Calculate p-values from z-scores, t statistics, chi-square statistics, and F statistics with one-tailed or two-tailed options, alpha-level decisions.
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Hypothesis testing
Convert a test statistic into a p-value.
Choose the reference distribution, tail direction, and significance level before entering the statistic. The calculator returns the p-value, the decision at your chosen α, common threshold checks, and the formula path used.
Quick examples
Test type
Tail
Input guide
Z uses the standard normal distribution and does not need degrees of freedom.
t and χ² use one degrees-of-freedom value; χ² is evaluated in the right tail.
F tests use numerator and denominator degrees of freedom, commonly for ANOVA or variance-ratio output.
P-Value
0.05
A two-tailed Z-test and a test statistic of 1.96 yields a p-value of 0.0500. The result is statistically significant at α = 0.05.
P-value
0.05
Test statistic
1.96
Decision at α = 0.05
Reject H₀
Significant at α = 0.01
No
Interpretation
The p-value of 0.05 is below your selected α of 0.05, suggesting sufficient evidence to reject the null hypothesis at that threshold.
Formula path
Standard normal CDF
Common threshold check
α 0.10: yes · α 0.05: yes · α 0.01: no
Caution
Statistical significance does not prove effect size, causality, or that the model assumptions were met.
P-value calculator: find statistical significance from test statistics
A p-value calculator converts a test statistic into a probability for hypothesis testing. This page also explains the main assumptions behind the p-value calculator result, highlights the supporting figures shown by the calculator, and helps the reader use the estimate without overstating what a quick online tool can prove.
Understanding p-values
A p-value is the probability of obtaining a test statistic at least as extreme as the one observed, assuming the null hypothesis is true. A small p-value (typically below 0.05) suggests that the observed result is unlikely under the null hypothesis, providing evidence to reject it.
For a z-test, the p-value comes from the standard normal distribution. For a t-test, it comes from the Student's t-distribution with the specified degrees of freedom. For a chi-square test, the p-value is computed from the chi-square distribution and is always right-tailed. For an F test, the p-value depends on both numerator and denominator degrees of freedom, which is why ANOVA and variance-ratio output must include both df values.
Two-tailed p = 2 × P(Z > |z|)
Two-tailed p-value from a z-score using the standard normal CDF.
Left-tailed p = P(T ≤ t)
Left-tailed p-value from the cumulative distribution function.
F right-tail p = 1 − Fcdf(F; df₁, df₂)
Right-tail F-test p-value from the F distribution with numerator and denominator degrees of freedom.
How to use this p-value calculator
Start by choosing the test family that produced your statistic: z for standard normal output, t for a t statistic and one degrees-of-freedom value, chi-square for a non-negative χ² statistic, or F for ANOVA and variance-ratio style results. Then select the tail direction before entering the statistic, because one-tailed and two-tailed p-values answer different alternative hypotheses.
Use the significance level control to set the alpha threshold you actually planned to use. The result area compares the calculated p-value against your selected α and also shows common reference thresholds, so you can distinguish a result that is significant at 0.10 from one that remains significant at 0.01.
One-tailed vs two-tailed p-values
A right-tailed p-value is the probability of getting a statistic at least as large as the observed value. A left-tailed p-value is the probability of getting a statistic at least as small. A two-tailed p-value checks for unusual results in either direction, which is why it is usually larger than the matching one-tailed p-value for symmetric z and t tests.
Chi-square tests are treated as right-tailed here because large chi-square statistics represent greater departure from the null model. F tests are usually right-tailed in ANOVA and variance-ratio workflows, but the calculator also supports left-tailed and two-tailed F lookups for textbook or software outputs that require them.
P-value vs statistical significance
The p-value is not the probability that the null hypothesis is true. It is the probability of seeing data this extreme, or more extreme, if the null hypothesis and model assumptions were true. That distinction matters because a very small p-value can still come from a biased study design, violated assumptions, or a practically tiny effect in a very large sample.
Use the decision text as a threshold comparison, not as a final research conclusion. If p is below α, the result is statistically significant at that threshold. You still need to review effect size, confidence intervals, multiple-testing adjustments, data quality, and whether the chosen test matches the design.
Worked examples
For a two-tailed z test with z = 1.96, the p-value is about 0.05. That is why 1.96 is a common 95% confidence and α = 0.05 reference point for standard normal tests.
For a two-tailed t test with t = 2.228 and 10 degrees of freedom, the p-value is about 0.05. The same statistic would have a different p-value with a different df because the t distribution changes shape as degrees of freedom change.
For a right-tailed chi-square test with χ² = 3.841 and 1 degree of freedom, the p-value is about 0.05. For an F statistic, you must also enter both df values; for example, an ANOVA-style F lookup needs numerator df and denominator df before the p-value can be interpreted.
No. The 0.05 threshold is a convention, not a universal rule. Some fields use stricter thresholds (0.01 or 0.001). The appropriate threshold depends on the consequences of a false positive and the norms of your discipline.
What is the difference between one-tailed and two-tailed tests?
A one-tailed test checks for an effect in one direction (greater than or less than). A two-tailed test checks for an effect in either direction. Two-tailed tests are more conservative because they split the significance level across both tails.
Can this calculator find a p-value from an F statistic?
Yes. Choose the F-test option, enter the F statistic, numerator degrees of freedom, denominator degrees of freedom, and the tail direction. This is useful when you already have ANOVA, regression F-test, or variance-ratio output and need to convert the statistic to a p-value.
Which p-value calculator option should I choose?
Choose z when your statistic follows the standard normal distribution, t when the output includes a t statistic and one degrees-of-freedom value, chi-square when the statistic is non-negative and comes from a χ² test, and F when the output includes an F statistic with numerator and denominator degrees of freedom.
Does a small p-value mean the effect is important?
Not by itself. A small p-value means the observed statistic would be unusual under the null hypothesis, but it does not measure effect size, practical importance, or whether the assumptions behind the test were satisfied.
How can I check the p-value calculator: find statistical significance from test statistics result manually?
The safest manual check is to follow the same formula or rule one step at a time and compare that working with the calculator output. That catches sign errors, bracket mistakes, and input-order mixups without requiring any extra method beyond the underlying maths itself.
