How Is P-Value Calculated


The P-Value is a crucial statistical measure used in hypothesis testing to determine the significance of observed results. It helps researchers and analysts make informed decisions about accepting or rejecting a null hypothesis based on the data collected from a sample.

Formula: The P-Value is calculated using the formula:

P-Value = 2 * (1 – 0.5 * (1 + erf(z-score / √2)))

where the z-score is obtained by the formula:

z = (X̄ – μ) / (σ / √n)

Here, X̄ is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

How to Use:

  1. Enter the observed value.
  2. Provide the sample mean, sample standard deviation, and sample size.
  3. Click the “Calculate” button to obtain the P-Value.

Example: Suppose you have a sample mean of 30, a sample standard deviation of 5, and a sample size of 50. If the observed value is 32, the P-Value can be calculated using the provided calculator.


  1. Q: What is the P-Value? A: The P-Value is a probability measure that helps assess the evidence against a null hypothesis in statistical hypothesis testing.
  2. Q: What does a low P-Value indicate? A: A low P-Value (typically less than 0.05) suggests that the observed results are unlikely to have occurred by random chance alone, leading to the rejection of the null hypothesis.
  3. Q: When is a high P-Value considered acceptable? A: A high P-Value (greater than 0.05) indicates that the observed results are likely to occur by random chance, and the null hypothesis cannot be rejected.
  4. Q: How is the z-score related to the P-Value? A: The z-score measures the standard deviations a data point is from the mean and is used to calculate the P-Value.

Conclusion: Understanding how to calculate the P-Value is essential for researchers and analysts engaged in statistical hypothesis testing. This online calculator simplifies the process, making it accessible for anyone involved in data analysis and research. Use it wisely to draw meaningful conclusions from your data.

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