PEARSON Function (Gnumeric)

Gnumeric’s PEARSON returns the Pearson product-moment correlation coefficient for two series of paired observations. It answers whether increases in one numeric variable tend to accompany increases or decreases in the other along a linear pattern. It does not measure causal influence or prove that a prediction model is suitable. The coefficient is unit-free: +1 is perfect positive linear alignment, −1 perfect inverse linear alignment, and 0 no linear association. The function and its names are established by the official PEARSON manual entry [S1].

=PEARSON(array1,array2)

The Gnumeric manual documents two array parameters; it does not document an optional method, degrees of freedom, p-value or confidence argument. It states strings and empty cells are ignored and labels the function Excel compatible. Align and inspect row pairs before using a missing-data worksheet. [S1]

Enter the following numeric values in a new sheet. The first row is a label, not part of the formula. Each row represents one observation; maintain that row pairing when copying or sorting.

All data cells A2:C6 contain genuine numbers. Their independent statistics are: mean(X) = 3, mean(Y) = 4, Σ(X−3)(Y−4) = 9, Σ(X−3)² = 10, Σ(Y−4)² = 10, with n = 5. The reverse-ranked column C makes it possible to test a deliberately negative relationship. The figures below are independently calculated expectations rather than observed output from a running Gnumeric installation.

Hand-check the first result: Mean X is 3; mean Y is 4. The products of paired centered observations sum to 9. The centered sums of squares are 10 and 10, so 9/SQRT(10*10) is exactly 0.9. This is a mathematical check independent of a Gnumeric process; no application result was observed.

Suppose a team tracks satisfaction (column B) against practice hours (A). Before drawing conclusions, record =PEARSON(A2:A6,B2:B6) beside the descriptive statistics and a scatter plot. To express a local review rule, enter:

=IF(ABS(PEARSON(A2:A6,B2:B6))>=0.8,"Check strong linear pattern","Review plot and data")

Expected: Check strong linear pattern. The 0.8 cutoff was selected to illustrate a team rule, not a published decision threshold or a significance test. ABS also flags strongly negative associations. A few highly influential points can dominate r, and a curved pattern can have a low r despite a strong relationship; review plots and sample size.

In a dashboard, compare =PEARSON(A2:A6,B2:B6)^2 (0.81 expected) with a simple one-variable linear regression’s explained variation. A squared correlation is not an independent check on multivariate regression; don’t extend this identity to unrelated fitted models. If units are changed (for example hours to minutes), multiplying all values of one variable by a positive constant does not change r, though covariance does change.

• CORREL is another separately named Gnumeric function documented to compute Pearson correlation. For the same five numerical pairs, its expected result is also 0.9; this is not evidence of identical behavior for every malformed input or version. [S2]
• COVAR measures population covariance with units; the example yields 1.8. It does not substitute for the normalized coefficient. [S3]
• SLOPE, INTERCEPT, LINEST and RSQ appear in Gnumeric’s Statistics reference as related regression tools. PEARSON by itself does not return a best-fit line, a p-value or a prediction interval. [S1]

• Different row counts or shifted rows: supply equal-shaped ranges containing genuinely corresponding observations. A pairwise measure has no meaning if X and Y were independently sorted. When copying formulas, inspect the highlighted ranges and lock rows/columns with $ where appropriate.
• Blank, text, or Boolean data: Gnumeric’s official Statistics reference explicitly says text and empty cells are ignored for this function; the release-tagged collection implementation also excludes Boolean values. It is safer to clean and verify pairs in a helper table first. Do not assume a missing measurement in one column is safely re-paired with the next row in the other column; the exact malformed-input behavior needs native testing.
• Error-valued cells: fix upstream errors rather than silently replacing them with zero. The behavior and exact error label for a referenced cell that already contains an error were not tested in Gnumeric.
• Zero useful pairs, unequal-length arrays or invalid argument types: these can prevent a meaningful result. Confirm inputs first and test the exact error code in your installed version; the current manual does not specify an error code for every such case.
• Locale-specific syntax: the examples use the English-language formula name, comma argument delimiter and dot decimal. Gnumeric follows the configured operating-system locale; use the separators/format accepted by your own installation. The exact locale-specific formula delimiter was not natively checked in this review.
• Interpretation: a pattern in two columns does not by itself establish causation, accuracy of the underlying measurements, or a statistically significant relationship.

PEARSON-specific limitations

A zero-variance X or Y series makes the denominator zero: Pearson’s r is undefined. Gnumeric’s precise runtime display for a zero-variance, one-pair, empty, or mismatched input was not observed; do not fabricate a precise error code. If the output is missing or nonsensical, inspect whether numeric-looking imported data are actually text, whether all pairs line up and whether the source range contains unfiltered labels.

The Gnumeric Statistics manual specifically marks PEARSON Excel compatible [S1]; treat that as the vendor’s compatibility classification, not as proof of other applications’ handling of errors, locale separators or blank patterns. It is a registered function in Gnumeric’s catalogue distinct from CORREL. Gnumeric 1.12.62 release-tagged source documentation associates gnumeric_pearson() with the CORREL implementation; this is code evidence, not a local runtime test. Data entry uses comma separators as pictured, subject to installed locale.

Gnumeric’s official 1.12-series Statistics manual documents this formula’s name, argument order and high-level behavior. The official Gnumeric 1.12.62 release announcement establishes release context; it does not establish that any example on this page was executed. The official function catalogue records catalogue registration and upstream implementation/test classifications, not a test run for this manuscript. The official localization manual documents locale configuration. Gnumeric is distributed primarily through supported operating-system packages; see its official download guidance for platform availability.

Validation limits: Official Gnumeric 1.12.62 source was checksum-verified and inspected, and numerical examples were independently calculated. Native Gnumeric execution, screenshots, locale regression and workbook round-trip tests were not performed.

• [S1] Gnumeric Statistics manual — PEARSON, official GNOME-hosted Gnumeric reference, accessed 2026-10-13; supports name, two arguments, strings/blanks policy, Excel compatibility, listed related functions.
• [S2] Gnumeric Statistics manual — CORREL, official Gnumeric manual, accessed 2026-10-13; independently confirms function identity and purpose.
• [S3] Gnumeric Statistics manual — COVAR, official Gnumeric manual, accessed 2026-10-13; confirms covariance is a separate measure.
• [S4] Official Gnumeric 1.12.62 source archive — checksum-verified plugins/fn-stat/functions.c confirms CORREL’s population-correlation callback, PEARSON’s delegation to CORREL, and COVAR’s population-covariance callback with text/Boolean/blank collection flags. Source inspection, not native execution.