P-value Calculator
Compute one-tailed or two-tailed p-values for Z, t, χ², and F test statistics.
Inputs
Use Z when the test statistic follows the standard normal distribution, often with large samples.
Use t when population standard deviation is unknown and the statistic follows Student’s t.
Use χ² for chi-square based tests, and F for variance-ratio / ANOVA style tests.
Type of p-value
For χ² and F distributions, the two-tailed result is shown as 2 × the smaller one-tail probability, capped at 1.
Results
p-value
—
CDF value F(x)
—
Decision (vs α)
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Distribution used
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Step-by-step derivation
- Select distribution Z (Normal) and tail two-tailed.
- Evaluate the cumulative probability at score —, giving —.
- Apply the selected tail rule: p = 2 × min(F, 1 − F).
- Compare p with α = 0.05 to determine statistical significance.
References
- Normal CDF: Φ(z) = 0.5 × [1 + erf(z / √2)]
- t CDF via the regularized incomplete beta function
- χ² CDF via the regularized lower incomplete gamma function
- F CDF via the regularized incomplete beta function