Math & Engineering
P-Value Calculator
Calculate p-values to determine statistical significance in hypothesis testing
Enter values to calculate the p-value
Related to P-Value Calculator
The p-value calculator determines the probability of obtaining test results at least as extreme as the observed results, assuming that the null hypothesis is true. It uses the Student's t-distribution to calculate p-values for various types of hypothesis tests.
Test Types
- Two-Tailed Test: Tests for differences in either direction from the null hypothesis
- Left-Tailed Test: Tests if the true value is less than the hypothesized value
- Right-Tailed Test: Tests if the true value is greater than the hypothesized value
Required Inputs
- Test Statistic (t-value): The calculated t-statistic from your data
- Degrees of Freedom: Number of independent values that can vary in the analysis
- Test Type: The direction of the alternative hypothesis
The p-value helps determine whether to reject the null hypothesis based on the level of statistical significance. A smaller p-value indicates stronger evidence against the null hypothesis.
Common Significance Levels
- p < 0.01: Very strong evidence against the null hypothesis
- p < 0.05: Strong evidence against the null hypothesis (commonly used threshold)
- p < 0.10: Weak evidence against the null hypothesis
- p ≥ 0.10: No significant evidence against the null hypothesis
1. What is a p-value?
A p-value is the probability of obtaining test results at least as extreme as the observed results, assuming that the null hypothesis is true. It helps quantify the strength of evidence against a null hypothesis.
2. When should I use a two-tailed vs. one-tailed test?
Use a two-tailed test when you want to test for differences in either direction from the null hypothesis. Use a one-tailed test (left or right) when you're only interested in differences in one specific direction.
3. What are degrees of freedom?
Degrees of freedom represent the number of independent values that can vary in a statistical calculation. In general, it equals the sample size minus the number of parameters being estimated.
4. Why is 0.05 commonly used as the significance level?
The 0.05 significance level has become a standard convention in statistical testing. It provides a good balance between the probability of falsely rejecting a true null hypothesis (Type I error) and having sufficient power to detect real effects.
5. What is the scientific source for this calculator?
This calculator implements the Student's t-distribution for p-value calculations, which was developed by William Sealy Gosset and published in Biometrika in 1908. The methodology is based on fundamental principles of statistical inference described in standard statistical textbooks, including "Statistical Inference" by Casella and Berger (2002). The implementation follows the standard computational procedures for hypothesis testing using t-distributions as outlined in the Journal of Statistical Software and widely accepted in statistical practice.