Zoho Sheet FINV: Inverse Right-Tail F and Critical Thresholds

• Introduced: The original introduction version and date are not established by the checked sources.
• Availability: Currently documented in Zoho Sheet’s rolling web-service help; no numbered release or retirement endpoint is established.
• Scope: English-language web-service documentation. Mobile and offline-client parity is outside the verified scope.
• Checked: October 14, 2026, against the official FINV reference. Documentation check; not a new native test.

FINV(p; r1; r2)

All three are required by the published Zoho syntax. There is no optional boolean cumulative argument, no documented fourth parameter, and no general default to infer. Zoho lists #NUM! for p outside 0–1 and df below 1 or above 10^10; exactly which p endpoints yield finite, infinite or error responses is not resolved by the article. Stick to 0<p<1 for reproducible finite thresholds [Z-FINV].

Right-tail, not left-tail: Decreasing p from 0.10 to 0.05 to 0.01 demands a more extreme upper-tail threshold. An F statistic has a nonnegative support; FINV’s critical values are not negative cutoffs. Do not pass 0.95 when you mean a 95th-percentile left-tail cutoff—the matching right-tail probability is 0.05 [M1].

Set A to right-tail p, B to numerator df, and C to denominator df. Enter each formula exactly as shown in the English Zoho syntax; column E records independent model expectations [M1].

For row 2, the mathematical round trip =FDIST(D2;B2;C2) should be close to the starting 0.05. Use the direct referenced D2 value rather than copying its rounded display as 2.99612. Neither native precision nor Zoho’s handling of fractional df was tested [Z-FDIST; M1].

Zoho’s own public examples state that =FINV(A2;B2;C2) can yield 0.2 for its embedded input case. The mathematical inverse of Zoho’s FDIST example is consistent with FINV(0.94233111437756;5;3) ≈ 0.2. This is an official example comparison plus independent SciPy check, not proof the public iframe was interacted with by this research run [Z-FINV; Z-FDIST; M1].

Two independent fictional equipment samples have six measurements each:

Assume each population is normally distributed for the classical variance-ratio model, samples are independently selected, and the pre-specified direction asks whether A has a larger variance than B.

Under these assumptions, the observed variance ratio 7.1515 exceeds the one-sided 5%-level F threshold 5.0503, and its mathematical upper-tail area is 0.02496. That is a one-sided result only. A two-sided claim requires separately defining both tails or consulting an appropriate test procedure. FINV calculates a numerical threshold; it does not establish normality, independence, equality of mean values or a clinically meaningful difference [M1].

For independent normal-population samples, a classical two-sided 95% interval for the ratio of underlying population variances (first divided by second) can be formed using both extreme F quantiles. Let R = VAR(A2:A7)/VAR(B2:B7) in D4, with df1=D5, df2=D6. The F quantiles are inverted in the following way:

Lower endpoint: =D4/FINV(0.025;D5;D6)
Upper endpoint: =D4/FINV(0.975;D5;D6)

Because FINV uses a right-tail probability, the upper F critical value corresponds to p=0.025, while the small lower F critical value corresponds to p=0.975. Reversing these arguments reverses the interval endpoints. For the fictional sample with both degrees of freedom 5, the independent results are:

This interval is very wide because each sample is small. It is not an interval for the difference of means, and it should not be used as a substitute for a robust analysis if normality is doubtful. The calculation follows standard F-distribution mathematics and was independently verified; no native Zoho inverse calculation is reported [M1].

More advanced interpretive cautions

A 95% central interval splits a total 5% error probability into 2.5% in each tail; it therefore uses FINV(0.025) and FINV(0.975) as above. That is different from the single 5% right-tail cutoff FINV(0.05). If you swap A and B, both the sample ratio and the degrees of freedom must swap, and the interval will describe the reciprocal underlying variance ratio. If the samples were paired, sequential, highly skewed, truncated or non-independent, the ordinary F-distribution ratio model could be inappropriate; adjusting p alone does not repair the assumptions [M1].

For ANOVA, an F statistic often compares a mean square between groups with a mean square within groups. When the analyst supplies a valid numerator and denominator df and chooses α, FINV(α;between_df;within_df) gives the theoretical upper-tail decision boundary. FINV does not conduct an ANOVA or compute its degrees of freedom [M1].

The help article lists no omitted argument defaults, a first-support release, specific plan restrictions, or precision tolerances. The procedure above uses public documented behavior and independently computed probability models, not native Zoho execution [Z-FINV].

Zoho calls the function FINV(p; r1; r2). Microsoft Excel documents legacy FINV(probability,deg_freedom1,deg_freedom2) but marks it a backward-compatibility function; modern F.INV.RT is the explicitly right-tail inverse. Excel’s F.INV without the .RT suffix is a different left-tail convention, so changing a formula’s name during migration without checking semantics is unsafe. Microsoft’s published iteration behavior and df truncation notes do not prove Zoho’s algorithm [Z-FINV; MS-FINV; MS-FINVRT].

Verified documentation platform: English public Zoho Sheet Help, accessed 2026-10-13. No logged-in cloud-account test, device parity check, mobile/offline certification, earliest-version identification, account licensing verification or locale-specific formula parsing test was performed. The examples use Zoho Help’s semicolon-separated notation; a different account/locale might display or accept punctuation differently. Record the actual environment when validating runtime behavior [Z-FINV].

Test on a clearly identified Zoho Sheet web account and locale: FINV(0.05;6;12); the inverse FDIST round trip; the 5/5 variance-ratio example; p=0 and 1; negative p, df=0, noninteger df; and an extreme-tail probability. Record the native outputs, source comparison, significant digits and any error text. No native computation is claimed.

• [Z-FINV] Zoho Sheet, “FINV,” official Statistical Help, checked 2026-10-13: right-tail inverse syntax, all arguments, documented examples/error table. https://help.zoho.com/portal/en/kb/sheet/functions/statistical/articles/finv
• [Z-FDIST] Zoho Sheet, “FDIST,” checked 2026-10-13: right-tail distribution used for inverse verification. https://help.zoho.com/portal/en/kb/sheet/functions/statistical/articles/fdist
• [MS-FINV] Microsoft Support, “FINV function,” checked 2026-10-13: legacy Excel migration caveats, not a Zoho runtime test. https://support.microsoft.com/en-us/excel/functions/finv-function
• [MS-FINVRT] Microsoft Support, “F.INV.RT function,” checked 2026-10-13: right-tail Excel successor documentation. https://support.microsoft.com/en-us/excel/functions/f-inv-rt-function
• [M1] Independent model verification, 2026-10-13: SciPy scipy.stats.f.isf, reciprocal relationships and sample variance arithmetic. No Zoho execution was performed.