T.DIST.2T in ONLYOFFICE: Two-Sided Student t Tail Areas

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 a two-tailed t probability. The mathematical event is |T|≥x for x≥0. This is an area, not a density and not the cumulative probability up to positive x.

At df=1 and x=1, each tail has area 1/4, so the total is 1/2. For the continuous distribution, strict or non-strict inclusion at the boundary does not change the probability.

Zero is accepted by the pinned guard even though the short help describes x as greater than zero. At zero, the two tails cover the whole distribution and give 1. Negative x is rejected with #NUM!: use a magnitude when that is what the statistical question requires.

For nonnegative x, the mathematical identity is T.DIST.2T(x,df)=2*T.DIST.RT(x,df). At x=1,df=1, this is twice 0.25. It also equals 2*(1-T.DIST(x,df,TRUE)) in exact mathematics, although subtraction can be less accurate in very small tails.

For a signed test statistic in D2, =T.DIST.2T(ABS(D2),B3) expresses a two-sided magnitude test. The absolute value is appropriate only if a two-sided question was intended. It does not turn every directional hypothesis into a valid two-sided analysis, nor does a small tail probability prove a practical effect size.

A two-sided probability is not the probability that an effect has the opposite sign or that the null hypothesis is true. It is a probability of values at least as extreme under the specified reference model. Degrees of freedom must come from the actual procedure rather than an arbitrary row count.

The source rejects x<0 or df<1. Thus =T.DIST.2T(-1,1) and =T.DIST.2T(1,0) are source-predicted #NUM!. It passes the degrees-of-freedom value to the helper without an explicit integer conversion, although the help specifies integer df. These examples use integers; do not infer that inverse functions have the same conversion rule.

=TDIST(1,1,2) has the same two-tail mathematical target. That legacy function also supports tails=1, whereas T.DIST.2T always selects two tails. T.DIST is a different CDF/density interface and must not be substituted merely by retaining a numeric 2 in the third argument.

The implementation calls the beta-based tail helper directly, which avoids the explicit subtraction of a near-one CDF in the displayed alternative identity. This is a source-path distinction, not a guarantee of arbitrary precision. Exact target-build tests are required for extreme probabilities, large parameters or imported workbook behavior.

For the reverse problem, T.INV.2T takes a total two-tail probability and returns the nonnegative cutoff. An input probability of 0.05 corresponds mathematically to 0.025 in each tail, not 0.05 per tail.

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