T.INV.2T in Collabora Office: Find a Two-Sided Student t Critical Magnitude
Use Collabora T.INV.2T to allocate probability across symmetric tails and construct transparent t-based margins.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
Quick answer: =T.INV.2T(0.05;10) has independently expected result approximately 2.228138852. The total probability below its negative and above its positive counterpart is 5%.
Syntax and the two-tail input
=T.INV.2T(Number; DegreesFreedom)
Number is the combined probability in both outside tails. DegreesFreedom selects the t distribution. Both arguments are required. Use 0<p<1 and positive integer degrees for ordinary finite, positive thresholds.
The output is a nonnegative magnitude. It is not the negative lower endpoint or a signed effect estimate. A symmetric interval uses both -q and +q, where q is the returned magnitude.
The dedicated Collabora help supplies the two-tailed interpretation and a probability-0.25 example. Current source approximately floors the degree count and rejects effective degrees below one or probabilities outside 0<p<=1. The endpoint p=1 is outside this guide’s interior controls.
Example 1: build critical values from total tail probability
Put 0.25, 0.1 and 0.05 in A2:A4. Enter =T.INV.2T(A2;10) in B2 and fill down. Independent thresholds are approximately 1.221255395, 1.812461123 and 2.228138852.
The first result reproduces the official example. Decreasing the total outside probability moves the two boundaries farther away from zero, so the positive magnitude increases.
Do not pass 0.025 merely because each tail of a 5% two-sided test contains 2.5%. T.INV.2T expects the combined 0.05 probability and performs the two-tail inversion itself.
Example 2: verify the reverse calculation
Enter =T.DIST.2T(B2;10) in C2 and fill down. The independent targets are 0.25, 0.1 and 0.05, matching A.
For the final row, =T.DIST.RT(B4;10) instead targets 0.025, while =T.DIST(B4;10;1) targets 0.975. These three values describe the same positive boundary under different probability conventions.
Keep full precision in B while comparing the forward result. Rounded printed critical-value tables are not an exact inverse-test fixture.
Advanced application: calculate a t-based margin
Suppose a mathematical example has sample mean 50, sample standard deviation 4, and 11 independent observations under an appropriate mean-inference model. The standard error is =4/SQRT(11), approximately 1.206045378.
The 95% two-sided margin is =T.INV.2T(0.05;10)*4/SQRT(11), independently approximately 2.687236565. Subtract and add the margin to 50, producing approximate endpoints 47.312763435 and 52.687236565.
Ten degrees comes from sample size minus one for this particular single-mean construction. T.INV.2T does not know the sample size and does not infer that relationship from the other worksheet values.
Advanced application: distinguish a one-sided bound
For a one-sided 95% upper bound with ten degrees, the relevant upper-tail probability is 0.05. The corresponding magnitude is approximately 1.812461123. It can be represented as T.INV(0.95;10) or, using symmetry deliberately, T.INV.2T(0.1;10).
This does not change a two-sided 95% procedure into a one-sided one automatically. The confidence statement, tail allocation and statistical design must agree before a threshold is selected.
Errors and troubleshooting
A returned magnitude is not itself a complete confidence interval. It requires a center and a standard error with compatible units. A margin computed from a standard deviation without dividing by the appropriate square root of sample size answers a different question.
Check probability units and degree counts before interpreting a large threshold. Heavy tails at low degrees can legitimately produce large critical values. Native endpoint behavior, all coercions and extreme-probability convergence are not certified. The cited source includes a numerical inversion path, so independent ordinary examples cannot guarantee every input will converge identically across versions.
Availability and evidence
The exact function is documented in Collabora Office 26.04 desktop help. That documentation snapshot was retrieved on 2026-10-13 and hash-verified on October 15, 2026. It does not establish Online or mobile support. First introduction and last functioning release are unknown in this evidence.
Additional implementation statements come from Collabora’s current engine source, retrieved October 15, 2026. This moving-main source is corroboration, not a pinned desktop 26.04 binary or a native execution. No native Collabora Office run occurred. Worked outputs are independent mathematical expectations.
Formulas use English names and semicolon separators. The help identifies namespace COM.MICROSOFT.T.INV.2T, outside its cited OpenFormula 1.3 standard; that does not establish identical behavior in another application.