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ZTEST Function (Calligra Sheets)

Statistical Intermediate Calligra Sheets

Inspect Calligra ZTEST’s central-normal output, verified tail alternatives and mixed-value conversion. Avoid interpreting its numeric result as a usual p-value.

Verification status: 29 selected formulas were executed through the Calligra Sheets 25.04.2 calculation engine library. Exact outputs, mathematical references and source limitations are documented separately. Version 26.08.2 was source-checked only; no GUI-cell or import claim. How formula examples are checked

This implementation returns a central probability, not a tail p-value. For data {1;2;3}, hypothesized mean 1 and supplied standard deviation 1, the tested ZTEST result was about 0.916735483336; the one-sided upper-tail probability is about 0.041632258332.

Quick answer: =ZTEST({1;2;3};2;1) gives approximately 0 in the tested Calligra calculation engine.

Availability and version history

  • Introduced: First release not established; the name is present in Calligra 2.4.0 source.
  • Supported in: Calligra Sheets 26.08.2, with no retirement established.
  • Scope: Desktop Sheets with the Statistical module. Compatibility names remain registered; no retirement is inferred. Examples use English semicolon-separated formulas.
  • Checked: October 14, 2026. Selected formulas ran through the official 25.04.2 engine library. Source and independent mathematics were checked. This is engine evidence, with no GUI-cell or import verification; 26.08.2 was source-checked only.

What ZTEST returns

ZTEST computes z=(sample mean−hypothesized mean)×√n/standardDeviation and returns 2Φ(|z|)−1. This is the standard-normal probability between −|z| and |z|. It increases with |z|, the opposite direction from a two-sided tail p-value. Omitting the deviation uses a sample standard deviation, but the final distribution is still normal. Function-specific official reference.

Syntax and arguments

=ZTEST(data;hypothesizedMean[;standardDeviation])

Data and hypothesizedMean are required; standardDeviation is optional. Supply at least two intended numeric observations and a strictly positive deviation. The source does not enforce the positive-deviation condition. Inline arrays below are engine inputs, not imported cell ranges. Brackets indicate optional arguments and are not entered in the formula. Registration and implementation.

Reproducible engine examples

The engine and mathematical columns are separate. Results are rounded to twelve decimal places, or thirteen significant digits in scientific notation for very small or large values. This is a display choice, not an accuracy guarantee. Inline arrays in braces are formula values, not a workbook-import test. Their semicolons separate columns and vertical bars separate rows. Strings remain explicitly quoted, and booleans use TRUE()/FALSE().

Formula Engine result Independent mathematical reference
=ZTEST({1;2;3};2;1) 0 0
=ZTEST({1;2;3};1;1) 0.916735483336 0.916735483336
=ZTEST({1;2;3};3;1) 0.916735483336 0.916735483336
=ZTEST({1;2;3};2) 0 0
=ZTEST({1;2;3};1) 0.916735483336 0.916735483336
=ZTEST({2;4;6;8};4;2) 0.682689492137 0.682689492137
=ZTEST({5;8;12;14;18};10) 0.46231377786 0.46231377786
=ZTEST({5;8;12;14;18};10;5) 0.468750014005 0.468750014005

Practical worksheet

For {1;2;3}, the mean is 2 and sample standard deviation is 1. Testing against mean 2 gives z=0 and native ZTEST=0. Testing against mean 1 gives z=√3 and a result near 0.916735483336. Testing against mean 3 gives the same output because the implementation takes |z|.

The mathematical reference column checks this central-probability formula; it does not label the result as a conventional Z-test p-value. The omitted-deviation version happens to match the supplied-deviation example because its sample deviation is 1.

Advanced interpretation and checks

For the stated positive z=√3, the executed =1-LEGACYNORMSDIST(SQRT(3)) returned the upper-tail probability near 0.041632258332. The executed =1-ZTEST({1;2;3};1;1) returned the two-sided tail near 0.083264516664. These alternatives require valid numeric data, positive deviation and the intended normal testing model. A negative directional z needs its sign preserved in the one-sided calculation.

Count and mean use full-value conversion: numeric strings are parsed, nonnumeric strings become zero and booleans become 1 or 0. The omitted-deviation helper instead uses numeric-only sample spread. The asymmetric {1;2;4;“9”}, {1;2;4;“abc”} and {1;2;4;TRUE()} cases expose that mixed path. Avoid such mixed-type samples rather than interpreting their output as a clean statistical model.

The executed advanced check was:

=ZTEST({1;2;3};1;1)+2*(1-LEGACYNORMSDIST(SQRT(3)))

Its engine result was 1.

Boundaries and troubleshooting

Zero supplied deviation and a constant sample returned 0 in the tested cases, because intermediate errors reached an unchecked conversion path. Negative deviation also produced a plausible central probability. An embedded division error was concealed by a final zero. These outputs do not validate the calculation.

Validate numeric types, errors, sample size and a positive deviation before use. When the deviation is estimated, whether a t-based procedure is appropriate is a separate modeling question; this implementation does not switch automatically.

Formula Engine result
=ZTEST({1};0;1) #VALUE!
=ZTEST({1;2;3};2;0) 0
=ZTEST({1;2;3};1;0) 0
=ZTEST({1;2;3};1;-1) 0.916735483336
=ZTEST({1;1;1};1) 0
=ZTEST({1;2;3;"9"};1;1) 0.99999996202
=ZTEST({1;2;3;"abc"};1;1) 0.682689492137
=ZTEST({1;2;3;TRUE()};1;1) 0.866385597462
=ZTEST({1;2;3;1/0};1;1) 0
=ZTEST({1;2;3};"abc";1) 0.999467994495
=ZTEST({1;2;3}) #VALUE!
=ZTEST({1;2;3};1;1;0) #VALUE!
=ZTEST({1;2;3;"9"};1) 0.99999996202
=ZTEST({1;2;3;"abc"};1) 0.682689492137
=ZTEST({1;2;3;TRUE()};1) 0.866385597462
=ZTEST({1;2;4;"9"};1) 0.99991431702
=ZTEST({1;2;4;"abc"};1) 0.673890548299
=ZTEST({1;2;4;TRUE()};1) 0.809569736174

Official evidence and precision scope

The statistical and math modules and value-calculation helpers are byte-identical between the inspected 25.04.2 and 26.08.2 sources. That comparison supports the source discussion but does not establish later-version execution, GUI-cell behavior or other locales.

NORMSDIST, GAUSS, STDEV.