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FDIST in Apple Numbers: F-Test Right-Tail Probabilities

Statistical Advanced Apple Numbers

Learn Apple Numbers FDIST syntax, degrees of freedom, right-tail F probabilities, reproducible examples and common mistakes.

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

FDIST calculates an upper-tail probability for a nonnegative F statistic. The result is the probability that a variable following an F distribution, with your two degrees-of-freedom parameters, would be at least as large as the statistic supplied: P(F ≥ x). That probability can be useful when reporting classical upper-tail F tests or checking a critical value. It is not the cumulative probability to the left of x, and it does not determine whether any test assumptions hold. Apple documents the three required number arguments and the degree-of-freedom restrictions in its 15.4 function reference. [A1]

Verification: Examples marked official below are published by Apple. Additional examples are independently calculated with SciPy’s F-distribution survival function; they are expected Numbers results, not results from executing Numbers.

Syntax and argument order

=FDIST(x-value, d-f-numerator, d-f-denominator)
Required argument Type and meaning Allowed inputs / behaviour
x-value Number; the observed F statistic x ≥ 0. A negative input is outside Apple’s documented domain.
d-f-numerator Number of numerator degrees of freedom At least 1. Apple says any fractional part is ignored (for example, 3.8 is treated as 3).
d-f-denominator Number of denominator degrees of freedom At least 1, with the fractional part ignored.

All three arguments are mandatory; Apple specifies no optional arguments or defaults. The ordering numerator first, denominator second matters: interchanging them changes the distribution and generally the answer. Apple calls the distribution F, Snedecor’s F, or Fisher–Snedecor. [A1]

In English-language function examples, commas separate arguments. Your document’s language and number format can change the argument separator (for example, to semicolons when a comma is the decimal separator). Do not replace decimal punctuation blindly; follow the Formula Editor’s syntax. [A3]

Build the example in Numbers

  1. Create a Numbers table named FTests. Keep the table header row, and enter these literal values; rows are not a CSV import and formulas need to be typed into their cells.
  2. In E2, enter =FDIST(B2,C2,D2) and copy E2 down through E4. The cell references are within the same table, so a plain B2 reference is sufficient. [A4]
  3. Select column E and format it as Number with enough decimal places, or as Percentage if you prefer the probability multiplied by 100.
FTests cell A (Scenario) B (F statistic) C (Numerator df) D (Denominator df) E (Right-tail p, formula/result)
Row 2 Case A 0.77 1 2 =FDIST(B2,C2,D2) → 0.472763488223567
Row 3 Case B 0.77 1 1 =FDIST(B3,C3,D3) → 0.541479597634413
Row 4 Case C 0.77 2 1 =FDIST(B4,C4,D4) → 0.627455805138159

The three values in E2:E4 reproduce Apple’s published examples, independently recalculated. They are deliberately different even though the F statistic is the same: changing the degrees of freedom changes the tail probability. [A1, M1]

A first interpretation

At x = 0.77 with numerator df 1 and denominator df 2, the calculated upper-tail probability is about 47.28%. This is not a 47.28% probability that your null hypothesis is true. It describes a reference distribution under the null model and its assumptions. The F statistic itself is normally produced by a separate analysis; FDIST merely converts a given statistic and df into the corresponding upper-tail area.

Advanced use: choose a 5% F-test threshold

Suppose a test has numerator df 3 and denominator df 12. A conventional right-tail significance threshold of 0.05 corresponds to a critical F value. With 0.05 entered in a cell D2 of a separate table Thresholds, 3 in E2 and 12 in F2, enter:

=FINV(D2,E2,F2)

The independently calculated critical value is approximately 3.4902948194976. You can check it with:

=FDIST(FINV(D2,E2,F2),E2,F2)

Expected result: approximately 0.05, subject to display rounding. To compare an observed F statistic stored in B2 of that table, use =FDIST(B2,E2,F2) and ask whether the resulting right-tail p-value falls below your preselected alpha, assuming this is an appropriate right-tail F test. Comparing statistics with =B2>FINV(D2,E2,F2) is mathematically equivalent for continuous F distributions away from numerical rounding. [A1, A2, M1]

Do not substitute =1-FDIST(...) for the upper-tail p-value. 1-FDIST gives a lower-tail cumulative probability when the model and inputs are valid. A two-sided variance-ratio procedure requires an explicitly defined two-sided method and care with reciprocal F values; do not treat FDIST alone as a generic two-tailed p-value calculator.

