Already have a test statistic? Get its p-value for a left, right or two-tailed test, and see whether it clears your significance level.
Significant at α = 0.05. Reject the null hypothesis.
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The p-value is an area in the tail of the test statistic’s distribution under the null hypothesis: the standard normal for z, Student’s t with the right degrees of freedom for t, and chi-square for χ². Two-tailed tests add both tails.
If you still need the test statistic itself, run the t-test or chi-square test on your raw data. A p-value alone says nothing about how big an effect is; report a confidence interval alongside it.
The probability of getting a test statistic at least as extreme as the one you observed, assuming the null hypothesis is true. A small p-value means your data would be surprising if there were really no effect. It is not the probability that the null hypothesis is true.
Use two-tailed unless you decided before seeing the data that only one direction matters and an effect in the other direction would be treated the same as no effect. A two-tailed p-value is double the one-tailed value for symmetric distributions (z and t).
That the result is statistically significant at the 5% level: if the null were true, data this extreme would turn up less than 5% of the time. The 0.05 cut-off is a convention from R. A. Fisher, not a law. The American Statistical Association’s 2016 statement warns against treating it as a bright line.
For goodness-of-fit and independence tests, yes. Large χ² values mean the observed counts are far from expected, so only the right tail counts as evidence against the null.
One-sample or paired t-test: n − 1. Welch two-sample t-test: the Welch–Satterthwaite value (the t-test calculator computes it). Chi-square goodness of fit: categories − 1. Chi-square independence: (rows − 1)(columns − 1).