T.INV.2T Function (LibreOffice Calc)

• Introduced: LibreOffice 4.3.
• Availability: Supported in LibreOffice 26.8.1.1, verified against its function registry. This identifies a supported release, not a final working version.
• Scope: Desktop Calc, using the English function name. Availability in other spreadsheet applications is separate.
• Checked: 2026-10-14 — function reference; versioned support. Documentation/source check; not a new native test. Existing example-specific test claims below retain their stated scope.

Historical validation scope: Native observations refer to saved LibreOffice Calc 25.2.3.2 Linux evidence from 13 October 2026 at 13:13 UTC. All 95 ODS/result pairs and manifest hashes agree. This review independently recalculated the 68 numerical assertions and the worked sample statistics. Calc was not rerun. The proposed input guards and full example layouts remain mathematical constructions, not separately native-tested worksheets.

T.INV.2T returns the positive t critical magnitude whose combined two tails of a Student’s t distribution contain the specified probability. Its most frequent uses are two-sided hypothesis tests and t-based confidence intervals for samples when a t distribution is appropriate. This is the inverse of the two-tailed probability function T.DIST.2T for nonnegative t magnitudes, not an inverse of the density function T.DIST(...;...;FALSE()).

Let α be a two-sided tail area (for example, 0.05) and ν the degrees of freedom. The function computes a nonnegative c satisfying

P(T_ν ≤ −c) + P(T_ν ≥ c) = α

For a conventional two-sided 95% t interval, alpha = 0.05. The rejection regions for an appropriate two-tailed t-test are t < -c or t > c, equivalently ABS(t)>c. A critical value is not itself a p-value, effect size, margin of error or probability of a hypothesis being true. LibreOffice Calc Help, “T.INV.2T” and “T.DIST.2T”; accessed 2026-10-13.

Native test: =T.INV.2T(0.25;10) returned 1.2212553950039222, agreeing with the official Help’s abbreviated 1.221255395 example. Official Help.

=T.INV.2T(Number; DegreesFreedom)

No optional arguments or defaults: The official signature requires both fields. The English Calc syntax uses semicolons. In localized Calc installations, separators, decimal notation and translated function names may vary; use Insert Function / the formula editor to verify them. Official LibreOffice syntax and meaning.

The Number parameter here refers to probability, not a measured t statistic. The percentile 0.05 is a two-sided tail area; each tail contains 0.025. Confusing 0.05 with a confidence level of 0.95 is one of the most consequential errors when choosing critical values. Prefer a positive integer df unless you have verified support for your specific fractional-df method; tested Calc truncated fractional values.

Every row below was actually evaluated in the Calc 25.2.3.2 Linux test workbook on 2026-10-13 and compared against an independent scipy.stats.t.isf(alpha/2, df) calculation using full numerical values.

The usual rule is: smaller alpha → larger positive critical t; larger df → typically a smaller critical value at the same conventional alpha. These are mathematical statements, not arbitrary fitted patterns.

Reproducible critical-value lookup worksheet

In a blank Calc worksheet, enter:

Expected values: B3 ≈ 2.042272456301238, B4 ≈ −2.042272456301238, B5 ≈ 1.021136228150619. The underlying =T.INV.2T(0.05;30) calculation was natively tested. The complete A1:B5 layout is a reproducible example, not a claim that the entire pasted worksheet was separately executed. Critical value and interval half-width are in different units: the latter inherits the units of the original measurements.

Suppose ten independent measurements have values 12, 14, 11, 10, 13, 9, 15, 12, 14, 10 in A2:A11. Assume the usual one-sample t confidence-interval conditions (a suitable random/independent sample and a reasonable normality assumption or justification for the small sample). In other cells, enter:

D2: =COUNT(A2:A11)
D3: =AVERAGE(A2:A11)
D4: =STDEV.S(A2:A11)
D5: =D4/SQRT(D2)
D6: =D2-1
D7: =T.INV.2T(0.05;D6)
D8: =D3-D7*D5
D9: =D3+D7*D5

Here D5: =D4/SQRT(D2) computes the sample standard error because D4 is the sample standard deviation and D2 is the sample size. The two-sided interval is mean ± t_critical × standard_error.

Expected independently calculated values for the sample: n 10, mean 12, sample SD 2, SE 0.632455532033676, df 9, critical t at alpha .05 ≈ 2.2621571627982053, and mean ± 1.43071381194... (approximately [10.5693, 13.4307]). The sample statistics and critical value have been independently checked using sample SD and SciPy; the full pasted D2:D9 example was not independently rerun inside Calc, and so is not counted in native assertions. Note this statistical interval is about the unknown population mean, not a prediction interval for the next individual observation.

Critical value and a hypothesis-test decision

For a valid t statistic in cell B6, df in B7, and two-tailed alpha in B8:

=IF(ABS(B6)>T.INV.2T(B8;B7);"Reject H0";"Do not reject H0")

Or compute the corresponding p-value with

=T.DIST.2T(ABS(B6);B7)

and compare p < alpha. Mathematical inversion means these agree aside from rounding and handling of equality at the boundary. The two-tail inverse formula does not check whether your sampling assumptions or t-statistic computation are valid.

