CONFIDENCE Function (Gnumeric)

=CONFIDENCE(alpha,stddev,size)

There are three required arguments in this order; no optional or omitted-argument defaults are documented. Official English-language formula examples use commas and a decimal point. Gnumeric’s user-interface locale can affect entry conventions; verify any localized separator or function translation in the actual application rather than substituting a syntax from Excel or LibreOffice. Manual, Gnumeric reference catalogue (checked 13 October 2026).

For 0 < α < 1, known population σ > 0 and sample size n > 0, the standard normal critical value is z(1 − α/2). The normal-theory margin is:

E = z_(1 - alpha/2) * sigma / sqrt(n)

The calculation represents the amount to add to and subtract from a sample mean. The formula does not prove that a sample was random, measurements independent, or the assumptions behind the confidence interval appropriate. With repeated valid sampling, the procedure targets the specified long-run coverage; it is not a probability that a fixed population mean changes after observing a particular interval. The source implementation uses the normal-distribution inverse, a positive population standard deviation and sqrt(size); see the source evidence below.

Imagine a production line where historical process qualification establishes a known population standard deviation of 12 units. You independently sample 36 items and observe a sample mean of 100 units. Set up this worksheet:

Independent calculation: NORMINV(0.975,0,1) would yield approximately 1.9599639845 in a compatible normal-quantile definition; multiplying by 12/SQRT(36) gives 3.9199279691. The interval is approximately [96.080072, 103.919928]. Here the endpoints are ordinary arithmetic combining the mean with the function’s single scalar result, not multiple values returned by CONFIDENCE. Validation level: SciPy/independent arithmetic only; native Gnumeric not run.

A second controlled check

=CONFIDENCE(0.1,8,25)

Expected independently calculated margin: 2.6317658031 using a 90% normal critical value (not an interval endpoint). You can vary only alpha while holding σ and n fixed to see how higher confidence widens the margin. At 99% confidence, =CONFIDENCE(0.01,5,16) has expected margin 3.2197866294.

Sample-size planning for a target maximum margin. If σ ≈ 12 is genuinely known, α = 0.05 and desired half-width ≤ 2, the algebraic requirement is n ≥ (z(0.975)*12/2)^2. The exact mathematical calculation requires rounding upward to 139 observations; using the rounded 1.96 constant is a planning approximation and may change boundary cases. An inspectable formula can be written as:

=ROUNDUP((NORMSINV(1-0.05/2)*12/2)^2,0)

This uses NORMSINV and ROUNDUP. The planning formula itself has not been executed in Gnumeric; the exact expected count was independently checked. The calculation is for the assumed normal model and does not account for finite-population corrections or survey design effects.

A spreadsheet audit trail. Keep alpha, σ, n, observed mean, margin and endpoints in separately labeled cells. That makes it harder to mislabel CONFIDENCE as the entire interval and simpler to recheck the meaning of σ. Report measurement units and the data collection assumptions alongside the interval, not only a percentage.

Avoid silently substituting a sample standard deviation for known σ. For an estimated σ in a small sample, prefer the separate CONFIDENCE.T method (with its own assumptions), rather than pretending the population spread is known. That is a statistical-method recommendation, not a claim that Gnumeric automatically detects whether a supplied σ is population- or sample-based.

If results seem unexpectedly small, check whether size is a count (not a percent), whether σ is in the same units as the mean, and whether you’re confusing the half-width with the full interval width 2*E. An apparent spreadsheet mismatch can also result from numeric display rounding rather than different underlying values. Avoid passing an already-computed standard error where the function expects σ or you will divide by √n twice.

Gnumeric’s official 1.12-series catalogue lists confidence as implementation Complete / testing Basic, and the published Statistics manual specifies the syntax and error cases above. Gnumeric announced release 1.12.62; this review uses that official release as its version context and additionally inspects the checksum-verified official 1.12.62 release source. These are documentary and source checks, not a native Gnumeric 1.12.62 execution on Linux or any other OS. The manual describes the function as Microsoft Excel compatible; no Excel, LibreOffice or XLSX/ODS round-trip test was performed here. Numbers may differ in final displayed digits across calculation engines.

For the mean and sample size, see AVERAGE and COUNT. For why using a sample deviation changes the choice of interval, compare STDEV and STDEVP, then CONFIDENCE.T. For normal-quantile planning, see NORMSINV.

• Gnumeric Statistics manual — CONFIDENCE: exact signature, arguments, σ interpretation, truncation, size <= 0 error distinction, official Excel-compatibility claim.
• Gnumeric public function catalogue: registered as implementation Complete, upstream testing Basic (does not validate these worksheet examples).
• Gnumeric 1.12.62 release announcement: public 1.12.62 release context; does not claim this function newly introduced or changed in that release.
• Official Gnumeric 1.12.62 source archive: checksum-verified release plugins/fn-stat/functions.c was inspected for the required arguments, inverse-distribution formula and explicit sample-size/standard-deviation error branches. Source inspection is not native execution.
• Validation: Official source and documentation checked; SciPy quantiles and independent arithmetic performed. Native Gnumeric execution, screenshots, locale and workbook round-trip tests were not performed.