T.DIST.RT Function (LibreOffice Calc)

=T.DIST.RT(1;10)

Native Calc result: 0.17044656615103 (approximately 17.0446566%). The complementary CDF is =T.DIST(1;10;TRUE()) → 0.82955343384897; their probabilities add to one. LibreOffice’s official example rounds the right tail to 0.1704465662. LibreOffice Help: Statistical Functions Part Five.

=T.DIST.RT(Number;DegreesFreedom)

Exactly two arguments are required; there is no third Cumulative or Tails argument, and no omitted-argument default. The English Calc/OpenFormula examples use the semicolon separator; localized Calc settings may differ.

The source definitions and notation come from LibreOffice’s T.DIST.RT entry. The OpenFormula/Calc formula separator is described in OASIS OpenDocument 1.4 §5.6.

What is meant by a right tail?

For Student’s t random variable T with ν degrees of freedom, T.DIST.RT(t;ν) returns P(T>t) = 1−F(t) mathematically, where F is the cumulative distribution function. Because the t distribution is continuous, choosing > versus ≥ does not change the probability. The t curve is symmetric about zero:

• at t = 0, the right-tail probability is 0.5;
• at a positive t, the right-tail probability is less than 0.5;
• at a negative t, the right-tail probability is greater than 0.5;
• at t = 1, df 10, right tail ≈ 0.1704465662;
• at t = −1, df 10, right tail ≈ 0.8295534338.

These direct t/df outputs were confirmed in the native Calc test workbook, not merely inferred from a different application’s distribution function.

Place the observed statistic and degrees of freedom into cells:

The corresponding direct-input formulas for C2 and D2 were both executed and passed native numerical assertions. The proposed cell-reference layout is reproducible, but it was not separately executed as a full sheet in the saved native test matrix. Format C2 as a percent to display about 17.04%; percentage formatting does not change the stored numeric probability.

Assume a random sample of n=25 independent measurements with sample mean 16 and sample standard deviation 2, compared to hypothesized population mean 15. Under the relevant t-test model and its assumptions, the test statistic is (16−15) / (2/√25) = 2.5, with ν = 24 degrees of freedom.

At conventional 0.05 as an illustration, the p-value is below that threshold; whether the result is meaningful depends on assumptions, study design, and the pre-specified hypothesis. B8’s stated numerical expectation is an independent SciPy calculation for (2.5,24); native Calc testing covered 32 other right-tail formulas, but this assembled sample sheet was not natively executed. A right-tail test is appropriate for a directional alternative of greater than, not an automatically chosen smaller p-value after seeing the data.

Left-sided and two-sided alternatives

For t in A2 and degrees of freedom in B2:

If A2=-1 and B2=10, T.DIST.RT(A2;B2) is about 0.8295534338, while the left tail is about 0.1704465662. Taking ABS() unconditionally before a directional right-tailed test would produce the wrong question. ABS belongs in the symmetric two-tail formula when the test statistic’s sign should not select the direction.

For a very extreme positive t statistic, the upper tail may be tiny. The direct right-tail formula retains precision without subtracting from a rounded-to-one CDF:

=T.DIST.RT(100;30)

Native Calc result: 9.92305898363502E-40, compared with independent SciPy expected 9.923058983635155E-40. Both appear in the archived diagnostic evidence. In contrast, 1-T.DIST(100;30;TRUE()) is mathematically the same probability but may evaluate to zero due to floating-point cancellation when the CDF rounds to one. The latter calculation was not separately native-executed as a formula in the saved tests, so it is presented as a numerical-analysis warning rather than an observed result for that exact expression.

This distinction also matters when calculating one-sided hypothesis-test p-values and upper-tail thresholds. The following additional native Calc results were recorded:

These are native execution observations from LibreOffice Calc 25.2.3.2 on Linux, not Excel results.

To see how df changes a right-tail probability, place a fixed t statistic, such as 2, in B1. Type positive integers 3, 5, 10, 20, 30, 100 down A2:A7. In B2 enter:

=T.DIST.RT($B$1;A2)

Fill B2 through B7. Graph the degrees-of-freedom column against the tail-probability column with a scatter plot; do not use a line connecting the points to imply degrees can be interpreted as any real input in this Calc version. The layout is a reproducible proposal, while the native verification spreadsheet separately tested numerous individual df/t combinations. If the statistic itself should depend on the sample size, recompute that statistic for each row; keeping it fixed answers a distribution-sensitivity question only.

