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Get the p-value for a test statistic from the z, t, F or chi-square distribution, with one- or two-tailed options.
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| p-value | 0.0486Significant at α = 0.05 |
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z, t, F or chi-square.
And its degrees of freedom where needed.
One- or two-tailed for z and t.
A p-value is the probability of a result at least as extreme as the one observed, assuming the null hypothesis is true. Small p-values suggest the data are unlikely under the null hypothesis.
Report p-values alongside effect sizes and confidence intervals, rather than relying on a single significance threshold.
The American Statistical Association's 2016 statement sets out six principles for using p-values. Among them: a p-value does not measure the probability that the studied hypothesis is true, or that the data were produced by chance alone; it does not measure the size of an effect or the importance of a result; and conclusions should not be based only on whether a p-value passes a threshold such as 0.05.
Worked examples: an independent-samples t-test with t = 2.31 and 28 degrees of freedom gives a two-tailed p = 0.028. A z statistic of 1.80 gives a two-tailed p = 0.072 but a one-tailed p = 0.036, which is why the number of tails must be decided before the analysis, not after. A chi-square statistic of 5.20 with 2 degrees of freedom gives p = 0.074.
Report the exact p-value (for example p = .028) rather than only p < .05, and write p < .001 for very small values. Always report it with the test statistic and its degrees of freedom, such as t(28) = 2.31, p = .028, so readers can check the result.
Use two-tailed unless you specified a direction in advance and an effect in the other direction would be meaningless.
If the null hypothesis and the model's assumptions were true, a result at least this extreme would occur less than 5% of the time. It does not mean there is a 95% chance the effect is real, and it says nothing about how large or important the effect is.
Check the degrees of freedom, whether the software reports a one- or two-tailed value, and whether the test statistic was rounded. F and chi-square tests are right-tailed by design.
Avoid that wording. Report the exact value with the effect size and confidence interval and interpret them together; 0.06 and 0.04 represent very similar strength of evidence.