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CHISQ.INV.RT Function (LibreOffice Calc)

Statistical Intermediate LibreOffice Calc LibreOffice 4.2

The CHISQ.INV.RT function returns the inverse of the right‑tailed chi-square distribution. It is used to compute critical values for hypothesis testing, goodness‑of‑fit tests, 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.RT** function returns the **critical value** of the chi-square distribution for a given **right‑tail probability**. CHIINV has the same right-tail orientation, while CHISQ.INV uses a left-tail probability. Check the probability convention rather than treating similar names as universal replacements.

What the CHISQ.INV.RT Function Does

  • Computes the inverse of the right‑tailed chi-square distribution
  • Returns the critical chi-square value for hypothesis testing
  • The COM.MICROSOFT.CHISQ.INV.RT compatibility entry, outside the OpenFormula 1.3 function set
  • Used in model evaluation, variance tests, and confidence intervals

Syntax

CHISQ.INV.RT(probability; degrees_freedom)

Arguments

  • probability:
    Right-tail probability 0 < p ≤ 1. In the cited release p=1 returns the lower boundary 0; p=0 is invalid.

  • degrees_freedom:
    Positive integer degree count; fractional values are floored before requiring at least 1.

Both arguments are required. The official function reference, inverse evaluator and dispatcher establish the current right-tail contract.

Basic Examples

Right‑tail critical value

=CHISQ.INV.RT(0.05; 10)
→ 18.307

Using cell references

=CHISQ.INV.RT(A1; B1)

Compare with left‑tail inverse

=CHISQ.INV(0.95; 10)

Compare with legacy function

=CHIINV(0.05; 10)

Advanced Examples

Two‑tailed chi-square test

Upper tail:

=CHISQ.INV.RT(0.025; df)

Lower tail:

=CHISQ.INV.RT(0.975; df)

Equivalently, the lower cutoff is =CHISQ.INV(0.025;df). Using CHISQ.INV(0.975;df) here would repeat the upper cutoff instead. With df=9, the lower and upper cutoffs are approximately 2.700389499980 and 19.022767798642.

Validate with CHISQ.DIST.RT

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

Normal-population variance confidence interval

For independent normal observations, let s² be sample variance with denominator df=n−1. The two-sided 95% bounds are:

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

For n=20 and s²=4, the corresponding formulas are =19*4/CHISQ.INV.RT(0.025;19) and =19*4/CHISQ.INV.RT(0.975;19), approximately 2.313382559472 and 8.533078016944. Multiplying variance by a quantile does not produce these bounds. Variance bounds have squared measurement units.

Use in Monte Carlo simulations

=CHISQ.INV.RT(1-RAND(); df)

RAND() can return 0, which is invalid for this right-tail inverse. The complemented probability lies in (0,1] and uses the accepted endpoint at 1.

Edge Cases and Behavior Details

CHISQ.INV.RT returns a nonnegative real number

The result is zero at probability 1 and positive for ordinary interior probabilities.

Accepts:

  • 0 < probability ≤ 1
  • degrees_freedom ≥ 1

Behavior details

  • Right‑tail only
  • Not symmetric
  • Uses gamma‑function internally
  • CHIINV remains a separately documented right-tail name

Invalid input → Err:502

CHISQ.INV.RT 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
  • Validate df ≥ 1
  • Validate imported text separately; the numeric guards do not establish every coercion result

Unexpected critical values

Cause:

  • Confusing left‑tail vs right‑tail

Fix:

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

Best Practices

  • Use CHISQ.INV.RT for right‑tail critical values
  • Use CHISQ.INV for left‑tail
  • Validate probability inputs carefully
  • Use CHISQ.TEST for full hypothesis testing
  • Use CHISQ.DIST.RT for probability calculations
CHISQ.INV.RT is essential for computing right‑tail chi-square critical values — a cornerstone of hypothesis testing and model evaluation.
  • CHISQ.INV — left‑tail inverse
  • CHISQ.DIST.RT — right‑tail probability
  • CHISQ.DIST — left‑tail probability
  • CHISQ.TEST — full chi-square test
  • GAMMA / GAMMALN — underlying math

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

Sources and verification scope

Official CHISQ.INV.RT Help and LibreOffice 26.8.1.1 implementation. The displayed numeric cases were independently calculated; no new native-application result or all-locale/extreme-tail certification is claimed.