When to use this calculator
Find an approximate normal-model p-value from a supplied z statistic and a chosen tail. Uses an approximate standard normal CDF and does not apply a t, chi-square or exact-test distribution. A p-value is not the probability that a hypothesis is true.
Explore the sampling uncertainty calculators for other questions in this topic. For a related calculation, use the Arithmetic Mean Calculator: Find the arithmetic mean of a variable-length list of numbers.
PUTTING IT INTO PRACTICE
Z Test P Value: a worked example
The values below are an illustrative example, not a recommendation. Replace them with measurements or assumptions that match your question.
| Input | Example value |
|---|---|
| Z statistic | 0 |
| Alternative tail | two |
| Result | 1 probability |
- Check the input labels and enter the example values above.
- Apply the relationship: Left p=Φ(z); right p=1−Φ(z); two-sided p=2×min(Φ(z),1−Φ(z))..
- The result is 1 probability, rounded for display.
How to interpret your result
Uses an approximate standard normal CDF and does not apply a t, chi-square or exact-test distribution. A p-value is not the probability that a hypothesis is true.
Use a critical value and model appropriate to the study. Simple random-sampling approximations do not correct for selection bias or clustered observations. Normal approximations can be poor for small samples or extreme proportions.
Frequently asked questions
Does a larger sample remove selection bias?
No. More observations can reduce sampling variability without repairing a systematically biased selection process.
When is the z test p value calculator useful?
Find an approximate normal-model p-value from a supplied z statistic and a chosen tail. Uses an approximate standard normal CDF and does not apply a t, chi-square or exact-test distribution. A p-value is not the probability that a hypothesis is true.
How do I use the z test p value calculator?
Enter z statistic, alternative tail. The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Left p=Φ(z); right p=1−Φ(z); two-sided p=2×min(Φ(z),1−Φ(z))..
What should I check before using the result?
Uses an approximate standard normal CDF and does not apply a t, chi-square or exact-test distribution. A p-value is not the probability that a hypothesis is true.
How are results rounded?
Scalar numbers display up to six decimal places, with scientific notation for very large or small values. Text, fraction, date and schedule outputs use the format described on the tool. Intermediate calculations use JavaScript floating-point arithmetic. Keep sensible precision for your measurements.
Further reading
For background on this topic, see NIST/SEMATECH statistical methods handbook ↗. This is a topic reference, not an external review or endorsement of this tool.
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