TDIST in WPS Spreadsheet: One- and Two-Tailed t Probabilities
Calculate positive-threshold Student t tail probabilities, distinguish tails 1 and 2 and preserve the lesson’s negative-argument ambiguity.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
TDIST evaluates a Student t tail probability. With a positive threshold x, tails=1 returns P(T>x), while tails=2 returns P(|T|>x). The second includes both symmetric tails; it is not the lower-tail cumulative probability.
Syntax and bounded input scope
=TDIST(x, degrees_freedom, tails)
Original examples use strictly positive x, positive integer degrees of freedom and an explicit tails value of 1 or 2. The formal WPS description excludes negative x, but its later workaround equations write TDIST with a negative argument. That conflict is not treated as evidence that negative input works. All controls avoid it.
The lesson’s platform and edition applicability are unspecified. Its historical menu instructions do not establish current UI behavior, platform parity or native execution of these examples.
Original one-degree example
A Student t distribution with one degree of freedom is a standard Cauchy distribution. Its positive right tail is 0.5−atan(x)/pi.
- Enter 1 in A2 and 1 in B2.
- Use
=TDIST(A2,B2,1)in C2. Since atan(1)=pi/4, the independent result is 0.25. - Use
=TDIST(A2,B2,2)in D2 for both tails. Symmetry gives 0.5.
The one-tail result concerns values above +1. The two-tail result concerns values above +1 or below −1. Neither result says that the null hypothesis has that probability of being true.
Independent controls
| Formula | Expected probability, approximately |
|---|---|
=TDIST(1,1,1) |
0.25 |
=TDIST(1,1,2) |
0.5 |
=TDIST(2,1,1) |
0.147583617650433 |
=TDIST(2,1,2) |
0.295167235300867 |
=TDIST(1,2,1) |
0.211324865405187 |
=TDIST(1,2,2) |
0.422649730810374 |
For two degrees of freedom, the independent positive right tail is 0.5−x/(2*sqrt(x^2+2)). These closed forms provide mathematical checks of the selected tail modes without executing WPS.
Derive a central interval
For one degree of freedom at threshold 2, the two-tail probability is about 0.295167235300867. The complementary central probability between −2 and +2 is approximately 0.704832764699133. This derives an interval probability from symmetry while keeping every function call’s x positive.
In an actual t procedure, the statistic and degrees of freedom must come from the appropriate sampling model. A one-sided alternative requires a direction chosen for the scientific question; switching between tails after seeing data changes that question. TDIST alone does not compute a t statistic from raw samples or establish that a t model is appropriate.
Vendor example and troubleshooting
The official walkthrough uses x=1.1, degrees of freedom 40 and tails=1, displaying 13.90% after percentage formatting. Formatting a probability changes its presentation, not the underlying decimal value. Do not multiply by 100 and then apply percentage formatting again.
WPS documents nonnumeric-input errors, invalid tails, degrees below one and negative x, and mentions truncating certain numeric arguments. The original controls avoid these cases and the contradictory negative-input workaround. No current argument coercion or extreme-tail accuracy claim is made.
See CONFIDENCE for a known-population-sigma normal margin; it is not automatically a substitute for a t-based interval with estimated sigma.
Availability and evidence scope
The official WPS lesson is dated 2019-06-18 and does not specify its applicability edition or platform. Its numeric build is unspecified. This documents the function by that date; it does not establish first introduction, the last functioning build, other-platform parity or a retirement/deprecation history.
The official lesson was rechecked on October 19, 2026. Original examples are documentation-derived independent calculations, not WPS or other spreadsheet-engine executions. Numeric reference values do not certify application precision or statistical model suitability.