P-Value Calculator
Calculate p-values for hypothesis testing. Supports Z-test, T-test, and Chi-square test with interpretation of statistical significance.
P-Value Calculator
Calculate p-values for hypothesis testing using Z-test, T-test, or Chi-square test
Formula
P(Z > |z|) using standard normal distributionThe p-value represents the probability of obtaining results at least as extreme as the observed results, assuming the null hypothesis is true.
Understanding P-Values
p < 0.05
Statistically significant. Strong evidence against the null hypothesis. The result is unlikely to have occurred by chance.
p ≥ 0.05
Not statistically significant. Insufficient evidence to reject the null hypothesis. The result could reasonably have occurred by chance.
How to Use
- 1Select test type — Choose the statistical test you want to use (Z-test, T-test, or Chi-square).
- 2Choose tail type — Select one-tailed (left or right) or two-tailed test based on your hypothesis.
- 3Enter test statistic — Input your calculated test statistic (z-score, t-statistic, or chi-square value).
- 4Enter degrees of freedom — For T-test and Chi-square, enter the degrees of freedom.
- 5View results — See the p-value and interpretation of statistical significance.
Frequently Asked Questions
What is a p-value?
A p-value is the probability of obtaining results at least as extreme as the observed results, assuming the null hypothesis is true. It helps determine whether to reject the null hypothesis.
What does statistical significance mean?
Statistical significance (typically p < 0.05) indicates that the observed results are unlikely to have occurred by chance alone. It suggests there may be a real effect or relationship.
When should I use a one-tailed vs two-tailed test?
Use a one-tailed test when you have a specific directional hypothesis (e.g., "A is greater than B"). Use a two-tailed test when you want to detect any difference regardless of direction.
What is the difference between Z-test and T-test?
Z-test is used when the population standard deviation is known or sample size is large (n > 30). T-test is used when the population standard deviation is unknown and sample size is small.
What are degrees of freedom?
Degrees of freedom represent the number of independent values that can vary in a statistical calculation. For a T-test with one sample, df = n - 1 where n is the sample size.