Z.TEST in Google Sheets: One-Tailed Mean-Test Probabilities

=Z.TEST(data, value, [standard_deviation])

The Google Z.TEST reference documents the data range, a reference value and an optional deviation. If the deviation is omitted, Google says it calculates STDEV(data). The older spelling ZTEST is explicitly supported.

Google labels value a test statistic, but its linked numerical examples use it as the hypothesized population mean against which the sample mean is compared. Independent reproduction of those examples confirms the standardized calculation (sample_mean-value)/(deviation/SQRT(n)) followed by an upper normal tail. Do not pass an already standardized z statistic as this second argument.

The optional argument changes the denominator. It does not select one versus two tails or switch the calculation to a t distribution.

Enter 8, 9, 10, 11 and 12 in A2:A6. Put 8, 10 and 12 in D2:D4 as reference means, and 2 in G1 as the assumed standard deviation.

In E2, enter and fill down:

=Z.TEST($A$2:$A$6,D2,$G$1)

The observed mean is 10. A reference below it gives a positive standardized difference and a small upper tail. A reference above it gives a negative difference and a large upper tail. The result is directional; it is not automatically the smaller of the two tails.

With reference mean 8 and deviation 2:

=(AVERAGE(A2:A6)-8)/(2/SQRT(COUNT(A2:A6)))

Expected standardized value: 2.2360679775. The standard-normal area above that value is approximately 0.0126736593. The normal mean standard-error relationship is described in NIST’s confidence-interval discussion.

Google’s published example uses ten observations with mean 89. Its results for reference means 88 and 90 are complementary, and the displayed explicit-deviation and omitted-deviation calculations independently reproduce this same upper-tail rule. Those are documentation checks, not execution of the new dataset here.

If E2 contains the one-tail result, the symmetric two-sided probability is:

=2*MIN(E2,1-E2)

For the reference-8 row, expected result: 0.0253473187. The reference-12 row gives the same two-sided probability because its standardized difference has equal magnitude and opposite sign. Google’s published examples explicitly demonstrate this two-sided transformation.

For a left-sided alternative, the corresponding probability is =1-E2. With reference mean 8, that is approximately 0.9873263407, reflecting that the observed sample mean lies above, not below, the reference.

Select the hypothesis direction before interpreting the data. Doubling every one-tail result without taking the smaller tail could produce a number above 1, which cannot be a probability.

Use:

=Z.TEST(A2:A6,8)

The sample standard deviation of these five values is approximately 1.5811388301. The resulting standardized difference is approximately 2.8284271247, and the expected upper normal tail is 0.0023388675.

This is different from the explicit-deviation result because 1.58114 is smaller than the supplied value 2. It remains a normal-tail calculation. Estimating variability from a small sample may instead call for a t-based statistical procedure; merely omitting sigma does not make Z.TEST perform that procedure.

The examples are arithmetic demonstrations, not a claim that five measurements are sufficient for a reliable real-world z-test.

Check that the reference is in the original measurement units, the deviation is positive and the range contains the intended numeric sample. Empty data, one-observation estimation, zero variability, text/blank coercion and exact native error tokens were not established by the reviewed help page.

A small p-value does not measure practical importance or the probability that the null hypothesis is false. It depends on the sampling model, assumed or estimated variability and the chosen direction. Biased sampling or dependent observations are not repaired by a small numerical result.

For repeated comparisons, interpreting many separate p-values also requires a suitable analysis plan rather than selecting only the smallest result.

Z.TEST and ZTEST are documented in current rolling Google Sheets. Original introduction date, first release and last functioning numbered version were not established.

NOT_TESTED_IN_GOOGLE_SHEETS. Google help, its linked read-only published examples and NIST mathematics were inspected on October 17, 2026. All original means, deviations, z values and probabilities were independently calculated. No native execution or screenshot is claimed.

Related published guides: AVERAGE, STDEV.S, COUNT, SQRT and MIN.