Compare Two Variances with Gnumeric's F-Test Tool

Gnumeric’s Claims About Two Variances dialog runs a two-sample F variance test. It produces summary statistics, an F ratio, both directional p-values and a two-sided p-value. Use it to compare population variability, not to test whether two means differ.

The sample order matters: F = sample variance of Variable 1 ÷ sample variance of Variable 2. Gnumeric does not automatically put the larger variance on top. The displayed probability labels also need care, as explained below.

Version and verification: This workflow is qualified to Gnumeric 1.12.62’s English GTK interface from its released menu, dialog and calculation source. Independent arithmetic and headless ssconvert 1.12.62 on Debian 13 x86-64 check the reconstructed example formulas. The graphical dialog and the analysis-tool engine were not executed. The tables below explain expected results; they are not application captures.

Decide what you are testing

The null hypothesis is that the two population variances are equal. Choose the alternative before examining the result:

• Two-sided: the variances differ in either direction.
• Right-sided: Variable 1’s population variance is greater than Variable 2’s.
• Left-sided: Variable 1’s population variance is less than Variable 2’s.

These directions and the F-ratio convention follow the NIST definition of the two-sample variance test. Do not select a one-sided test afterward merely because it produces the smaller p-value.

The classical test assumes independent observations within and between samples drawn from normal populations. Repeated measurements of the same subjects are not automatically independent samples. Normality matters particularly for this variance test: NIST notes its sensitivity to departures from normality, and the R statistical reference describes the normal-population scope. A spreadsheet result cannot establish those assumptions for you.

For this tutorial, use complete numeric samples with at least two observations each and positive sample variances. Leave blanks, text, Boolean values, errors and constant samples out of this first exercise. Do not replace missing measurements with zero. A genuine measured zero is valid numeric data.

Enter a small practice example

Enter the following synthetic data in A1:B6. The two columns are separate samples; matching row numbers do not imply paired observations.

Sheet row	A	B
1	Sample A	Sample B
2	0	4
3	3	5
4	6	6
5	9	7
6	12	8

The numbers are constructed to make the calculation easy to check, not to demonstrate normality or support a real-world population claim. For the exercise, choose the two-sided question and alpha = 0.05 in advance.

Open the correct analysis dialog

1. Choose Statistics → Two Sample Tests → Claims About Two Variances. The menu item is not named FTEST, and it is not under the general Tools menu. The exact path comes from the released menu hierarchy and English action labels.
2. On Input, set Variable 1 range to A1:A6 and Variable 2 range to B1:B6. Select the ranges separately, not A1:B6 in both boxes.
3. Select Labels, because each range starts with a heading. This consumes the first cell of each selected column as its name and leaves five numeric observations per sample. If instead you select A2:A6 and B2:B6, clear Labels.
4. There is no Grouped by Columns/Rows control in this dialog. The two separate range fields identify the samples. Keep this exercise to one contiguous column per field; do not borrow grouping instructions from another analysis dialog.
5. On Test, set Alpha to 0.05, the default. It must be greater than 0 and less than 1. This tab does not ask you to choose a tail: the calculation supplies both directional results and the two-sided result.
6. On Output, choose New sheet. Use this route for 1.12.62 rather than a fixed Output range; the source-size discrepancy is explained below. Leave Autofit columns enabled to make the long row labels readable.
7. Choose Formulæ rather than Values if you want existing input-cell edits to recalculate the results. Formula output is enabled by default. Values give a snapshot. Adding observations beyond the selected ranges still requires updating the analysis, and changing the dialog’s Alpha requires rerunning it.
8. Select OK. Check both sample names, counts and variances before interpreting a probability. If your result does not match the following checks, resolve the input or output problem first.

The released variance dialog, dialog handler, and shared output controls establish these controls. Their presence in source is not a claim of a completed GUI run.

Read the result without mixing the tails

The released calculation writes the following layout. Numbers are rounded here, and blank cells mean that the statistic is not repeated in the second column.

Output row	Sample A	Sample B
Mean	6	6
Variance	22.5	2.5
Observations	5	5
df	4	4
F	9
P (F<=f) right-tail	0.028
F Critical right-tail	6.388233
P (f<=F) left-tail	0.972
F Critical left-tail	0.156538
P two-tail	0.056
F Critical two-tail	0.104118	9.604530

Read the tail names, not the inequality typography alone. The source literally labels the right-tail row P (F<=f) right-tail, but calculates it with FDIST, the right-tail survival function. Using T for a random F-distributed statistic and 9 for this observed ratio, that row means P(T ≥ 9) = 0.028. The row labeled P (f<=F) left-tail calculates 1 minus that value, or P(T ≤ 9) = 0.972. Treating capital F as the random statistic in those displayed labels would reverse their meanings. The released calculation source and FDIST definition settle the intended direction.

The two numbers in F Critical two-tail are the lower and upper boundaries for the same F ratio. Their placement under the sample headings does not make them separate tests of Sample A and Sample B. At alpha 0.05, each outside tail has probability 0.025 under the null. Reject equality for an F ratio below the lower boundary or above the upper boundary.

