Documentation/How Tos/Calc: ZTEST function

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Returns the result of a z-test.


ZTEST(data; μ σ)

data is a range or array containing a random sample from a population (population assumed to have a normal distribution).
μ is the (known) mean of the population.
σ is the (known) standard deviation of the population. If omitted, it is estimated from the sample data by STDEV(data).
ZTEST calculates the z statistic:
Calc z formula.png
where m is the sample mean and n the number in the sample. When the mean and standard deviation of the population are known, the z statistic forms a standard normal distribution - that is, a normal distribution with mean=0 and standard deviation=1.
ZTEST returns the one-sided cumulative probability - the area under the standard normal curve to the right of the z value (shaded blue here):
Calc ztest graph2.png Calc ztest graph1.png


ZTEST(A2:A20; 9; 2)

returns the result of a z-test on a sample A2:A20 drawn from a population with known mean 9 and known standard deviation 2.


  • Excel has referred to this as both a one-tailed and a two-tailed test. Neither is correct - the test is one-sided as described above. For example when z = -1.5 part of the left tail and all of the right tail are included. This is an unconventional measure, but can be used.
  • Calc has produced incorrect results for the 3 parameter version of this function. See issue 90759.
  • As with all statistics, a good understanding is needed for reliable results.


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