A statistically meaningful p-value begins with an appropriate model and test statistic, not a built-in function alone. The one-sample t statistic is t=(sample_mean−null_mean)/(sample_s/sqrt(n)), with df=n-1 for the standard one-sample t-test under its assumptions. Paired tests instead use the differences; Welch’s two-sample test can have noninteger effective degrees of freedom, and this is precisely where a version-specific rounding issue becomes important.

Caution for Welch tests: the mathematical Welch–Satterthwaite df may be fractional. In Calc 25.2.3.2, native T.DIST.RT inputs with fractional df returned results matching the integer truncation rather than independent continuous-df SciPy. Do not report the returned p-value as though it used exact fractional df. Document any deliberate df approximation and independently check the implications, or use a verified statistical tool that supports real-valued df accurately. This is a material warning for scientific reproducibility, not just cosmetic rounding.

The inverse critical-value counterpart is T.INV.2T for a two-sided critical value, or T.INV for lower-cumulative inversion.

Native fractional-degrees limitation

The observed Calc outputs match the distribution evaluated with df=2 and df=5, respectively. That is not a validated assumption for all Calc versions or a claim of conformity with the continuous real-df mathematical model. It is a directly recorded behavioral difference in the native test workbook. The current T.DIST.RT Help entry does not explicitly describe fractional-df truncation, whereas the legacy TDIST entry includes a note for integer arguments. See LibreOffice Help, T.DIST.RT and TDIST.

A worksheet that requires positive integer degrees of freedom can reject ambiguous inputs before running the function:

=IF(NOT(ISNUMBER(A2));NA();IF(NOT(ISNUMBER(B2));NA();IF(AND(B2>0;B2=INT(B2));T.DIST.RT(A2;B2);NA())))

This guard formula is a proposed reproducible workflow, not an individually native-executed test case. For scientific work that naturally requires fractional degrees of freedom, rejecting such df is only a safety check—not a substitute for correct real-df statistical evaluation.

The official LibreOffice Help says T.DIST.RT has been available since LibreOffice 4.3 and was not part of the OpenFormula 1.3 standardized functions. Its designated namespace is COM.MICROSOFT.T.DIST.RT. The OpenDocument 1.4 specification (§5.7) describes vendor-prefixed names for functions not defined by that standard, so file interchange can retain a vendor function without guaranteeing another program computes it the same way. Official LibreOffice Help; OASIS OpenDocument 1.4, §§5.6–5.7.

What was actually tested: LibreOffice Calc 25.2.3.2 on Linux, recomputing an OOXML test workbook (import formulas encoded _xlfn.T.DIST.RT) into native ODS and exporting recalculated XLSX. _xlfn. is an imported OOXML metadata prefix and not user-editable Calc formula syntax. No Excel installation was run; Excel parity, behavior on macOS/Windows, other LibreOffice builds, locale-specific decimal parsing, and third-party editors remain unverified. Keep any interoperability claim limited to the observed import/recalculation path.

• T.DIST — density and left-cumulative t distribution
• T.DIST.2T — two-tail probability
• TDIST — legacy t-distribution function
• T.INV — inverse t distribution
• T.INV.2T — inverse two-tailed t distribution
• T.TEST — t-test for arrays

Does the function need a TRUE/FALSE cumulative argument? No. T.DIST.RT has two arguments and always returns the right-tail probability. A third argument belongs to T.DIST, not this function.

Can a negative t statistic be entered? Yes. It gives a large right-tail probability. Do not automatically use ABS unless you’re computing a two-sided test by design.

Why use T.DIST.RT instead of 1−T.DIST? They are mathematically equal, but the directly calculated survival function can retain very small upper-tail probabilities without cancellation.

Can I use noninteger degrees of freedom? The mathematical Student t distribution permits them, but this tested LibreOffice version truncated them, so the resulting number may differ materially. See the verified discrepancy table and do not claim that the exact fractional df was used.

Does a p-value tell me the probability that the null hypothesis is true? No. The value is a tail probability of the statistic under the specified null model and assumptions, not a posterior probability that a hypothesis is true.

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