Hypothesis Test P-Value Calculator
Calculate P-values for Z-tests, T-tests, and Chi-Squared tests with instant visualization.
P-Value Result
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Distribution Graph
P-Value Region
Understanding P-Values
The P-value is the probability of obtaining test results at least as extreme as the results actually observed, assuming that the null hypothesis is true. It serves as a measure of evidence against the null hypothesis.
Low P-Value ($p \le \alpha$)
Strong evidence against the null hypothesis. We Reject the Null Hypothesis. The result is statistically significant.
High P-Value ($p > \alpha$)
Weak evidence against the null hypothesis. We Fail to Reject the Null Hypothesis. The result is not statistically significant.
Common Tests
- Z-Test: Used for large samples ($n \ge 30$) or when population variance is known. Follows the standard Normal Distribution.
- T-Test: Used for small samples ($n < 30$) when population variance is unknown. Follows the Student’s t-Distribution, which changes shape based on Degrees of Freedom ($df$).
- Chi-Squared ($\chi^2$): Used for variance tests or goodness-of-fit. This distribution is skewed right and only allows right-tailed tests in this context.
FAQ
What is a Two-Tailed Test?
A two-tailed test checks for a difference in either direction (e.g., is the mean different from 0?). The P-value is the sum of the probabilities in both tails (extreme high and extreme low values).
Why does Chi-Squared only show Right-Tail?
In most introductory hypothesis tests involving Chi-Squared (like Goodness of Fit or Independence), we are looking for large deviations between observed and expected values. These large deviations produce large $\chi^2$ statistics, falling in the right tail.
What is ‘Alpha’ ($\alpha$)?
Alpha is the Significance Level, the threshold for rejecting the null hypothesis. Commonly set to 0.05 (5%), meaning we accept a 5% risk of rejecting the null hypothesis when it is actually true (Type I error).