Enter your test statistic and select a distribution (Z, t, χ², or F) to compute the p-value. Choose between two-tailed, left-tailed, or right-tailed tests, and provide degrees of freedom where required. You'll get the p-value along with a significance decision based on your chosen alpha level.
P-Value
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Significance Decision
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Alpha Level Used
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Test Type
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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. It is reported as a number between 0 and 1. A smaller p-value provides stronger evidence against the null hypothesis.
If the p-value is less than or equal to your chosen significance level (α, typically 0.05), you reject the null hypothesis — the result is statistically significant. If the p-value is greater than α, you fail to reject the null hypothesis. A p-value does not measure the size or practical importance of an effect.
A two-tailed test checks for an effect in either direction (greater or smaller), making it more conservative. A one-tailed test (left or right) checks for an effect in only one direction. Use a two-tailed test unless you have a strong prior reason to expect the effect in only one direction.
A Z-score measures how many standard deviations an observed value is from the mean of a standard normal distribution. Use a Z-test (and Z-score) when your sample size is large (n > 30) and the population standard deviation is known.
A t-score comes from the Student's t-distribution and is used when the sample size is small or the population standard deviation is unknown. You need to specify degrees of freedom (typically n − 1 for a one-sample test).
The chi-square statistic is used in tests of independence and goodness-of-fit. It measures the discrepancy between observed and expected frequencies. The p-value from χ² is almost always right-tailed, since χ² values are always non-negative.
The F-statistic is a ratio of two variances, used in ANOVA and regression analysis to test whether group means differ or whether a model fits the data. It requires two degrees of freedom: one for the numerator (df1) and one for the denominator (df2).
No, a p-value can never be negative. It is a probability, so it always falls between 0 and 1. If you obtain a negative value, there is an error in the calculation or input.