Find P Value with Test Statistic and N Calculator

This calculator helps you find the p-value when you know the test statistic and sample size n. The p-value is a key measure in statistical hypothesis testing that helps determine whether results are statistically significant.

What is a p-value?

The p-value (probability value) is a statistical measure that helps determine the significance of your results. It represents the probability of obtaining results as extreme as, or more extreme than, what was observed, assuming that the null hypothesis is true.

In hypothesis testing, the null hypothesis (H₀) typically states that there is no effect or no difference. The p-value helps you decide whether to reject the null hypothesis.

Key points about p-values

P-values range from 0 to 1
A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis
A large p-value (> 0.05) suggests weak evidence against the null hypothesis
P-values do not measure the size or importance of an effect

How to use this calculator

To find the p-value, you need to provide:

The test statistic (z-score, t-score, or chi-square value)
The sample size n
The type of test (one-tailed or two-tailed)

For a one-tailed test: p-value = P(X ≥ |z|)

For a two-tailed test: p-value = 2 × P(X ≥ |z|)

Enter these values in the calculator on the right, then click "Calculate" to get your p-value.

Interpreting results

Once you have your p-value, you can interpret it as follows:

P-value range	Interpretation
p ≤ 0.05	Statistically significant result (reject null hypothesis)
0.05 < p ≤ 0.10	Marginally significant result
p > 0.10	Not statistically significant (fail to reject null hypothesis)

Remember that statistical significance does not imply practical significance. Always consider the effect size and context when interpreting results.

Worked example

Let's say you conducted a study with n = 50 participants and obtained a test statistic of z = 2.1. You want to find the p-value for a two-tailed test.

Enter 2.1 in the test statistic field
Enter 50 in the sample size field
Select "Two-tailed" from the test type dropdown
Click "Calculate"

The calculator will show you the p-value, which in this case would be approximately 0.035. This means there's a 3.5% chance of observing a result as extreme as 2.1 if the null hypothesis were true.

Since 0.035 ≤ 0.05, you would reject the null hypothesis and conclude that your results are statistically significant.

FAQ

What is the difference between a one-tailed and two-tailed test?: A one-tailed test looks for an effect in a specific direction (either increase or decrease), while a two-tailed test looks for any effect regardless of direction.
What does a p-value of 0.05 mean?: A p-value of 0.05 means there's a 5% chance of getting results as extreme as yours if the null hypothesis were true. This is the conventional threshold for statistical significance.
Can I use this calculator for any type of test?: This calculator works for z-tests, t-tests, and chi-square tests. For other test types, you may need a different calculator.
What if my p-value is very small?: A very small p-value (e.g., 0.001) indicates very strong evidence against the null hypothesis. However, always consider the practical significance of your results.
How accurate is this calculator?: This calculator uses standard statistical formulas and provides accurate results based on the inputs you provide. For critical applications, you may want to verify with specialized statistical software.

About this calculator

This calculator uses standard statistical formulas to compute p-values. The formulas are displayed on the page for transparency. All calculations are performed client-side in your browser for privacy.

Last updated: October 2023