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CHISQ.INV Function (LibreOffice Calc)

Statistical Intermediate LibreOffice Calc LibreOffice 4.2

The CHISQ.INV function returns the inverse of the left‑tailed chi-square distribution. It is used to compute critical values for hypothesis testing, confidence intervals, and statistical modeling.

Verification status: Consult the documentation, examples and any stated test scope below. How formula examples are checked

Availability and version history

  • Introduced: LibreOffice 4.2.
  • Availability: Supported in LibreOffice 26.8.1.1, verified against its function registry. This identifies a supported release, not a final working version.
  • Scope: Desktop Calc, using the English function name. Availability in other spreadsheet applications is separate.
  • Checked: 2026-10-14 — function reference; versioned support. Documentation/source check; not a new native test. Existing example-specific test claims below retain their stated scope.
The **CHISQ.INV** function returns a chi-square cutoff for a given **left-tail probability**. CHIINV uses a right-tail probability, so its argument must be complemented before comparing the two. Neither name is a direct drop-in replacement with an unchanged probability.

What the CHISQ.INV Function Does

  • Computes the inverse of the left‑tailed chi-square distribution
  • Returns the critical chi-square value for a given probability
  • Used in hypothesis testing and model evaluation
  • The COM.MICROSOFT.CHISQ.INV compatibility entry documented by Calc

Syntax

CHISQ.INV(probability; degrees_freedom)

Arguments

  • probability:
    Left-tail probability 0 ≤ p < 1 in LibreOffice 26.8.1.1. Zero returns the lower boundary 0; 1 is invalid.

  • degrees_freedom:
    Positive integer degrees of freedom. Fractional inputs are floored before the implementation checks that the result is at least 1.

The documented function dispatches to the same left-tail inverse evaluator as CHISQINV. This establishes the stated boundary behavior; no new native run is claimed.

Basic Examples

Left‑tail critical value

=CHISQ.INV(0.95; 10)
→ 18.307

Using cell references

=CHISQ.INV(A1; B1)

Compare with right‑tail inverse

=CHISQ.INV.RT(0.05; 10)

Compare with legacy function

=CHIINV(1 - p; df)

Advanced Examples

Two‑tailed chi-square test

Upper tail:

=CHISQ.INV.RT(0.025; df)

Lower tail:

=CHISQ.INV(0.025; df)

Validate with CHISQ.DIST

=CHISQ.DIST(CHISQ.INV(p; df); df; TRUE)
→ returns p

Confidence interval for a normal population variance

For independent observations from a normal population, let s² be the sample variance calculated with denominator n−1, and let df=n−1. The two-sided 95% bounds for the population variance are:

Lower = df * s_squared / CHISQ.INV(0.975; df)
Upper = df * s_squared / CHISQ.INV(0.025; df)

The larger chi-square quantile is in the lower-bound denominator. Multiplying the sample variance by a quantile does not give these confidence bounds. With n=20 and s²=4:

=19*4/CHISQ.INV(0.975;19)
→ approximately 2.313382559472

=19*4/CHISQ.INV(0.025;19)
→ approximately 8.533078016944

These bounds have squared measurement units. Take their square roots only when an interval for the population standard deviation is required.

Use in Monte Carlo simulations

=CHISQ.INV(RAND(); df)

Edge Cases and Behavior Details

CHISQ.INV returns a nonnegative real number

The result is 0 at probability 0 and positive for ordinary interior probabilities.

Accepts:

  • 0 ≤ probability < 1
  • degrees_freedom ≥ 1

Behavior details

  • Left‑tail only
  • Not symmetric
  • Uses gamma‑function internally
  • CHIINV uses the complementary right-tail probability

Invalid input → Err:502

CHISQ.INV of an error → error propagates

Common Errors and Fixes

Err:502 — Invalid argument

Cause:

  • probability < 0 or ≥ 1
  • degrees_freedom < 1

Fix:

  • Ensure 0 ≤ p < 1; a displayed 100% may hide a stored interior probability
  • Validate df ≥ 1
  • Use explicit numeric probabilities and degree counts

Unexpected critical values

Cause:

  • Confusing left‑tail vs right‑tail

Fix:

  • Use CHISQ.INV for left‑tail
  • Use CHISQ.INV.RT for right‑tail

Best Practices

  • Use CHISQ.INV for left‑tail critical values
  • Use CHISQ.INV.RT for right‑tail
  • Validate probability inputs carefully
  • Use CHISQ.TEST for full hypothesis testing
  • Use CHISQ.DIST for probability calculations
Use CHISQ.INV for left-tail cutoffs and keep statistical assumptions separate from the formula. The Help identifies this dotted name as an extension outside the OpenFormula 1.3 function set; it does not establish retirement of CHIINV or CHISQINV.
  • CHISQ.INV.RT — right‑tail inverse
  • CHISQ.DIST — left‑tail probability
  • CHISQ.DIST.RT — right‑tail probability
  • CHISQ.TEST — full chi-square test
  • GAMMA / GAMMALN — underlying math

By mastering CHISQ.INV, you can compute accurate chi-square critical values for any statistical model or hypothesis test in LibreOffice Calc.

Sources and scope of these examples

Official CHISQ.INV Help and LibreOffice 26.8.1.1 evaluator. Numeric examples were independently calculated. They are not new native-application test results and do not certify every locale or extreme input.