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About This Calculator
The p-value represents the probability of observing your results if the null hypothesis were true, serving as the cornerstone of hypothesis testing across scientific disciplines. This calculator computes p-values from test statistics like z-scores or t-values, helping you decide whether to reject or fail to reject your null hypothesis. A p-value below your significance threshold suggests the observed effect is unlikely due to chance alone.
Quick Tips
- 1 A p-value below 0.05 is conventional but not a universal truth threshold.
- 2 Low p-value means the result is unlikely under the null, not that it's important.
- 3 P-values don't measure effect size — a tiny effect can have a tiny p-value.
Example Calculation
A two-tailed test with z-score 2.15 testing whether a new drug differs from placebo.
P-value: 0.0316 | Significant at alpha = 0.05 | Reject the null hypothesis
What Is a P-value?
A p-value is the probability of obtaining 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. A smaller p-value indicates stronger evidence that the observed effect is real, not due to random chance.
How to Interpret P-values
Common significance thresholds: p < 0.05 (statistically significant), p < 0.01 (highly significant), p < 0.001 (very highly significant). If p < α (your chosen significance level), reject the null hypothesis. However, statistical significance does not necessarily mean practical significance — always consider effect size.
One-Tailed vs Two-Tailed Tests
A one-tailed test checks for an effect in a specific direction (e.g., "is A greater than B?"). A two-tailed test checks for any difference in either direction (e.g., "is A different from B?"). Two-tailed tests are more conservative and are the default in most research. One-tailed p-values are half of two-tailed p-values.
Common Misinterpretations
A p-value is NOT the probability that the null hypothesis is true. It is NOT the probability that your results occurred by chance. It IS the probability of seeing data this extreme if the null hypothesis were true. Also, "not significant" does not mean "no effect" — it means insufficient evidence to conclude an effect.
Frequently Asked Questions
The most common threshold is p < 0.05 (5%), but this is a convention, not a universal rule. Some fields use stricter thresholds: particle physics uses p < 0.0000003 (5σ), while exploratory studies may use p < 0.10.
Use a z-test when the population standard deviation is known or the sample size is large (n > 30). Use a t-test when the population SD is unknown and the sample is small. For large samples, both give nearly identical results.
Degrees of freedom (df) represent the number of independent values that can vary. For a one-sample t-test, df = n - 1. For a two-sample t-test, the calculation depends on the method used. More degrees of freedom make the t-distribution closer to the normal distribution.
Theoretically no, but computationally it can round to zero for extremely large test statistics. In practice, very small p-values are reported as p < 0.001 or p < 0.0001 rather than as zero.