Calculate Statistical Significance with Step-by-Step Derivation
Test Statistic (z/t)
DF (if t-test)
Results
P-Value
Significance
Step-by-Step Derivation
P Value Calculation
Z-test: p = 2 × (1 - Φ(|z|)) for two-tailed
T-test: p = 2 × (1 - T(|t|, df)) for two-tailed
One-tailed: p = 1 - Φ(z) or T(t, df)
P-value measures the strength of evidence against the null hypothesis in statistical testing.
⚠DF required for t-test. Use z-test for large samples (n ≥ 30) with known σ.
What is P Value?
The p-value is the probability of obtaining results at least as extreme as the observed results of a statistical hypothesis test, assuming that the null hypothesis is correct.
p < 0.05
Statistically significant
p ≥ 0.05
Not statistically significant
One-tailed
Tests directional hypothesis
Two-tailed
Tests non-directional hypothesis
💡 Example: z=2.08, two-tailed. p = 2 × (1 - Φ(2.08)) = 2 × (1 - 0.9812) = 0.0376. This is statistically significant at α=0.05.
P-value is the probability of observing a test statistic at least as extreme as the one observed, assuming the null hypothesis is true. Lower p-value indicates stronger evidence against null hypothesis.
What does p-value < 0.05 mean?▼
p < 0.05 means statistically significant at 5% significance level. There is less than 5% chance of observing this data if null hypothesis is true.
One-tailed vs two-tailed test?▼
One-tailed: tests directional hypothesis (greater than or less than). Two-tailed: tests non-directional hypothesis (difference exists). Two-tailed p-value = 2 × one-tailed p-value.
How to interpret p-value?▼
p < 0.01: very strong evidence against H₀. p < 0.05: strong evidence. p < 0.10: weak evidence. p ≥ 0.05: no sufficient evidence to reject H₀.
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