P-Value Calculator
Calculate the P-value from Z-score, T-score, or Chi-Square statistic. Determine statistical significance for hypothesis testing.
What is a P-Value?
The P-value (probability value) is the probability of obtaining test results at least as extreme as the results actually observed, assuming that the null hypothesis is true.
In simpler terms, it tells you how likely it is that your data occurred by random chance.
Common Significance Levels
- p < 0.05: Statistically significant. Strong evidence against the null hypothesis.
- p < 0.01: Highly significant. Very strong evidence against the null hypothesis.
- p > 0.05: Not significant. Not enough evidence to reject the null hypothesis.
Distributions Supported
- Normal Distribution (Z): Used when the population variance is known or sample size is large.
- Student's t-Distribution (t): Used when population variance is unknown and sample size is small. Requires Degrees of Freedom.
- Chi-Square Distribution (χ²): Used for categorical data analysis (goodness of fit, independence).
? Frequently Asked Questions
A P-value of 0.05 means there is a 5% chance that your results would happen randomly if the null hypothesis were true. This is the standard threshold for significance in many fields.
Use a two-tailed test if you are testing for *any* difference (e.g., Group A ≠ Group B). Use a one-tailed test if you have a specific directional hypothesis (e.g., Group A > Group B).
For T and Chi-Square distributions, the shape of the curve changes based on the sample size. Degrees of Freedom (usually N-1) help the calculator use the correct curve shape for your specific data set.