P-Value Calculator
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Understanding P-Values
What is a P-Value?
A p-value (probability 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 determine whether to reject or fail to reject a null hypothesis in statistical testing.
Interpreting P-Values
Small P-Value (p < 0.05)
Strong evidence against the null hypothesis. The result is statistically significant. Consider rejecting the null hypothesis.
Large P-Value (p >= 0.05)
Weak evidence against the null hypothesis. The result is not statistically significant. Fail to reject the null hypothesis.
Common Statistical Tests
| Test | Use Case |
|---|---|
| Z-test | Large samples (n > 30), known population variance |
| T-test | Small samples, unknown population variance |
| Chi-square | Categorical data, goodness of fit |
| F-test | Comparing variances, ANOVA |
Important Note
A p-value does NOT tell you the probability that the null hypothesis is true. It only tells you how likely you would see the observed data (or more extreme) if the null hypothesis were true. Statistical significance does not imply practical significance or importance.
Frequently Asked Questions
What does a p-value of 0.05 actually mean?
A p-value of 0.05 means there's a 5% probability of seeing results this extreme (or more extreme) if the null hypothesis is true. It does NOT mean there's a 5% chance the null hypothesis is true. The 0.05 threshold is a convention, not a magic number.
When should I use a one-tailed vs two-tailed test?
Use a one-tailed test when you predict a specific direction (e.g., 'Drug A is better than placebo'). Use a two-tailed test when you're testing for any difference (e.g., 'Drug A is different from placebo'). Two-tailed is more conservative and generally preferred unless you have strong prior justification.
What is the difference between a z-test and t-test?
Use a z-test when you know the population standard deviation and have a large sample (n > 30). Use a t-test when the population standard deviation is unknown (using sample standard deviation instead) or with smaller samples. The t-distribution has heavier tails to account for additional uncertainty.
Can a result be statistically significant but not practically important?
Yes, absolutely. With large enough samples, even tiny differences become statistically significant. A medication that lowers blood pressure by 0.1 mmHg might achieve p < 0.001 with thousands of participants, but this effect is clinically meaningless. Always consider effect size alongside p-values.