Check normality before choosing a statistical test

Use Statistics > One Sample Tests > Normality Tests to examine whether a sample is inconsistent with a normal-distribution model. Combine the test with a normal probability plot and knowledge of the sampling design; a large p-value does not prove normality.

Scope and two fixed samples

This exercise is grounded in Gnumeric 1.12.62 GTK desktop source and the upstream 1.12 manual, using English controls. It has not been executed natively and is not a test of the older 1.12.57 runtime. Use a disposable .gnumeric workbook.

Enter Symmetric in A1 and Outlier in B1. Enter these 20 observations down A2:A21, one per cell:

-1.9, -1.4, -1.1, -0.9, -0.7, -0.6, -0.4, -0.3, -0.2, -0.1, 0.1, 0.2, 0.3, 0.4, 0.6, 0.7, 0.9, 1.1, 1.4, 1.9.

Copy the numbers to B2:B21, then replace B21 with 8. The first sample has count 20, sum 0 and mean 0. The second also has count 20, but sum 6.1 and mean 0.305. Those are deterministic input checks, not test p-values. The first sample is deliberately symmetric; symmetry alone does not establish normality.

Configure a specific test

1. Choose Statistics > One Sample Tests > Normality Tests.
2. On Input set Input range to A1:B21, Grouped by Columns, and select Labels.
3. On Test select Anderson-Darling Test. Set Alpha to 0.05 and enable Create Normal Probability Plot.
4. On Output choose a new sheet so the results cannot overwrite the samples.
5. Confirm with OK and inspect the report.

The versioned implementation produces Alpha, p-Value, Statistic, N and Conclusion fields. Check N=20 for both samples before interpreting any test statistic. A count of 19 or an unexpected label suggests a range/header mistake rather than a scientific finding.

The tool also offers Cramér-von Mises, Lilliefors and Shapiro-Francia tests. Pick a method for a reason and record it; do not cycle through methods until one gives the answer you hoped for. The Anderson-Darling implementation documents a minimum sample size of eight, which this fixture exceeds.

Interpret the evidence cautiously

Record the actual p-values produced by your installation rather than copying invented expected numbers. At the chosen 0.05 level, a sufficiently small p-value is evidence against the normal model. A result that does not reject means the test did not find sufficient evidence against it, not that the distribution has been certified normal.

Compare the probability-plot patterns. The extreme value 8 should visibly separate from the main body of the Outlier sample. Investigate its origin: a transcription error can be corrected against an authoritative source, while a valid extreme observation should not be deleted solely to improve a p-value.

These two columns are not independent datasets for a treatment comparison; one was constructed from the other. They demonstrate a diagnostic response, not an experimental effect. For a paired t-test, the relevant normality assumption concerns the paired differences, not necessarily each raw column separately. For ANOVA, residual behavior and the experimental design matter as well.

Change one observation and check the boundary

Restore B21 from 8 to 1.9 and rerun the same test to a new output sheet. The columns now contain identical values, so their chosen-test statistics and p-values should agree within display precision. This is a stronger reproducibility check than demanding a guessed p-value for the original outlier case.

As a separate failure exercise, select fewer than eight observations for Anderson-Darling. Treat an error or invalid result as a sample-size problem, not as evidence of non-normality. A constant column is also not a valid ordinary normality diagnostic because its variance is zero.

Save the input and clearly named output sheets. Reopen the workbook and confirm labels, N, test name and alpha. If the inputs change later, rerun and identify the new report rather than assuming an old report still represents the current data.

Official references

Gnumeric manual, Statistical Analysis and Normality Tests; official Gnumeric 1.12.62 source archive, normality-tests.ui and analysis-normality.c. The manual was captured 20 October 2026; source members were recovered from the official archive. No native p-values or probability-plot screenshot is claimed.