P-value Calculator
Compute one- or two-sided p-values for Z, t, χ², or F.
Inputs
We use the Z-score if the test statistic approximately follows the standard normal distribution.
You can count on the approximation if you have a large sample (say at least 50 data points) and treat your distribution as normal.
Type of p-value
Results
p-value
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Decision (vs α)
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Step-by-step derivation
- Select distribution Z and tail two-tailed.
- Compute CDF (F(x)) at your score —.
- Apply tail rule: p = 2·min(F, 1−F).
- Compare with α = 0.05 to state the decision.
References
- Normal CDF: (Phi(z)=frac{1+mathrm{erf}(z/sqrt{2})}{2})
- t-CDF via regularized incomplete beta (I_x(a,b))
- χ²-CDF via regularized lower incomplete gamma (P(s,x))
- F-CDF via (I_{d_1 f/(d_1 f+d_2)}(d_1/2,d_2/2))