Z.TEST Function (LibreOffice Calc)

Math Advanced LibreOffice Calc Introduced in LibreOffice 4.0
hypothesis-testing statistics probability z-test inferential-statistics

The Z.TEST function in LibreOffice Calc performs a one-sample z-test and returns the probability that the sample mean is greater than the hypothesized population mean. This guide explains syntax, interpretation, examples, errors, and best practices.

Compatibility

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What the Z.TEST Function Does ▾

  • Performs a one-sample z-test
  • Returns the one-tailed probability that the sample mean > hypothesized mean
  • Assumes known or approximated population standard deviation
  • Useful for hypothesis testing and probability evaluation
  • Works across sheets

Z.TEST answers the question:

“If the true mean were μ₀, what is the probability of observing a sample mean this large or larger?”

Syntax ▾

Z.TEST(array; x; sigma)

Where:

  • array — sample data
  • x — hypothesized population mean (μ₀)
  • sigma — (optional) population standard deviation
    • If omitted, Calc uses STDEV.S(array) as an estimate
Z.TEST always returns a one-tailed probability.
For two-tailed tests, multiply the result by 2.

Interpretation of Z.TEST Results ▾

Z.TEST Output Meaning
Near 1 Sample mean is much larger than μ₀
~0.5 Sample mean close to μ₀
Near 0 Sample mean is much smaller than μ₀
< 0.05 Statistically significant (one-tailed)
< 0.025 Statistically significant (two-tailed)

Basic Examples ▾

One-sample z-test with known sigma

=Z.TEST(A1:A30; 50; 10)

Z-test using sample SD (sigma omitted)

=Z.TEST(A1:A30; 50)

Z-test across sheets

=Z.TEST(Sheet1.A1:A50; Sheet2.B1)

Two-tailed z-test

=2 * Z.TEST(A1:A30; 50)

Advanced Examples ▾

Z-test ignoring errors

=Z.TEST(IF(ISNUMBER(A1:A100); A1:A100); 50)

(Confirm with Ctrl+Shift+Enter in older Calc.)

Z-test using filtered (visible) data only

Use SUBTOTAL helper column to filter values before passing to Z.TEST.

Z-test after removing outliers

=Z.TEST(FILTER(A1:A100; A1:A100<1000); 50)

Z-test for standardized data

=Z.TEST(STANDARDIZE(A1:A30; Mean; SD); 0)

Z-test for quality control (process mean)

=Z.TEST(Measurements; TargetValue; KnownSigma)

Z-test for large-sample approximations

=Z.TEST(A1:A500; HypothesizedMean)

How Z.TEST Calculates the Probability ▾

  1. Compute sample mean:

[ \bar{x} = \text{AVERAGE}(array) ]

  1. Compute standard deviation:
  • If sigma provided: ( \sigma )
  • Else: ( s = \text{STDEV.S}(array) )
  1. Compute z-score:

[ z = \frac{\bar{x} - \mu_0}{\sigma / \sqrt{n}} ]

  1. Compute one-tailed probability:

[ p = 1 - \Phi(z) ]

Where ( \Phi ) is the standard normal CDF.

Common Errors and Fixes ▾

Err:502 — Invalid argument

Occurs when:

  • Array contains no numeric values
  • Sigma ≤ 0
  • x is non-numeric

Err:504 — Parameter error

Occurs when:

  • Semicolons are incorrect
  • Range references malformed

Z.TEST returns unexpected value

Possible causes:

  • Wrong sigma (population vs sample)
  • Two-tailed test not adjusted
  • Outliers affecting mean and SD
  • Non-normal data (z-test assumes approximate normality)

Best Practices ▾

  • Use Z.TEST when population SD is known or sample size is large
  • Use T.TEST when population SD is unknown and sample size is small
  • Remove outliers before testing
  • Use named ranges for cleaner formulas
  • Multiply by 2 for two-tailed tests
  • Use STANDARDIZE for manual z-score checks
Z.TEST is your go-to tool for fast, reliable hypothesis testing — perfect for quality control, scientific analysis, and any situation where you need to know whether a sample mean is significantly different from a target value.

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