CHIINV Function (Gnumeric)

• Introduced: Gnumeric 0.25, explicitly listed among the new functions in its release notes.
• Availability: Supported in Gnumeric 1.12.62 according to its function-specific registration. No retirement endpoint is established.
• Scope: Desktop Gnumeric with the fn-stat module enabled. Examples use English comma-separated formulas.
• Checked: October 14, 2026. Reference and boundary tables were recalculated by Gnumeric 1.12.57 and checked independently. The 1.12.62 contract was source-checked, not executed.

The returned x satisfies CHIDIST(x,dof)=p. For two degrees of freedom, x=−2×LN(p). A smaller positive upper-tail probability gives a larger cutoff. The result is a statistic value, not a percentage. Official CHIINV reference.

=CHIINV(p,dof)

All arguments shown are required. Use numeric cells or numeric inputs. The formulas use decimal points and commas; localized entry conventions require separate checks. Gnumeric 1.12.62 help and evaluator.

Enter each formula in a separate cell. The displayed references are rounded to twelve decimal places and agree with the recorded Gnumeric 1.12.57 recalculation within ordinary floating-point precision. Keep the stored result for subsequent calculations.

Put upper-tail probability 0.05 in A2 and degrees of freedom 2 in B2. =CHIINV(A2,B2) gives approximately 5.991464547108. Check it with =CHIDIST(CHIINV(A2,B2),B2), which should recover 0.05 using the full stored cutoff.

Entering 0.95 asks for a low cutoff with 95% of the distribution above it. It does not request the familiar upper 5% critical point. Name the input cell “upper-tail probability” to make this convention visible.

Bound a variance under a normal model

For a sample of ten independent normally distributed observations with sample variance 4, degrees of freedom are 9. A central 95% interval for the population variance uses lower bound =9*4/CHIINV(0.025,9) and upper bound =9*4/CHIINV(0.975,9).

The larger chi-squared quantile appears in the denominator of the lower variance bound. Keep the two tails in the correct order. This interval depends on the normal-sample assumptions and is not a distribution-free procedure. Retaining the unrounded quantiles avoids unnecessary error in the final bounds.

At p=1 the observed cutoff is 0. At p=0 the mathematical inverse is unbounded and the tested cell returns #NUM!. Out-of-range probabilities and degrees of freedom below 1 are invalid. Gnumeric floors dof before using it. The short help contains an OpenFormula cross-reference naming LEGACY.CHIDIST for CHIINV; the function’s own evaluator and inverse round trip establish the actual inverse behavior.

The following are observed cell results from the same 1.12.57 command-line recalculation. F5 was genuinely empty. A blank is not necessarily an omitted argument or a valid observation, so validate required data instead of treating every defaulted zero as intentional.

The fixtures do not certify every locale, extreme tail, imported type or newer binary build. The current wrapper agrees with the documented argument contract; shared numerical helpers can change between releases.

• CHIDIST
• CHITEST
• CHIINV official manual entry
• Version-pinned argument contract and calculation
• Nonfinite numeric results