F.INV.RT in Collabora Office: Find an F Upper-Tail Critical Value
Use Collabora F.INV.RT to calculate upper-tail thresholds, distinguish them from left-tail percentiles and check reciprocal distribution identities.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
Quick answer: =F.INV.RT(0.05;5;10) has independently expected result approximately 3.325834530. Five percent of the F distribution with five numerator and ten denominator degrees lies above it.
Syntax and upper-tail probability
=F.INV.RT(Number; DegreesFreedom1; DegreesFreedom2)
Number is the right-tail probability. DegreesFreedom1 belongs to the numerator and DegreesFreedom2 to the denominator. All three arguments are required. Use interior probabilities and positive integer degree counts for the finite worked examples.
The result is a threshold on the F-ratio scale. A smaller upper-tail probability produces a larger threshold for the same degrees. This is the opposite direction from a left-tail inverse evaluated at an increasing cumulative probability.
The function does not calculate a variance ratio or decide which degrees apply. Record the statistic’s numerator and denominator definitions separately before interpreting its critical value.
Example 1: verify a simple inverse table
Put 0.05, 0.5 and 0.95 in A2:A4. In B2 enter =F.INV.RT(A2;2;2) and fill down. Independent targets are 19, 1 and approximately 0.052631579.
For the two-by-two degree case, the right-tail probability at x is 1/(1+x). Solving for x gives (1-p)/p. Enter =(1-A2)/A2 in C2 and fill down as an independent algebraic check.
Notice the order of the table: the upper-tail probability increases down the rows while the threshold decreases. A table increasing in both columns likely uses a left-tail inverse or a complemented probability.
Example 2: check the upper-tail round trip
In D2 enter =F.DIST.RT(B2;2;2) and fill down. The independent target values are 0.05, 0.5 and 0.95.
The equivalent left-tail cumulative checks are 0.95, 0.5 and 0.05 using =F.DIST(B2;2;2;1). Use explicit cumulative mode; a density is not the complementary probability.
Retain the original probability in column A and the unrounded threshold in B. A rounded report can still display a few decimals while the calculation uses the stored value.
Advanced application: reproduce the official median and a nonmedian threshold
The dedicated help gives =F.INV.RT(0.5;5;10) with independent target approximately 0.931933161. At probability one half, the left- and right-tail inverse inputs happen to coincide.
To distinguish the conventions, use the 5% right-tail example. =F.INV.RT(0.05;5;10) targets approximately 3.325834530, the same threshold as F.INV(0.95;5;10), not F.INV(0.05;5;10).
A median-only check cannot expose a left/right probability swap. Include at least one nonmedian case when validating an imported formula family.
Advanced application: audit a reciprocal ratio
For positive F ratios, taking the reciprocal exchanges numerator and denominator degrees. The right-tail quantile at p with degrees d1,d2 equals the reciprocal of the left-tail quantile at p with degrees d2,d1.
For the 5% example, compare =F.INV.RT(0.05;5;10) with =1/F.INV(0.05;10;5). Both have independent target approximately 3.325834530.
Changing only the degree order without also changing the ratio and probability interpretation would define a different threshold. Keep every step visible when comparing results from sources that use opposite variance-ratio orientations.
Errors and troubleshooting
Validate probabilities as fractions or percentage literals and keep both degree counts positive integers. Endpoint behavior, fractional-degree coercion and exact native error displays are not established by the dedicated help or these interior examples.
An upper-tail threshold is not automatically a two-sided testing rule. The statistical procedure must define its rejection regions, assumptions and significance level separately. The function does not tell you the probability that a hypothesis is true.
Direct right-tail inversion avoids an explicit 1-p step when p is tiny, which can be useful numerically, but these independent examples do not certify all native tail accuracy or convergence. Test critical extreme-probability calculations in the actual installed application.
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.F.INV.RT and places the function outside the cited OpenFormula 1.3 standard. This format disclosure does not prove identical behavior in another product.