.5. Total sum of squares is 53.5; row-factor sum of squares is 25; column-factor sum of squares is 28â…™; the remaining sum of squares is â…“. Degrees of freedom are 2 for rows, 1 for columns and 2 for the residual. These provide a layout check without inventing application output.
There is no independent replication within a factor combination, so this analysis cannot separately estimate interaction and pure error. Its additive interpretation depends on an assumption about interaction. Do not describe its residual as a direct interaction test or substitute an unreplicated design just because it is easier to enter.
Validate and preserve
Check range, Labels and Rows per sample before interpreting results. The manual describes missing-value estimation for replicated data, but this fixture has no missing observations; do not silently replace missing records with zero. Consider independence, residual normality and variance assumptions before using ANOVA for a real decision.
Save the source block and clearly named reports. Close and reopen the workbook and confirm both analyses remain distinguishable. After editing source data, rerun rather than assuming an existing output sheet is current.
Official references
Gnumeric Multiple Sample Tests, captured 20 October 2026; official 1.12.62 source archive, anova-two.ui. Arithmetic is independently reconciled; no native ANOVA execution is claimed.