R.QT Function (Gnumeric)

• Introduced: First release not established; present in the retained 1.12.57 source.
• Supported in: Gnumeric 1.12.62; no retirement is established.
• Scope: Desktop Gnumeric with its Statistical Functions From R plugin. English comma-separated formulas are shown.
• Checked: October 14, 2026. Tables and the named advanced check use 1.12.57 ssconvert. Current 1.12.62 source was inspected; that release was not executed.

R.QT returns the signed quantile of the central Student t distribution. By default p is a lower cumulative probability. With lower_tail FALSE, p is an upper-tail probability, so a small p gives a positive critical value. Versioned function help.

=R.QT(probability,degrees_freedom[,lower_tail[,log_p]])

• probability: 0<p<1 for a finite ordinary quantile; with log_p TRUE supply LN(p).
• degrees_freedom: positive real parameter, including fractions.
• lower_tail: optional TRUE for the lower cumulative probability; FALSE requests the upper tail.
• log_p: optional FALSE. TRUE uses natural-log probabilities, not base-10 logarithms.

Brackets mark optional arguments; do not type them. Current worksheet implementation.

These self-contained formulas were recalculated natively. Ordinary-domain results were checked against independent mathematics; source guards explain the boundary cases. Results are rounded to twelve decimal places, or thirteen significant digits for small nonzero values. This is presentation precision, not a universal accuracy guarantee.

For five degrees of freedom, lower probability 0.975 gives 2.570581835636. Upper probability 0.025 gives the same critical value. The value 0.025 is one tail of a symmetric 95% central interval; supplying 0.95 directly would select a different cutoff.

For an independent normal sample with n=6, mean 10 and sample standard deviation 2, the stated t interval uses R.QT(0.975,5)*2/SQRT(6). Independent arithmetic gives a margin 2.098871279792 and endpoints 7.901128720208 and 12.098871279792. These numbers illustrate the specified model rather than automatically validating a real sample.

At one degree of freedom, lower probabilities 0.25 and 0.75 give −1 and 1. The median is zero. Quantile symmetry is q(1−p)=−q(p), while evaluating the CDF at an interior quantile recovers the supplied lower probability within numerical precision.

A positive fractional degree below one is also accepted: the tested q(0.75;0.5) is approximately 1.553773974030. Log mode takes LN(0.025), not the ordinary number 0.025; a positive log-probability input is invalid.

The saved advanced-check result for =R.PT(R.QT(.975,5),5) was 0.975.

At ordinary probabilities 0 and 1 the mathematical t endpoints are infinite. The worksheet returns #NUM! for those endpoints in both tail orientations, and also for outside-domain probabilities or nonpositive degrees of freedom. Those causes are different even though their displayed error is the same.

An empty first argument becomes zero and therefore reaches an infinite endpoint. Nonnumeric text gives #VALUE!; the missing-degree and surplus-argument cases give #N/A. The tested cases do not establish uniform accuracy at every extreme probability.

F5 is genuinely empty, rather than a cell containing an empty string.

• Current worksheet callback
• Tested-version worksheet callback
• Current qt calculation
• Tested-version qt calculation
• Nonfinite worksheet-value handling
• Statistical Functions From R plugin declaration

The relevant complete worksheet callback and main calculation helper are unchanged between the inspected versions. That does not establish later-version numerical execution. Both stale and uncached SUM controls recalculated correctly. Native XML preserves the R.* identities. The secondary ODF export keeps these calls in the ORG.GNUMERIC namespace; it does not establish execution in another product. GUI entry, other locales and other spreadsheet products were not tested.

R.DT, TINV, R.QNORM.