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FINV in Apple Numbers: Find Critical F Values

Statistical Advanced Apple Numbers

Calculate critical F statistics from right-tail probabilities in Apple Numbers with step-by-step examples and input rules.

Verification status: Official documentation referenced; example outcomes independently reasoned or arithmetically checked where stated. Not executed in Apple Numbers. How formula examples are checked

FINV returns the F statistic cutoff associated with an upper-tail probability for two specified degrees of freedom. For example, it finds the value x satisfying P(F ≥ x) = p for a Fisher–Snedecor F distribution. Use this when you know a desired one-sided upper-tail significance level and must find a critical F value to compare with an observed statistic. FINV returns a statistic, not a p-value. Apple’s 15.4 reference publishes syntax, requirements and three values; the upper-tail interpretation is independently corroborated by solving FDIST/FINV against those exact published examples. [A1, A2, M1]

Verification: Apple’s published numerical results are labelled as such. Calculated extensions were checked with independent SciPy arithmetic, not by executing Numbers.

Syntax, parameter order and defaults

=FINV(prob, d-f-numerator, d-f-denominator)
Argument (all required) Apple type Rule
prob Number probability in the right tail 0 < prob ≤ 1. This upper-tail meaning follows the official examples together with the FDIST relationship.
d-f-numerator Number degrees of freedom for F numerator Must be ≥1. Any decimal part is ignored according to Apple.
d-f-denominator Number degrees of freedom for F denominator Must be ≥1. Decimal part is ignored.

The two df parameters are distinct; do not reverse them accidentally. There is no optional parameter or documented default. Enter 0.05 for a 5% tail, not 5. prob=0 is outside Apple’s accepted domain, whereas prob=1 is within it. The mathematical limiting critical value at p=1 is 0, but this boundary has not been verified by native Numbers execution. [A1]

Numbers function names in this English guide use commas between arguments and periods for decimal fractions; localized documents can require a different separator. Look at your Formula Editor’s prompt rather than assuming a copied English formula can be pasted unchanged in every region. [A3]

Reproduce Apple’s three official examples

Create a Numbers table named FCritical, enter the cells in columns B through D, then type =FINV(B2,C2,D2) in E2 and fill E2 through E4. Use a Number format with multiple decimal places to compare the expected outputs. The formulas below are independent of how another spreadsheet might name or interpret a similarly named function.

Row A (Purpose) B (Right-tail probability) C (Numerator df) D (Denominator df) E (formula and expected result)
2 Official case 1 0.77 1 2 =FINV(B2,C2,D2) → 0.111709428782599
3 Official case 2 0.77 1 1 =FINV(B3,C3,D3) → 0.142784612191674
4 Official case 3 0.77 2 1 =FINV(B4,C4,D4) → 0.34331253162422

These three are Apple’s 15.4 published examples, and their values matched the independent inverse survival function scipy.stats.f.isf. They should be regarded as expected results, not captured screenshots or native Numbers test output. [A1, M1]

Verify the result by going back through FDIST

In F2, enter =FDIST(E2,C2,D2) and copy down. The expected result is approximately 0.77 for all three official examples; display rounding may affect the final digits. This is a useful bidirectional worksheet self-check after entering data. The check can uncover swapped df columns or a percentage mistakenly entered as a whole number. [A1, A2, M1]

Advanced use: 95% upper-tail F critical value

Suppose an independent analysis produces an F statistic of 3.60 with numerator df 3 and denominator df 12. Enter 3.60 in G2, 0.05 in H2, 3 in I2 and 12 in J2 of a table named Decisions.

=FINV(H2,I2,J2)

The independently calculated critical value is 3.4902948194976. A separate p-value can be calculated with =FDIST(G2,I2,J2) and is approximately 0.0461052340101496; since 3.60 is greater than the 3.4902948194976 cutoff, its right-tail p-value is below 0.05. The logic depends on a valid right-tail testing design. Do not infer that the model fits, the null hypothesis has a particular probability of being true, or the groups meet all assumptions simply because a critical value exists. [A1, A2, M1]

If the statistic and parameters are in different tables, use a qualified reference such as =FINV(Decisions::H2,Decisions::I2,Decisions::J2) from another table. It is safer to click each cross-table cell in the Formula Editor than to hand-type unusual table names or sheet qualifiers. A fixed-alpha cell can be preserved when filling formulas down with an absolute reference, for example =FINV($H$2,I3,J3) within the same table, where all rows intentionally use H2 as alpha. [A4]

Advanced use: compare 1%, 5% and 10% thresholds

For numerator df 4 and denominator df 20, enter tail probabilities 0.01, 0.05 and 0.10 in A2:A4; put the common degrees of freedom 4 and 20 in B2:C4. Enter =FINV(A2,B2,C2) in D2 and fill down.

Tail probability Degrees of freedom (num, den) Formula Independently calculated expected cutoff
0.01 4, 20 =FINV(0.01,4,20) 4.43069016143778
0.05 4, 20 =FINV(0.05,4,20) 2.86608140201566
0.10 4, 20 =FINV(0.10,4,20) 2.24893440177304

As the upper-tail probability gets smaller, the required critical F value increases for fixed degrees of freedom. For a consistent test, pick alpha before inspecting the result rather than choosing the threshold that yields a desired finding. [M1]

F distribution and precision notes

Mathematically FINV(p,d1,d2) is an inverse upper-tail quantile: it solves S_F(x;d1,d2)=p. This inverse is not the same as asking for the lower-tail percentile CDF_F(x)=p, which would use the complementary probability, 1-p, when defined and numerically stable. Avoid 1-p subtraction for vanishingly tiny upper-tail probabilities when its precision may be lost. For p very near 0, F critical values can be extremely large; choose appropriate display precision or scientific notation. [A1, A2, M1]

Troubleshooting in Numbers

Symptom Explanation / corrective action
Invalid probability Apple’s interval is strictly above zero and at most one (0 < p ≤ 1). A 5% probability is entered as 0.05 or a percentage-formatted 5%, never as numeric 5.
Invalid or insufficient degrees of freedom Both df arguments must be ≥1. Check sample sizes or ANOVA design; if df are calculated, audit the upstream formulas.
Decimal df look ignored Apple says FINV ignores the fractional part of either df. Do not silently assume a fractional approximation will be honoured.
Back-check fails Ensure FDIST(FINV(p,d1,d2),d1,d2) uses the same df order and the same right-tail probability.
Wrong column after filling In Numbers, relative cell references move when copied. Preserve fixed alpha and shared df cells intentionally.
Number looks much smaller than expected You may have asked for an inverse of 0.95 when the intended upper-tail alpha was 0.05. The F right-tail inverse uses alpha directly.
Strange precision or an apparent zero Increase decimal places or use scientific notation; displayed rounding is distinct from the underlying number.
Cross-table reference fails Use the Formula Editor to select the referenced cells and qualify table/sheet names rather than treating all sheets as one global coordinate grid.

Apple’s FINV documentation does not enumerate a reliable error-message mapping for every invalid input. The checks above represent published argument constraints and inference guidance, not a claim to have observed any particular error code. [A1, A4]

Apple’s Formulas and Functions Help 15.4 documents FINV and its related function FDIST. This does not establish which earlier Numbers release first included FINV; no minimum historical version is asserted here. General Apple functions help supports the Numbers interface on Mac/iPhone/iPad and associated editor contexts, but we did not run this formula natively on any platform, nor validate all device-specific versions. [A1, A5]

This guide uses the English function name FINV; localized labels may differ. For the corresponding probability calculation, see FDIST. Apple direct official FDIST reference. [A2]

Official claim ledger and validation scope (2026-10-13)