Advanced use: copy a calculation across tables

If the original data and result are in different Numbers tables, use a qualified reference. For example, from a separate table named Summary, =FDIST(FTests::B2,FTests::C2,FTests::D2) refers to cells in FTests (adjust or insert table names via the Formula Editor if the actual table name differs). Quoting special table names and referencing other sheets may require a sheet qualifier; choose the reference by clicking the intended cell to let Numbers build its syntax. [A4]

For a varying statistic but fixed df stored in FTests::C2 and FTests::D2, lock the parameter cells while filling down. Insert dollar signs using the Formula Editor’s reference-preservation controls: the intended structure is =FDIST(B2,$C$2,$D$2) within FTests. Verify that each copied formula still refers to its intended df cells. [A4]

Mathematical note and independent checks

For F distributed with d1 and d2 degrees of freedom, FDIST corresponds to S_F(x) = 1-CDF_F(x), also called the survival function. That relationship was inferred by matching Apple’s published examples to an independently calculated F survival function; Apple’s reference gives syntax/examples rather than naming the upper tail explicitly. It is essential to state this distinction rather than infer Numbers behaviour from some other spreadsheet. [A1, M1]

Test Numbers formula Expected output How verified
Apple’s example =FDIST(0.77,1,2) 0.472763488223567 Apple + SciPy
Apple’s example =FDIST(0.77,1,1) 0.541479597634413 Apple + SciPy
Apple’s example =FDIST(0.77,2,1) 0.627455805138159 Apple + SciPy
Zero boundary =FDIST(0,3,12) 1 Mathematical distribution check; not native-tested
Larger statistic =FDIST(2,3,12) 0.167831556445817 Independent SciPy calculation
Fractional df =FDIST(2,3.9,12.4) Mathematically equals FDIST(2,3,12) Apple documents fractional-part truncation; not native-tested

Troubleshooting and interpretation limits

Symptom Check and remedy
Formula cannot be evaluated Check for a missing third argument, a pasted text value, an invalid separator, or a reference to the wrong table. Use actual number cells rather than text such as "0.77" until the formula works.
Negative statistic Apple’s x-value must be ≥0. Confirm the upstream F statistic formula rather than taking its absolute value to conceal an error.
Zero or negative degrees of freedom Apple requires each df ≥1. Check sample sizes, data groups, and the formula used to calculate df.
Fractional degrees of freedom FDIST’s reference explicitly ignores fractional parts of both df arguments. Decide whether truncation is appropriate for your analysis before applying this function.
Unexpected results after copying Recheck numerator versus denominator order, anchored references and qualified table names.
Probability looks like 47.28 instead of 0.4728 Check whether the cell is formatted as a percentage or number; a probability of 0.4728 displays as 47.28% in Percentage format.
Right-tail versus left-tail confusion FDIST is the upper tail: a large F leads to a smaller p-value for fixed df. Its complement is a lower-tail probability, not the same answer.
Model assumptions violated F-based inferences may require independence, appropriate variance assumptions, normal errors or a valid analysis design. FDIST does not validate those assumptions.
Extremely small tail probabilities Display formats can show 0 after rounding although the mathematical value is nonzero. Expand precision or use scientific notation before claiming a zero p-value.

An error-cell label is implementation- and input-specific; the official FDIST reference does not enumerate specific Numbers error strings for every invalid argument. The conditions above are documented constraints and diagnostic advice, not a claim of observed errors. [A1, A3]

  • Documented context: Apple Formulas and Functions Help 15.4, retrieved 2026-10-13. This confirms Apple’s current reference and syntax, not the release where FDIST was introduced or historical availability in every macOS, iOS, iPadOS or iCloud Numbers build. Apple’s general help applies to its spreadsheet/function editors, but device support for FDIST has not been independently exercised. [A1, A5]
  • Locale: Formula punctuation and decimal conventions follow document language/region settings. The English identifier FDIST is used here; translated labels may differ. [A3]
  • Related: FINV computes an F critical value for a right-tail probability. Apple also provides direct FINV reference.

Source and validation ledger (checked 2026-10-13)