Contact
12 programs
Explore the site

CHIDIST in Apple Numbers: right-tail chi-square probabilities

Statistical Intermediate Apple Numbers

Compute one-tailed chi-square probabilities in Apple Numbers, with numeric thresholds, examples and common tail-direction mistakes.

Verification status: See the evidence and test scope described in this guide. How formula examples are checked

Quick answer. =CHIDIST(5,2) has the independently computed value 0.0820849986238988. It is the probability of a chi-square random variable with 2 degrees of freedom being at least 5, not the left-tail cumulative probability. Apple’s English documentation defines CHIDIST(x-value, degrees-freedom) and describes a one-tailed result. [A1, C1]

Availability and version history

  • Introduced: Documented in Apple’s Formulas and Functions Help 15.4; the original introduction release is not established.
  • Availability: Currently documented for Numbers in that help version; it is not a final supported-version endpoint.
  • Scope: Shared iWork function help. Availability in individual clients and older releases is not established by this check.
  • Checked: October 14, 2026, against the official CHIDIST reference. Documentation check; not a new native test.

What CHIDIST measures

For a test statistic X following a chi-square distribution with ν degrees of freedom, this function returns the upper-tail survival probability P(X ≥ x). A smaller result means an x this large or larger is unusual under that reference distribution. A distribution calculation is not, by itself, proof that a model’s assumptions or the degrees-of-freedom selection are correct. Chi-square distributions are continuous: an equality at a precise x has zero probability, so P(X≥x) and P(X>x) have equal mathematical values. [A1, C1]

Use CHIDIST when you already have a nonnegative statistic, have identified appropriate degrees of freedom, and want the right-tail area; common contexts include right-tailed goodness-of-fit and contingency-table statistics. It does not calculate the chi-square test statistic from a raw table; Apple’s separate CHITEST reference serves a different purpose. [A1, A6]

Exact syntax and argument types

=CHIDIST(x-value, degrees-freedom)
Position Official argument Type Required Documented restriction Default
1 x-value Number value Yes x-value ≥ 0 None
2 degrees-freedom Number value Yes degrees-freedom ≥ 1 None

Apple provides no optional arguments. Enter the statistic first and the degrees of freedom second: reversing them changes the distribution, potentially without making the formula visibly invalid. The Apple reference calls both inputs numeric; it does not document a universal rounding/coercion rule for noninteger degrees of freedom. Use a legitimate, typically integer df from your statistical method rather than claiming Numbers rounds it in a specified way. [A1, A2]

Build a reproducible Numbers worksheet

Create one Numbers table named ChiSquareTail. Use column B for Statistic x, column C for Degrees df, and column D for Right-tail probability. Put these headers in row 1. Enter B2:C7 according to the table; put =CHIDIST(B2,C2) in D2, then fill D2 down to D7. Cell references are relative within the same Numbers table, not Excel sheet-name notation. Format D2:D7 as Number (for example, 8–12 decimals) rather than percentage if you want to see the small tail values clearly. [A2, A3]

Row B: statistic x C: df Formula in D Expected upper-tail result
2 0 2 =CHIDIST(B2,C2) 1
3 1 2 =CHIDIST(B3,C3) 0.606530659712633
4 5 2 =CHIDIST(B4,C4) 0.0820849986238988
5 10 10 =CHIDIST(B5,C5) 0.440493285065212
6 5 1 =CHIDIST(B6,C6) 0.0253473186774683
7 4 4 =CHIDIST(B7,C7) 0.406005849709838

Rows 4–6 reproduce the input values and reported outputs in Apple’s published examples; other rows are independent mathematical predictions. Do not imply this table was actually entered into the Numbers application. [A1, C1]

Advanced patterns worth understanding

1. Interpret a right-tail p-value without reversing it

=CHIDIST(6,2) mathematically gives 0.0497870683678639, just under 0.05. For a valid chi-square right-tailed test with ν=2 this meets the conventional 5% rejection threshold. It does not establish that every chi-square procedure is right-tailed, nor replace checks of expected counts or independence. The left-tail mathematical probability at the same x is 1-CHIDIST(6,2), approximately 0.950212931632136; this subtraction is a calculation from probability theory, not a separately documented Numbers function mode. [A1, C1]

