CHISQ.INV.RT in Collabora Office: Find a Right-Tail Chi-Square Threshold
Use Collabora CHISQ.INV.RT to find chi-square critical values from upper-tail probabilities and verify their direction with reproducible controls.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
Quick answer: =CHISQ.INV.RT(0.05;5) has independently expected result approximately 11.070497694. Five percent of a five-degree chi-square distribution lies above that threshold.
Syntax and upper-tail convention
=CHISQ.INV.RT(Number; DegreesFreedom)
Number is the right-tail probability, often denoted alpha in a critical-value calculation. DegreesFreedom is the distribution’s degree count. Both arguments are required. Use interior probabilities and positive integer degrees of freedom in the worked examples.
The output is a threshold on the chi-square scale. It is not the probability of a hypothesis being true, and it does not calculate an observed statistic. The reference model and its degrees of freedom must be justified separately.
The RT suffix is important: decreasing the right-tail probability raises the threshold. CHISQ.INV uses the opposite, left-tail convention, so matching thresholds requires complementary probability inputs.
Example 1: reproduce the official critical values
Put 0.05 and 0.02 in A2:A3. Put degrees of freedom 5 in F2. Enter =CHISQ.INV.RT(A2;$F$2) in B2 and fill down.
Independent expected thresholds are approximately 11.070497694 and 13.388222599. The smaller upper-tail probability corresponds to a larger chi-square value, as expected.
In C2 use =CHISQ.DIST.RT(B2;$F$2) and fill down. The independent round-trip targets are 0.05 and 0.02. Keep B unrounded while checking the inverse relationship.
Example 2: use a closed-form two-degree case
For two degrees of freedom, the right-tail function is EXP(-x/2), so its inverse is =-2*LN(p). For upper-tail probabilities 0.05, 0.5 and 0.95, independent thresholds are approximately 5.991464547, 1.386294361 and 0.102586589.
Compare =CHISQ.INV.RT(A6;2) with =-2*LN(A6) using those probabilities in A6:A8. This algebraic check is specific to two degrees of freedom and should not replace the general function for other degree counts.
The p=0.5 threshold is the median. At that one probability the left-tail and right-tail inverse inputs coincide; this special case must not be mistaken for general equality of the two inverse functions.
Advanced application: translate an upper-tail request
=CHISQ.INV.RT(0.05;5) and =CHISQ.INV(0.95;5) have the same independent threshold, approximately 11.070497694.
Use a label such as “Upper-tail probability” next to the first argument. A spreadsheet copied from a source using left-tail percentiles can otherwise retain a valid-looking probability but answer the opposite question.
Advanced application: compare a statistic without overstating the conclusion
The official example uses a rounded observed statistic of 13.27 with five degrees of freedom. It lies above the 5% threshold 11.070497694 but below the 2% threshold 13.388222599.
Under an appropriate preselected upper-tail testing rule, this means the statistic crosses the 5% critical value but not the 2% critical value. It does not mean that a hypothesis is confirmed at one level or that its truth has a measured probability. Non-rejection is not proof of truth.
Keep the unrounded statistic when it is available. Near a threshold, rounding the observation and the critical value independently can change a displayed comparison. The function itself does not establish that a particular chi-square approximation or independence assumption is appropriate for the observed data.
Errors and troubleshooting
Validate probability direction, probability units and degrees of freedom. Use 0.05 or 5%, not the bare number five for a 5% tail. Ordinary interior examples avoid endpoint limits and do not certify their native error displays.
For extreme small probabilities, using a direct right-tail inverse expresses the intent without first subtracting the probability from one. Actual numerical accuracy still depends on the implementation and must be checked when critical. The dedicated section does not establish every count coercion or argument bound.
Availability and verification
The exact function is documented in Collabora Office 26.04 desktop help. Its source snapshot was retrieved on 2026-10-13 and hash-verified on October 15, 2026. Desktop documentation does not establish Online or mobile support. First introduced release and last functioning version are unknown; the dedicated source does not establish them.
No native Collabora Office run occurred. All worked values are independent mathematical expectations, not verification of native error codes or every numerical limit. Formulas use English names and semicolon separators.
The help identifies namespace COM.MICROSOFT.CHISQ.INV.RT and places the function outside the cited OpenFormula 1.3 standard. This format disclosure does not prove identical behavior in another product.