COVARIANCE.P in Collabora Office: Population Covariance and Hidden Group Differences

• Introduced: original Collabora release and launch date are not established by the reviewed sources.
• Availability: currently documented in Collabora Office 26.04 desktop help.
• Platform scope: online and mobile deployments are not inferred from this desktop-help release.
• Checked: October 14, 2026. Function-specific documentation and independent calculations; no native Collabora execution.

=COVARIANCE.P(data1;data2)

Both datasets are required. Each pair must describe the same record. The dedicated Collabora section explicitly names the whole-population interpretation, distinguishing it from COVARIANCE.S.

The worked examples contain equally sized, complete numeric columns. Their population model divides the centered cross-product total by n, the number of pairs. Mixed-type exclusion, mismatched missing positions and native invalid-input errors are not specified by this compact source and remain unverified.

Enter A1:B5:

=COVARIANCE.P(A2:A5;B2:B5)

Expected result: 8. Both means are 5. X deviations are -4,-2,2,4; Y deviations are -2,-4,4,2. Every paired product is 8, giving a total of 32. The population denominator is four.

A positive covariance summarizes same-direction centered variation across the complete population. It does not mean every adjacent change in Y follows the adjacent change in X.

Multiply each Y by ten, producing 30,10,90,70. Expected population covariance becomes 80. Adding 100 to each original Y instead gives 103,101,109,107, with covariance still 8.

Negating original Y gives -8. Multiplying X by two and Y by three gives 48, six times the original covariance. The covariance unit is the product of the X and Y measurement units.

A bigger absolute covariance after unit conversion does not establish a stronger relationship. PEARSON supplies a separately defined dimensionless coefficient; its independent value for the original pairs is 0.8.

Treat the first two pairs as one group and the last two as another:

=COVARIANCE.P(A2:A3;B2:B3)
=COVARIANCE.P(A4:A5;B4:B5)

Both independently expected results are -1. Each group contains an inverse two-point pattern around its own center. The first group’s two means are 2; the second group’s are 8.

The combined population covariance is nevertheless 8, because the separation between group centers contributes positive paired variation. Simply averaging the two -1 subgroup results would lose that information.

Preserve group membership when interpreting a pooled measure. Its sign alone cannot summarize every within-group relationship.

Duplicate all four complete pairs. The centered-product total doubles from 32 to 64, while the population count doubles from four to eight. Expected COVARIANCE.P stays 8.

For the original four pairs, the sample model instead divides 32 by three and gives 32/3, approximately 10.666667. COVARIANCE.S has that separately documented sample purpose.

The appropriate interpretation follows how the data relate to the reporting population. It should not be chosen merely because one denominator gives a preferred number.

Keep the original Y values but set every X to 5. Every centered X deviation is zero, so the independent covariance model gives 0. This is a numeric arithmetic control; it does not certify a separate native constant-data error matrix for related correlation functions.

Covariance can be zero when a constant series makes correlation mathematically undefined. Different statistical measures have different denominators.

The help identifies COM.MICROSOFT.COVARIANCE.P outside the cited OpenFormula 1.3 standard. This is a format detail, not universal export/import evidence or an introduction date.

The compact section leaves empty data, singletons, Boolean/text conversion, source errors and unaligned ranges unresolved. Preserve complete record pairing and verify those boundaries in the intended Collabora build before automating a real incomplete dataset.

• Collabora Office 26.04: COVARIANCE.P.
• Editorial testing standards.

Complete function-specific documentation reviewed. Worked outputs are independent statistical models or explicitly documented rules, not application screenshots or native test results. Unverified type, error and numerical boundaries retain their stated scope.