A round-trip verification you can try

Use the identity:

=T.DIST.2T(T.INV.2T(0.05;30);30)

Expected approximately 0.05. Six closely related native round-trip checks, written as =T.DIST.2T(T.INV.2T(alpha;df);df)-alpha, returned 0 for selected alpha/df pairs in the Calc 25.2.3.2 test run. This identity applies for supported valid inputs; tiny values and extreme tails may exhibit floating-point limits. Unlike copying a result between programs, this cross-check recalculated both named Calc functions in the same native workbook.

The T.INV function in LibreOffice’s English Help is a left-tail inverse, with its input specifying the left cumulative probability. It can return negative values, such as =T.INV(0.1;6) ≈ −1.4397557473 according to official Help. T.INV.2T instead accepts combined two-tail probability and returns a nonnegative critical magnitude for symmetric cutoffs. Both official function descriptions.

It is wrong to replace T.INV.2T(0.05;df) with T.INV(0.05;df). In a left-tail convention the corresponding positive two-sided critical point is the 97.5th percentile for a 95% interval. Use T.INV(1-alpha/2;df) only when you have verified T.INV’s left-tail argument behavior for your version and data. The direct T.INV.2T call is clearer and less error-prone.

Version-dependent df warning (native observation): Calc 25.2.3.2 computed =T.INV.2T(0.25;2.5) as 1.603567451474546, the same as =T.INV.2T(0.25;2) in the tested case. Fractional df were truncated rather than treated as exactly 2.5. A Welch–Satterthwaite degrees-of-freedom approximation can be fractional; if you need such tests, do not assume the native Calc function uses the mathematical real-valued df. Verify explicitly or use a tool/approach that supports noninteger df. This claim is specific to tested Calc 25.2.3.2 Linux; the official Help does not warrant generalization to every release.

Very small alpha: =T.INV.2T(1E-50;10) returned approximately 274859.0609393741 in a diagnostic native observation, illustrating that a very small probability can produce a very large finite cutoff. Large cutoffs are not a licence to ignore numerical limitations, misuse degrees of freedom, or equate statistical significance with importance.

Defensive entry check: For conventional integer df in B2 and two-tail area in B1:

=IF(NOT(ISNUMBER(B1));NA();IF(NOT(ISNUMBER(B2));NA();IF(OR(B1<=0;B1>1;B2<1;B2<>INT(B2));NA();T.INV.2T(B1;B2))))

This formula is a recommended guard, not separately natively tested in the saved tests. It intentionally disallows fractional df to avoid silent truncation. If your statistical procedure fundamentally needs a fractional df, do not round it casually: change the calculation method after proper verification instead.

This table is observed behavior in one named version and environment, not a universal cross-version error guarantee. #VALUE!, Err:502, and Err:511 are not interchangeable with Excel errors. Format result cells as numbers, not percentages: a t critical value of 2.04 is not a probability of 204%.

• Actual runtime verification: LibreOffice Calc 25.2.3.2 Linux, native UNO-driven formulas and spreadsheet cells, 13 October 2026. 28 independent numerical assertions and six cross-function round-trip assertions matched; 14 diagnostic observations were logged separately. SciPy 1.17’s Student t inverse survival function (t.isf(alpha/2,df)) provided independent mathematical checks, not evidence of other spreadsheet execution.
• Official scope: Current English LibreOffice Help, labeled 26.8 Help on access 2026-10-13, states the function exists since LibreOffice 4.3. This run did not execute Calc 4.3, 26.8, Windows, macOS or other office suites. Official Help technical section.
• Name/portability: The official Help states T.INV.2T is not in OpenDocument 1.3 OpenFormula and gives namespace COM.MICROSOFT.T.INV.2T. This is an application-compatibility extension; a workbook containing the formula is not automatically guaranteed to work in any other ODF engine or Excel/Google Sheets version. For standards background see OASIS OpenDocument 1.4 Part 4; no unsupported claim of universally identical implementations is made.
• Legacy relationship: LibreOffice Help lists older TINV(Number;DegreesFreedom) as a two-tailed inverse. This is a related legacy name, rather than a guarantee of identical behavior in every version. Verify the intended argument rules and desired document portability if migrating an old sheet. Official Help: TINV.
• Locale: The examples use English-language names, semicolon separators and decimal periods. If your language locale uses decimal commas or translated function names, apply the Calc locale’s own parsing rules before assuming a formula is invalid.

• T.DIST.2T — two-sided tail probability
• T.DIST.RT — one upper tail
• T.DIST — left-tail CDF or density
• T.INV — left-tail inverse
• TINV — older two-tailed inverse syntax

See LibreOffice statistical function documentation for syntax, examples, version availability and compatibility details.