Mathematics

P-Value Statistical Test

P-Value Calculator

Z-score (test statistic)

What is P-Value Statistical Test?

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A p-value is the probability of obtaining a test result at least as extreme as the observed result, assuming the null hypothesis is true. A small p-value (typically < 0.05) suggests the result is unlikely due to chance alone.

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How to P-Value Statistical Test

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1State your null hypothesis (H₀) — usually "no effect" or "no difference"
2Calculate the test statistic (Z-score, t-score, etc.)
3Look up the p-value from the appropriate distribution
4If p < α (significance level), reject H₀

Worked Examples

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Example 1

Given:Z = 2.0, two-tailed

Result:p = 0.0455

Significant at α = 0.05 (p < 0.05)

Example 2

Given:Z = 1.5, two-tailed

Result:p = 0.1336

Not significant at α = 0.05

P-value Significance Levels

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P-value	Significance	Interpretation
p < 0.001	***	Highly significant
p < 0.01	**	Very significant
p < 0.05	*	Significant (conventional threshold)
p < 0.10	†	Marginally significant (some fields)
p ≥ 0.10	n.s.	Not significant

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Pro Tip

P-values do NOT measure the size of an effect or its practical importance. A tiny, unimportant effect can have p < 0.001 with a large enough sample. Always report effect sizes too.

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Did you know?

The p < 0.05 threshold was proposed by Ronald Fisher in 1925 almost arbitrarily — he suggested it as a convenient rule of thumb, not as a definitive standard. It has since been criticized as causing a reproducibility crisis in science.

References

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Reviewed October 2026

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