T.INV.2T in ONLYOFFICE: Two-Tail t Critical Values and the TINV Alias

Create TModel. Put Parameter in A1 and Value in B1. Enter Threshold in A2 and 1 in B2; Degrees of freedom in A3 and 1 in B3; Tail area in A4 and 0.05 in B4. Keep these cells unchanged when adding controls.

One degree of freedom is chosen because the t distribution then has the Cauchy closed form: its CDF is 1/2+atan(t)/π and its density is 1/[π(1+t²)]. This lets the examples be checked independently without running ONLYOFFICE. It is an arithmetic teaching case, not a recommendation to base practical inference on a tiny sample.

A t distribution is symmetric around zero. Its tail heaviness depends on degrees of freedom; a t value is not a raw measurement in minutes or grams. In a statistical test, its construction and degrees of freedom must come from the appropriate sampling model. A distribution formula alone does not establish those assumptions.

The official reference describes the inverse two-tailed t distribution. The cutoff q is nonnegative and satisfies P(|T|≥q)=p. At p=0.5 and df=1, each tail contains 0.25, giving q=1.

For an ordinary valid probability, the mathematical relation is T.INV.2T(p,df)=T.INV(1-p/2,df). It is not T.INV(p,df). The distinction matters most when p is small: a small two-tail probability requires a large positive cutoff, while a small left-CDF probability gives a negative quantile.

For df=1, q=cot(πp/2) gives an independent closed-form check. Reducing total tail area increases the cutoff. The round trip is a mathematical consistency target, not a native calculation or an exact-digit guarantee.

A central 95% model region leaves p=0.05 outside. At df=1, use bounds −12.7062047361747 and +12.7062047361747. Each tail has area 0.025. Entering 0.025 in T.INV.2T would instead request total tail area 0.025, giving a central 97.5% region and a larger cutoff.

For a statistical interval in original units, a justified center and standard error are also needed. The t cutoff alone does not define the sample design, establish normality of a relevant estimator or guarantee coverage. Extremely small degrees of freedom illustrate why uncertainty can be wide even with apparently precise input numbers.

Help states probability strictly between 0 and 1. The tagged guard accepts p=1 but rejects p≤0 or p>1. At p=1 the mathematical cutoff is zero, and the bounded source search reaches the zero endpoint in the df=1 control. This is a source-predicted boundary, not a native observation. By contrast, T.INV(1,1) is rejected because the signed left-tail inverse has no finite endpoint there.

The inverse parses df with parseInt and rejects the parsed value below 1. For ordinary positive fractional df, this differs from the forward distribution functions’ untruncated helper inputs. Use documented integer df. Negative probabilities, zero probability and df=0 are source-predicted #NUM!.

The legacy TINV help has the same two-argument role, and its class directly inherits T.INV.2T in this pinned source. This is verified implementation inheritance, not punctuation-based equivalence. It supports one combined guide while leaving older releases, import formulas and native array behavior unverified.

The inverse implementation searches through a shared numerical helper. It can expand a bracket up to 1000 times, then refine for up to 500 iterations using interpolation and bisection. A failed bracket is reported through an error flag and becomes #NUM!, but reaching the refinement iteration cap alone does not set that flag. Do not describe every finite return as a certified convergence result.

These are implementation bounds, not a measured runtime guarantee. Very small probabilities and extreme degrees of freedom need exact-build accuracy checks; the moderate closed-form examples here do not validate all tails. Array-oriented source preparation does not prove a native spill or array-entry workflow.

Checked October 18, 2026 against current official help and SDKJS tag v10.0.0.169, commit 3679e0375a758d7dc59d31337a45461be3525ed8. Introduction dates and a final supported-version endpoint are not established. Desktop Editors, Docs, mobile releases and imported files require separate compatibility checks.

Neither the ONLYOFFICE application nor its calculation engine was executed for this guide. The numerical targets are independently calculated mathematical values; code-path and error observations are manual source traces. They are not screenshots, displayed workbook results or promises of identical final digits. Use English function names and comma separators as shown, adapting separators to the editor’s locale.

Keep inputs and intermediate probabilities numeric and unrounded. Format the display rather than replacing values with rounded strings. These moderate scalar examples do not certify extreme-tail accuracy, unusual type coercion, array entry or dynamic spill. Model assumptions must be checked separately from arithmetic correctness.

• Official T.INV.2T help, checked October 18, 2026.
• Pinned function definition.
• T-probability helper, inverse solver and test calculations.
• T.DIST.
• T.DIST.2T.
• T.DIST.RT.
• T.INV.
• TDIST.
• T.TEST.