For the preselected two-sided exercise, 0.056 > 0.05, and 9 lies between 0.104118 and 9.604530. The result does not reject equal population variances at the 5% level. It does not prove they are equal. If a right-sided alternative had genuinely been specified beforehand, its p-value would instead be 0.028, with 9 > 6.388233, giving rejection at that level. This difference is why the question must come first.

The bundled manual describes the displayed p-value as a probability of making a Type I error. Do not report it that way. A p-value is a tail probability under the null model, not the probability that this conclusion is wrong or that the null hypothesis is true. Alpha is the preselected test’s Type I-error rate under its assumptions.

Independently check the arithmetic

Both means are 6. Sample A’s squared deviations sum to 90; Sample B’s sum to 10. Dividing by n − 1 = 4 gives 22.5 and 2.5, so F = 22.5/2.5 = 9. The denominator is not n: the tool uses VAR, the sample-variance function, not VARP.

These ordinary formulas check the probability and cutoff rows for the example. Enter them outside the input data, for example in spare cells on the original sheet. They are a reconstruction of the relevant arithmetic, not an execution of the analysis dialog.

Formula	Expected result
=VAR(A2:A6)/VAR(B2:B6)	9
=FDIST(9,4,4)	0.028
=1-FDIST(9,4,4)	0.972
=2*MIN(FDIST(9,4,4),1-FDIST(9,4,4))	0.056
=FINV(0.05,4,4)	6.388232909
=FINV(0.95,4,4)	0.156537812
=FINV(0.975,4,4)	0.104117537
=FINV(0.025,4,4)	9.604529885

FDIST takes the numerator df first, then the denominator df. FINV takes a right-tail probability, which is why the lower two-sided cutoff uses 1 − alpha/2, not alpha/2. These examples use English function names and comma separators; use your installed locale’s formula separator if different.

For an extra check, =FTEST(A2:A6,B2:B6) returns 0.056. FTEST returns a two-sided p-value, not the F statistic and not the dialog’s entire report. The analysis-tool source builds its report from VAR, COUNT, FDIST, FINV and other expressions rather than simply displaying FTEST.

Reverse the two sample ranges and the F ratio becomes 1/9 ≈ 0.111111. The right-tail probability becomes 0.972, the left-tail probability becomes 0.028, and the two-sided p-value stays 0.056. This confirms why a ratio less than 1 is valid and why sample order must stay attached to the hypothesis. With unequal sample sizes, swap the degrees of freedom too.

Why this guide uses New sheet

The bundled manual’s fixed-range size advice is stale for this output. The 1.12.62 F-test writer populates three columns and twelve rows including the header, but its size-request code says two columns and ten rows. Merely selecting a bigger fixed range should not be assumed to fix that mismatch.

The released output writer explicitly creates a full-size sheet for New sheet and applies fixed-output-region clipping only to the Output range mode. This is a source-established reason to use New sheet, not an observed workaround from a GUI test. Fixed-range output, its truncation behavior and subsequent GUI editing remain outside this tutorial’s verified scope.

Troubleshooting and limits

• Wrong count or variance: Check the two ranges and Labels together. Selecting Labels on numeric-only ranges removes the first observation from each. Selecting a combined two-column block is not the same as entering two sample ranges.
• OK is unavailable: Verify both range expressions, a valid output choice, and 0 < Alpha < 1. Enabled OK does not certify normality, independence or enough numeric observations.
• F is the reciprocal of your calculation: Check which sample is Variable 1. Do not reorder samples to force F above 1 without also reconsidering the direction and degrees of freedom.
• One-sided and two-sided conclusions differ: Compare the row matching the preselected alternative. Two-sided testing splits alpha between two rejection tails.
• A column or final rows are absent: Do not invent the missing values or interpret a partial table. Rerun to New sheet and inspect the full layout; this guide does not validate fixed-range output.
• Results do not update: Values are static. Formula results refer to the originally selected ranges and retain the chosen alpha in the generated expressions. Rerun after changing the sample extent or significance level.
• Errors, constant samples or nonnumeric entries: Stop and inspect the input. This tutorial does not claim tested dialog behavior for these branches or prescribe automatic omission. A tiny p-value does not repair a zero variance, a broken study design or non-normal data.

The native checks cover reconstructed formulas for the example, reversed samples, unequal sample counts and their reversal, a changed alpha, and scaling the first sample. They do not validate the graphical tool, output formatting, save/reopen behavior, error handling, every locale or another platform. Contingency tests are a separate workflow.

First-party references

• Gnumeric manual: F-Test, Two-Sample for Variances. The version-pinned bundled manual source was inspected with the corrections above.
• Official Gnumeric 1.12.62 source archive and published SHA-256 checksum. The cited released source files were checked against that archive.
• NIST: F-Test for Equality of Two Variances, for statistical alternatives and rejection regions, not Gnumeric interface behavior.