R.PT 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.PT returns P(T≤x) for a central Student t distribution. Its upper-tail mode returns P(T>x). The cutoff is signed: a negative observation is not silently replaced by its absolute value. Versioned function help.

=R.PT(x,degrees_freedom[,lower_tail[,log_p]])

• x: real cutoff on the t scale.
• degrees_freedom: positive real parameter; fractional values are retained.
• 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.

A statistic of 2 with five degrees of freedom gives lower probability 0.949030260585 and upper probability 0.050969739415. Choose the tail from a hypothesis specified before inspecting the result. A lower-tail probability close to one does not itself mean a small two-sided p-value.

For a symmetric, central t model, the independent two-sided calculation is =2*R.PT(ABS(2),5,FALSE()), approximately 0.101939478830. The ABS is appropriate to that stated two-sided calculation; it is not an intrinsic feature of R.PT.

At one degree of freedom, the distribution is standard Cauchy. Its CDF is 0.5+ATAN(x)/PI(), which independently gives 0.75 at x=1 and 0.25 at x=−1. Symmetry also gives P(T≤x)+P(T≤−x)=1.

Use FALSE directly for a small upper tail rather than subtracting an almost-one lower probability. The native million-unit Cauchy cutoff retains approximately 3.183098861837E-7, and log mode returns approximately −14.960240443814. A log probability is a negative real number, not a percentage.

The saved advanced-check result for =R.PT(2,5)+R.PT(-2,5) was 1.

Zero or negative degrees of freedom produce #NUM!; positive fractional degrees such as 2.5 are valid. Numeric text is converted in the tested direct argument, nonnumeric text produces #VALUE!, and the empty F5 cutoff acts as zero. A numeric nonzero tail flag acts as TRUE.

Missing required or surplus arguments produce #N/A. Degrees of freedom alone do not establish that a dataset meets a t-model assumption; this function evaluates the distribution supplied to it.

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

• Current worksheet callback
• Tested-version worksheet callback
• Current pt calculation
• Tested-version pt 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, TDIST, TINV.