Calculadora de p-valor (bilateral, z)
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
p = 2·(1 − Φ(|z|))
About this calculator
The p-value Calculator (two-tailed, z) is a statistical tool that computes the two-tailed p-value from a z-score (or standardized test statistic). The p-value represents the probability of obtaining a result as extreme as the observed one, assuming the null hypothesis is true. This calculation is fundamental in hypothesis testing to determine statistical significance.
The operation is simple: you enter the absolute value of the z-score (|z|). The calculator uses the cumulative distribution function of the standard normal distribution (Φ) to obtain the probability of a value less than |z|. The two-tailed p-value is then calculated as 2 × (1 − Φ(|z|)), which corresponds to the area in both tails of the normal distribution.
This calculator is useful in various fields such as scientific research, quality control, data analysis, and experiments. For example, when testing whether the mean of a sample differs significantly from a reference value, or when comparing two groups in a clinical study. The p-value helps decide whether to reject the null hypothesis.
Important considerations: The p-value does not measure the effect size nor the probability that the null hypothesis is true. It depends on sample size and data variability. Additionally, this calculation assumes the test statistic follows a standard normal distribution, which is valid for large samples or when the variance is known. For small samples, other distributions (like Student's t) may be more appropriate.
Frequently asked questions
What does a p-value less than 0.05 mean?
A p-value less than 0.05 indicates that the probability of observing such an extreme result under the null hypothesis is less than 5%. This is generally considered statistically significant, leading to rejection of the null hypothesis.
Can I use this calculator for one-tailed tests?
No, this calculator is specific for two-tailed tests. For one-tailed tests, the p-value would be 1 − Φ(z) for an upper-tail test or Φ(z) for a lower-tail test.
What is the difference between p-value and significance level?
The p-value is calculated from the data and indicates the evidence against the null hypothesis. The significance level (α) is a threshold chosen by the researcher before the test, usually 0.05. If p-value < α, the null hypothesis is rejected.
What if the z-score is very large?
If |z| is very large (e.g., greater than 4), the p-value will be extremely small (close to zero). This indicates strong evidence against the null hypothesis. The calculator may return a very small value, such as 0.0001 or less.
Does this calculator work for any normal distribution?
It works for the standard normal distribution (mean 0 and standard deviation 1). If your data follows a normal distribution with other parameters, you need to standardize the value to obtain the z-score before using.