P-Value Calculator
Calculate p-values for various statistical tests including t-tests, z-tests, chi-square tests, and F-tests. Essential for hypothesis testing and statistical significance analysis.
Test Parameters
Results
Significance at Common α Levels
Critical Values (α = 0.05)
How to Use
Select the appropriate statistical test type (t-test, z-test, chi-square, or F-test).
Enter your test statistic and degrees of freedom (if applicable).
For t-tests and z-tests, specify whether it's a one-tailed or two-tailed test.
View the calculated p-value and significance at common α levels.
Understanding P-Values
What is a P-Value?
A p-value is the probability of obtaining test results at least as extreme as the observed results, assuming the null hypothesis is true. It measures the strength of evidence against the null hypothesis.
Interpreting P-Values
p ≤ 0.01: Very strong evidence against null hypothesis
0.01 < p ≤ 0.05: Strong evidence against null hypothesis
0.05 < p ≤ 0.10: Weak evidence against null hypothesis
p > 0.10: Little or no evidence against null hypothesis
Statistical Tests
T-Test
Used when population standard deviation is unknown and sample size is small.
Z-Test
Used when population standard deviation is known or sample size is large.
Chi-Square Test
Used for testing independence or goodness of fit in categorical data.
F-Test
Used for comparing variances or in ANOVA to compare multiple means.
Applications
Medical Research
- • Clinical trial analysis
- • Drug efficacy testing
- • Treatment comparisons
- • Diagnostic test validation
Business & Marketing
- • A/B testing
- • Quality control
- • Customer satisfaction
- • Market research
Academic Research
- • Hypothesis testing
- • Experimental design
- • Survey analysis
- • Behavioral studies
Example Calculations
Example 1: Two-Sample T-Test
Scenario: Comparing mean test scores between two groups
Result: Significant at α = 0.05 level
Example 2: Chi-Square Test
Scenario: Testing independence in a contingency table
Result: Marginally significant at α = 0.05 level
Frequently Asked Questions
What does a small p-value mean?
A small p-value (typically ≤ 0.05) suggests strong evidence against the null hypothesis, leading to its rejection in favor of the alternative hypothesis.
When should I use a one-tailed vs. two-tailed test?
Use a one-tailed test when you have a specific directional hypothesis (greater than or less than). Use a two-tailed test when you're testing for any difference (not equal to).
What's the difference between statistical and practical significance?
Statistical significance (low p-value) doesn't guarantee practical importance. Consider effect size and real-world relevance alongside p-values.
Can I use this calculator for multiple comparisons?
This calculator is for single comparisons. For multiple comparisons, consider adjusting α levels using methods like Bonferroni correction to control family-wise error rate.
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