2. Compute a varying-df quality-control column

If a results table has x statistics in B2:B101 and degrees of freedom in C2:C101, fill =CHIDIST(B2,C2) down column D. Each row uses its own ν; do not accidentally freeze the df to a first row unless every test truly shares a df. For a constant df stored in C2, Numbers’ absolute-reference form =CHIDIST(B2,$C$2) can keep that cell fixed when copied. [A1, A3]

3. Compare a statistic to a critical value

=CHIINV(0.05,2) has independently calculated critical value 5.99146454710798. For a χ² right-tailed test with 2 df, x=6 exceeds that cutoff and has CHIDIST result 0.049787…. This is the same decision expressed as statistic-versus-threshold and tail-probability-versus-alpha; CHIINV is an upper-tail inverse, not a left-tail percentile. [A1, A6, C1]

4. Numerically cross-check the inverse

=CHIDIST(CHIINV(0.1,10),10)

The independent mathematical expectation is 0.1 (subject to finite floating-point precision). If a rounded display shows 0.100000, that is usually formatting rather than an error. This check tests the mathematical relationship; it is not a native Numbers formula-execution result. [A1, A6, C1]

Troubleshooting and limitations

Symptom or formula Why it is problematic Corrective step
=CHIDIST(-1,2) x violates Apple’s nonnegative documented domain. Supply a genuine x≥0 statistic; don’t take ABS merely to force validity.
=CHIDIST(5,0) df violates the documented minimum 1. Recalculate the proper degrees of freedom.
=CHIDIST(5) The second required argument is missing. Add df, e.g. =CHIDIST(5,2).
=CHIDIST(2,5) when x=5, df=2 Arguments were reversed. Put x first, df second.
Expecting ~0.918 for =CHIDIST(5,2) Mistakes the right-tail for the left-tail probability. The right-tail is ~0.082085; left-tail is 1−that.
Entering '5' as text The function is documented for numeric values, not unspecified text conversion. Store the cell as a Number and remove text-only characters.
Copying a formula to a second table Spreadsheet references may require explicit table names. Use Numbers table references and confirm referenced table headers.

Apple does not prescribe a specific error-message token for every invalid case in this function article; we therefore do not promise #NUM! or other Excel-style errors. Nor is cross-platform rounding/precision guaranteed in the article. [A1, A3]

Accuracy, compatibility, locale, and edition

The English 15.4 help entry documents CHIDIST and its argument order. It does not certify that this identifier existed in every historical Mac/iPhone/iPad release, nor certify parity after exporting a spreadsheet to other apps. Apple documents that =CHIDIST(...) can be typed in either letter case. Where the comma is the decimal separator, use semicolons between arguments—for example =CHIDIST(5;2). Decimal point and comma display depend on the document locale. [A1, A2, A4, A5]

For Numbers’ cross-table references, the documented syntax uses the table’s actual name, for example =CHIDIST(ChiSquareTail::B4,ChiSquareTail::C4) from another table; cross-sheet references may include a sheet-qualified name. Prefer clicking cells in the formula editor rather than guessing a renamed table’s syntax. [A3]

Frequently asked questions

Is a CHIDIST result the chance the null hypothesis is true? No. It is a tail probability under a specified reference distribution and modeling assumptions, not a probability assigned to the truth of a hypothesis.

Can CHIDIST replace CHITEST? Not without first computing an appropriate chi-square statistic and df. They are separately documented functions with different inputs.

Is CHIDIST(0,2) invalid? No; Apple allows x≥0, and the chi-square upper-tail survival at x=0 is mathematically 1.

Official references and validation record

Native-validation limitations: Formulas were not executed in Numbers on Mac, iPhone, iPad, or iCloud. Screenshots, localized behavior and historical edition support have not been verified.